CN115577788A

CN115577788A - Quantum entropy determination method, device, equipment and storage medium

Info

Publication number: CN115577788A
Application number: CN202211196193.3A
Authority: CN
Inventors: 余展; 张磊; 王友乐; 王鑫
Original assignee: Beijing Baidu Netcom Science and Technology Co Ltd
Current assignee: Beijing Baidu Netcom Science and Technology Co Ltd
Priority date: 2022-09-28
Filing date: 2022-09-28
Publication date: 2023-01-06

Abstract

The disclosure provides a quantum entropy determination method, a quantum entropy determination device, quantum entropy determination equipment and a storage medium, and relates to the technical field of computers, in particular to the field of quantum computation. The specific implementation scheme is as follows: determining a target parameter value of a target adjustable parameter in a sub-circuit of a target quantum circuit; the target quantum circuit comprises an auxiliary register and a main register, and the sub-circuit acts on the auxiliary register; the target quantum circuit also comprises a target controlled unitary gate, the target controlled unitary gate is used for estimating a Rayleigh entropy corresponding to the first quantum state, and the Rayleigh entropy is used for measuring the chaos degree of a total subsystem corresponding to the first quantum state; under the conditions that the target adjustable parameter is a target parameter value, the first input state of the auxiliary register is a preset initial state, and the second input state of the main register at least comprises a first quantum state, acquiring state information of the auxiliary register in the target quantum circuit; and estimating to obtain Rayleigh entropy corresponding to the first quantum state under the first error condition based on the state information of the auxiliary register.

Description

Quantum entropy determination method, device, equipment and storage medium

Technical Field

The present disclosure relates to the field of computer technology, and more particularly, to the field of quantum computing.

Background

The recent field of quantum computing is rapidly developed, and the scale and the practicability are steadily advanced from quantum algorithms and quantum hardware equipment to a quantum software-hardware integrated platform. Among them, the study of rayleigh entropy is a very important issue.

Disclosure of Invention

The disclosure provides a quantum entropy determination method, a quantum entropy determination device and a storage medium.

According to an aspect of the present disclosure, there is provided a quantum entropy determination method, including:

determining a target parameter value of a target adjustable parameter in a sub-circuit of a target quantum circuit; wherein the target parameter value satisfies a first error condition; the target quantum circuit comprises an auxiliary register and a main register, and the sub-circuit acts on the auxiliary register; the target quantum circuit also comprises a target controlled unitary gate which is controlled by the auxiliary register and acts on the main register, the target controlled unitary gate is used for estimating Rayleigh entropy corresponding to a first quantum state, and the Rayleigh entropy is used for measuring the chaos degree of a total subsystem corresponding to the first quantum state; the target controlled unitary gate comprises a first controlled unitary gate equivalent to unitary operator U and a transpose to the unitary operator U

An equivalent second controlled unitary gate; the unitary operator is a unitary operator corresponding to a first quantum system, and the first quantum system is a quantum system corresponding to the first quantum state;

acquiring state information of the auxiliary register in the target quantum circuit under the condition that the target adjustable parameter is the target parameter value, the first input state of the auxiliary register is a preset initial state, and the second input state of the main register at least comprises the first quantum state; and

and estimating to obtain Rayleigh entropy corresponding to the first quantum state under the first error condition based on the state information of the auxiliary register.

According to another aspect of the present disclosure, there is provided a quantum entropy determination apparatus including:

the parameter processing unit is used for determining a target parameter value of a target adjustable parameter in a sub-circuit of the target quantum circuit; wherein the target parameter value satisfies a first error condition; the target quantum circuit comprises an auxiliary register and a main register, and the sub-circuit acts on the auxiliary register; the target quantum circuit also comprises a target controlled unitary gate which is controlled by the auxiliary register and acts on the main register, the target controlled unitary gate is used for estimating Rayleigh entropy corresponding to a first quantum state, and the Rayleigh entropy is used for measuring the chaos degree of a total subsystem corresponding to the first quantum state; the target controlled unitary gate comprises a first controlled unitary gate equivalent to a unitary operator U and a transpose of the unitary operator U

the measurement unit is used for acquiring the state information of the auxiliary register in the target quantum circuit under the condition that the target adjustable parameter is the target parameter value, the first input state of the auxiliary register is a preset initial state, and the second input state of the main register at least comprises the first quantum state; and

and the output unit is used for estimating and obtaining Rayleigh entropy corresponding to the first quantum state under the first error condition based on the state information of the auxiliary register.

According to yet another aspect of the present disclosure, there is provided a computing device comprising:

at least one quantum processing unit;

a memory coupled to the at least one QPU and configured to store executable instructions,

the instructions are executable by the at least one quantum processing unit to enable the at least one quantum processing unit to perform the method described above;

alternatively, the method comprises the following steps:

at least one processor; and

a memory communicatively coupled to the at least one processor; wherein,

the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method described above.

According to yet another aspect of the present disclosure, there is provided a non-transitory computer readable storage medium having stored thereon computer instructions which, when executed by at least one quantum processing unit, cause the at least one quantum processing unit to perform the method described above;

alternatively, the computer instructions are for causing the computer to perform the method described above.

According to yet another aspect of the present disclosure, there is provided a computer program product comprising a computer program which, when executed by at least one quantum processing unit, implements the method described above;

or which, when being executed by a processor, carries out the method as described above.

Therefore, the scheme of the disclosure provides a novel Rayleigh entropy estimation scheme, which can be implemented on a recent quantum computer, and has strong practicability.

It should be understood that the statements in this section do not necessarily identify key or critical features of the embodiments of the present disclosure, nor do they limit the scope of the present disclosure. Other features of the present disclosure will become apparent from the following description.

Drawings

The drawings are included to provide a better understanding of the present solution and are not to be construed as limiting the present disclosure. Wherein:

fig. 1 is a first schematic flow chart of an implementation of a quantum entropy determination method according to an embodiment of the present disclosure;

FIG. 2 is a schematic diagram of a second implementation flow of a quantum entropy determination method according to an embodiment of the present disclosure;

fig. 3 (a) to 3 (f) are schematic structural diagrams of a pre-parameterized quantum circuit according to an embodiment of the present disclosure;

fig. 4 (a) to 4 (f) are schematic structural diagrams of a target quantum circuit according to an embodiment of the present disclosure;

FIG. 5 is a flow chart of an implementation of a method of pre-parameterizing quantum circuit training according to an embodiment of the present disclosure;

FIG. 6 is a schematic flow chart diagram illustrating an implementation of a quantum entropy determination method in a specific embodiment according to an embodiment of the present disclosure;

fig. 7 is a schematic structural diagram of a quantum entropy determination apparatus according to an embodiment of the present disclosure;

FIG. 8 is a block diagram of a computing device used to implement a quantum entropy determination method of an embodiment of the present disclosure.

Detailed Description

Exemplary embodiments of the present disclosure are described below with reference to the accompanying drawings, in which various details of the embodiments of the disclosure are included to assist understanding, and which are to be considered as merely exemplary. Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the disclosure. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.

The term "and/or" herein is merely an association describing an associated object, meaning that three relationships may exist, e.g., a and/or B, may mean: a exists alone, A and B exist simultaneously, and B exists alone. The term "at least one" herein means any combination of any one or more of a plurality, for example, including at least one of a, B, C, and may mean including any one or more elements selected from the group consisting of a, B, and C. The terms "first" and "second" used herein refer to and distinguish one from another in the similar art, without necessarily implying a sequence or order, or implying only two, such as first and second, to indicate that there are two types/two, first and second, and first and second may also be one or more.

Furthermore, in the following detailed description, numerous specific details are set forth in order to provide a better understanding of the present disclosure. It will be understood by those skilled in the art that the present disclosure may be practiced without some of these specific details. In some instances, methods, means, elements and circuits that are well known to those skilled in the art have not been described in detail so as not to obscure the present disclosure.

The recent quantum computing field is rapidly developed, and the scale and the practicability are steadily advanced from quantum algorithms and quantum hardware equipment to quantum software and hardware integrated platforms. More and more quantum technologies are emerging continuously, the quantum hardware technology is promoted year by year, and quantum communication and quantum internet are developing continuously. With the development of quantum computing, quantum applications have been expanded into many fields and solved important problems. One of the important issues is the Entropy (Entropy) of the computing system. The concept of entropy, originally derived from thermodynamics, was developed to quantify the efficiency of steam engines, and later turned to describe the degree of disorder or complexity in the physical system. Entropy has important applications in other fields as well. In statistical physics, entropy is used to characterize the number of different microscopic states that are compatible with a given macroscopic state; in mathematical statistics, it corresponds to the inference function of the update process; in the information theory, it determines the limits of the achievable coding scheme. In addition, entropy is also used to calculate energy density, which is an important issue in lithium battery technology. Therefore, the entropy of quantum states can be calculated efficiently, and the method has important significance for scientific research and industrial development.

There are many definitions of entropy of quantum systems, and one of the more common ones is rayleigh entropy (renyi entropy), which is mainly used to measure the complexity of a quantum system. It should be noted that the complexity level described herein may also be referred to as a degree of confusion, such as a degree of uncertainty and a degree of randomness; in practical application, the larger the rayleigh entropy, the higher the complexity inside the quantum system, and conversely, the lower the rayleigh entropy. The Rayleigh entropy is a basic problem in scientific research and has wide application in industrial production; in addition to the applications described above, it can also be used to study Condensed physics (coherent physics), high-energy physics (High-energy physics), gravity theory (Gravity theory), black hole theory (Black hole), construct decision trees in machine learning, and analyze Financial data (Financial data analysis).

Also, in general, it is very difficult to calculate the rayleigh entropy of quantum states. Classical calculations, which are intended to accomplish such tasks, require operations such as chromatography on unitary operators, and are more difficult to implement in the case of exponentially growing quantum systems. Moreover, the current scheme capable of quantum entropy estimation has high requirements on the aspects of quantum circuits and the like. Therefore, a more efficient and practical quantum entropy estimation scheme is urgently needed, which can solve the problem of the quantum system on one hand and can promote the development of quantum computing in industrial application on the other hand. Therefore, it is a practical problem to efficiently obtain the estimated value of the rayleigh entropy and simultaneously have a plurality of extended applications.

Based on this, the scheme of the disclosure provides a quantum entropy determination scheme, which can efficiently estimate and obtain the rayleigh entropy corresponding to the quantum state.

Specifically, fig. 1 is a first schematic flow chart illustrating an implementation process of a quantum entropy determination method according to an embodiment of the present disclosure; the method is optionally applied to a quantum computing device with classical computing capability, and may also be applied to a classical computing device with quantum computing capability, or may be directly applied to a classical computing device, for example, an electronic device with classical computing capability such as a personal computer, a server cluster, or may be directly applied to a quantum computer, and the present disclosure is not limited thereto.

Further, the method includes at least part of the following. As shown in fig. 1, the quantum computing processing method includes:

step S101: a target parameter value for a target tunable parameter in a sub-circuit of the target quantum circuit is determined.

Wherein the target parameter value satisfies a first error condition; the target quantum circuit comprises an auxiliary register and a main register, and the sub-circuit acts on the auxiliary register; the target quantum circuit further comprises a target controlled unitary gate which is controlled by the auxiliary register and acts on the main register, the target controlled unitary gate is used for estimating Rayleigh entropy corresponding to the first quantum state, and the Rayleigh entropy is used for measuring the chaos degree of a total subsystem corresponding to the first quantum state.

Further, the target controlled unitary gate comprises a first controlled unitary gate equivalent to a unitary operator U and a conjugate transpose of the unitary operator U

An equivalent second controlled unitary gate; that is, the first controlled unitary gate is controlled by the auxiliary register and acts on the main register, and similarly, the second controlled unitary gate is controlled by the auxiliary register and acts on the main register.

Further, the unitary operator is a unitary operator corresponding to the first quantum system; the first quantum system is a system corresponding to the first quantum state. It is understood that at least part of the sub-circuit containing the target adjustable parameter in the target quantum circuit is the sub-circuit, that is, the sub-circuit is a parametric quantum circuit containing the target adjustable parameter.

Step S102: and acquiring the state information of the auxiliary register in the target quantum circuit under the conditions that the target adjustable parameter is the target parameter value, the first input state of the auxiliary register is a preset initial state, and the second input state of the main register at least comprises the first quantum state.

Step S103: and estimating to obtain Rayleigh entropy corresponding to the first quantum state under the first error condition based on the state information of the auxiliary register.

At this time, the rayleigh entropy corresponding to the first quantum state may be used to measure the physical property of the total subsystem corresponding to the first quantum state, for example, to measure the degree of disorder of the total subsystem.

Thus, the scheme of the present disclosure provides a novel scheme for estimating the rayleigh entropy corresponding to the first quantum state. Specifically, the scheme of the disclosure adopts a target quantum circuit including an auxiliary register and a main register, and obtains state information of the auxiliary register by inputting a first input state and a second input state under the condition that a target adjustable parameter is a target parameter value, and obtains a rayleigh entropy corresponding to the first quantum state, thereby measuring a chaos degree of a total subsystem corresponding to the first quantum state.

Furthermore, the scheme disclosed by the invention can be realized on a recent quantum computer, so that the practicability is strong; in addition, the scheme disclosed by the invention can also be applied to large-scale quantum states, so that the scheme also has expansibility.

In a specific example, the unitary operator is a unitary operator corresponding to a first quantum system, for example, the unitary operator is obtained based on the first quantum system; or, the unitary operator is obtained based on the total subsystem corresponding to the first quantum state.

In a specific example, the auxiliary register includes at least one qubit, such as one, two, or more than two qubits. Further, the number of qubits contained in the main register is related to the number of qubits contained in the first quantum system, or the number of qubits contained in the main register is related to the number of qubits contained in the first quantum system and the number of qubits contained in the total quantum system.

Further, in a specific example, when the unitary operator U is obtained based on the first quantum system, the number of qubits included in the main register is the same as the number of qubits included in the first quantum system corresponding to the unitary operator U. At this time, the second input state of the main register may be specifically the first quantum state.

Here, for the sake of convenience of distinction, the qubits contained in the auxiliary register may be referred to as auxiliary qubits; accordingly, the qubits contained by the master register are referred to as master qubits.

For example, the first quantum system comprises n quantum bits, and in this case, in order to estimate the rayleigh entropy corresponding to the first quantum state, the master register in the target quantum circuit may comprise n master quantum bits; and n is a positive integer greater than or equal to 1.

Or, in another specific example, in a case where the unitary operator U is obtained based on a total quantum system corresponding to the first quantum system, the number of qubits included in the main register is related to the number of qubits included in the first quantum system and the number of qubits included in the total quantum system. For example, the number of qubits included in the main register = the number of qubits included in the first quantum system + the number of qubits included in the quantum subsystems. At this time, the second input state of the main register includes the first quantum state. Furthermore, the method also comprises a preset initial state.

In a specific example, the acquiring of the state information of the auxiliary register in the target quantum circuit in step S102 may specifically include: obtaining observables for the target quantum circuit

The expected value of (a);

here, the observables are

Expected value of<Z>I.e. the state information of said auxiliary register.

Further, the observables are

In particular, the measurement operator Z is applied to the auxiliary register, and remainsThe following qubits (i.e., the master register) do not operate, where I represents the identity matrix. Thus, the state information of the auxiliary register can be obtained.

In a specific example of the disclosure, the rayleigh entropy corresponding to the first quantum state is: and the alpha-order Rayleigh entropy corresponding to the first quantum state, wherein alpha is a preset order.

Here, α ∈ (0, 1) — (1, ∞).

Therefore, a scheme for efficiently estimating the alpha-order Rayleigh entropy corresponding to the first quantum state is provided, and the physical properties of the total subsystem corresponding to the first quantum state can be measured based on the alpha-order Rayleigh entropy.

In a specific example, the estimated rayleigh entropy of the order α (which may be denoted as R) corresponding to the first quantum state (which may be represented by its density matrix ρ, i.e. the first quantum state ρ) is _α (p)) and status information of the auxiliary register, such as an expected value<Z>Satisfies the following relationship:

when the alpha is greater than 1, the alpha is,

when the alpha is less than 1, the alpha is more than 1,

thus, the status information, such as the expected value, of the auxiliary register is obtained<Z>Then, the alpha-order Rayleigh entropy R corresponding to the first quantum state can be estimated _α (ρ) the process is efficient and convenient.

In a specific example, the preset initial state may be specifically |0>, or |1>. The present disclosure is not particularly limited in this regard.

In a specific example, in the case that the first quantum system is any one of the quantum systems, the first quantum state corresponds to an α -order rayleigh entropy R _α (ρ) which may also be referred to as the alpha-order Rayleigh entropy R of the gross subsystem _α (ρ) at this time, rayleigh entropy R of order α _α (p) is used to measure the degree of misordering in the aggregate subsystem.

Further, in the case that the total quantum system is composed of a first quantum system and a second quantum system, at this time, the scheme of the present disclosure may be used to estimate the rayleigh entropy of the order α of the first quantum state corresponding to the first quantum system, and may also be used to estimate the rayleigh entropy of the order α of the second quantum state corresponding to the second quantum system.

Further, in an example, in the case that the target adjustable parameter is the target parameter value, the first input state of the auxiliary register is a preset initial state, and the second input state of the main register in the target quantum circuit includes the first quantum state, the state information of the auxiliary register is obtained through measurement, and then the alpha-order rayleigh entropy corresponding to the first quantum state under the first error condition is estimated, at this time, the first quantum state (which may be further denoted as ρ for convenience of distinguishing from the second quantum state), is used for estimating the alpha-order rayleigh entropy, where the first quantum state (which may be further denoted as ρ for convenience of distinguishing from the second quantum state) _A ) The corresponding alpha-order rayleigh entropy can be used to measure the degree of misordering of the population subsystem.

In another example, when the target adjustable parameter is the target parameter value, the first input state of the auxiliary register is a preset initial state, and the second input state of the main register in the target quantum circuit includes the second quantum state of the second quantum system, the state information of the auxiliary register is obtained by measurement, and then the alpha-order rayleigh entropy corresponding to the second quantum state under the first error condition is estimated, and at this time, the second quantum state (which is convenient for distinguishing from the first quantum state and may also be denoted as ρ |) _B ) The corresponding alpha-order rayleigh entropy can be used to measure the degree of misordering of the population subsystem.

Here, it is understood that the α -order rayleigh entropy described in the present disclosure is a property of the quantum system, based on which, for the quantum system formed by the first quantum system a and the second quantum system B, whether based on the first quantum state ρ _A The obtained alpha-order Rayleigh entropy is also based on the second quantum state rho _B The obtained alpha-order Rayleigh entropy represents the alpha-order Rayleigh entropy corresponding to the total subsystem,thus, the first quantum state ρ _A Corresponding alpha-order Rayleigh entropy and second quantum state rho _B The corresponding alpha-order Rayleigh entropy is the same.

It should be noted that the total subsystem and the sub-quantum system described in the present disclosure are relative concepts, in other words, the total subsystem may also be one of other larger subsystems, and the present disclosure is not limited in this respect. For example, for a larger number of subsystems, any two of the larger number of subsystems may be combined into a total number of subsystems, and the disclosed solution may be used to estimate the degree of misordering of the total number of subsystems.

Fig. 2 is a schematic diagram of an implementation flow of a quantum entropy determination method according to an embodiment of the present disclosure. The method may be optionally applied to a quantum computing device with classical computing capability, or may be directly applied to a classical computing device with quantum computing capability, for example, an electronic device with classical computing capability such as a personal computer, a server cluster, or a quantum computer, and the present disclosure is not limited thereto.

It is understood that the related content of the method shown in fig. 1 above can also be applied to this example, and the description of the related content in this example is omitted.

Further, the method includes at least part of the following. Specifically, as shown in fig. 2, the method includes:

step S201: and taking the target parameter value of the target adjustable parameter in the trained preset parameterized quantum circuit as the target parameter value of the target adjustable parameter in the sub-circuit. Here, the target parameter value satisfies a first error condition.

That is to say, the preset parameterized quantum circuit includes the target adjustable parameter, so that the target parameter value of the target adjustable parameter in the trained preset parameterized quantum circuit is used as the target parameter value of the target adjustable parameter in the sub-circuit. In other words, in this example, the target parameter value of the target tunable parameter in the sub-circuit may be obtained by training other parameterized quantum circuits.

It is understood that, in this example, the description of the sub-circuit and the target quantum circuit can be referred to the above description, and the description is omitted here.

It should be noted that the preset parameterized quantum circuit may further include other adjustable parameters, which is not particularly limited in the present disclosure as long as the preset parameterized quantum circuit includes target adjustable parameters required by the sub-circuit.

Further, the trained preset parameterized quantum circuit is used for simulating the objective function y (x).

Further, the objective function y (x) satisfies the following requirements:

under the condition that a preset order alpha is a rational number larger than 1, the objective function y (x) is used for representing the incidence relation between the preset order alpha and the independent variable x;

under the condition that the preset order alpha is a rational number which is larger than 0 and smaller than 1, the objective function y (x) is used for representing the association relationship among the preset order alpha, the preset threshold gamma and the independent variable x; or, in the case that the preset order α is a rational number greater than 0 and less than 1, the objective function y (x) is used to represent an association relationship among the preset order α, a normalization coefficient c and an argument x, where the normalization coefficient c is related to the preset threshold γ, and the preset threshold γ is a constant less than a non-zero eigenvalue corresponding to the first quantum state. For example, the preset threshold γ is a real number smaller than a non-zero eigenvalue corresponding to the first quantum state. Here, in practical applications, the non-zero eigenvalue is generally a real number greater than 0 and smaller than 1, and in this case, the preset threshold γ is also a real number greater than 0 and smaller than 1. That is, in the case where the preset order α is different in value, the objective function y (x) is different.

Further, the target quantum circuit is based on the following:

and taking the quantum bit in the preset parameterized quantum circuit as an auxiliary register, expanding a main register, and meanwhile, replacing a first target revolving gate acting on the auxiliary register in the preset parameterized quantum circuit with the first controlled unitary gate, and replacing a second target revolving gate acting on the auxiliary register in the preset parameterized quantum circuit with the second controlled unitary gate. That is, the target quantum circuit is expanded on the basis of the preset parameterized quantum circuit.

Here, the first rotation parameter of the first target revolving door and the second rotation parameter of the second target revolving door are both arguments x of the objective function y (x).

Further, the sub-circuit comprises at least part of the circuit except the first target revolving gate and the second target revolving gate in the preset parameterized quantum circuit; here, the first target revolving gate and the second target revolving gate may be collectively referred to as a target revolving gate, and in this case, the sub-circuit includes at least a part of the preset parameterized quantum circuit except the target revolving gate.

It can be understood that, since the target quantum circuit is obtained by expanding on the basis of the preset parameterized quantum circuit, the sub-circuit can also be obtained on the basis of the preset parameterized quantum circuit, and a partial circuit structure corresponding to the target adjustable parameter in the preset parameterized quantum circuit is included, so that a basis is laid for obtaining the target parameter value of the target adjustable parameter of the sub-circuit by training the preset parameterized quantum circuit.

Step S202: and acquiring the state information of the auxiliary register in the target quantum circuit under the condition that the target adjustable parameter is the target parameter value, the first input state of the auxiliary register is a preset initial state, and the second input state of the main register at least comprises the first quantum state.

Step S203: and estimating to obtain Rayleigh entropy corresponding to the first quantum state under the first error condition based on the state information of the auxiliary register.

It can be understood that, because the preset parameterized quantum circuit has a simple circuit structure compared with the target quantum circuit, the calculated amount can be effectively reduced by training the preset parameterized quantum circuit to obtain the target parameter value of the target adjustable parameter, and a foundation is laid for efficiently solving and obtaining the rayleigh entropy corresponding to the first quantum state.

Furthermore, in practical application, the preset parameterized quantum circuit can be obtained in a classical computing device in a simulation mode, and accordingly, the training to obtain the target parameter value of the target adjustable parameter can be realized in the classical computing device, so that the method for obtaining the target parameter value of the target adjustable parameter in the scheme disclosed by the invention can not occupy quantum computing resources, and thus, the calculation cost is effectively reduced while a foundation is laid for efficiently estimating the rayleigh entropy corresponding to the first quantum state.

In addition, the first quantum state is not limited at all, in other words, the rayleigh entropy corresponding to any quantum state can be estimated, so that the disorder degree of the total subsystem corresponding to the quantum state can be measured, and the universality is high. Meanwhile, the scheme disclosed by the invention can be realized on a recent quantum computer, and the practicability is high; in addition, the scheme disclosed by the invention can also be applied to large-scale quantum states, so that the scheme also has expansibility. In conclusion, the scheme disclosed by the invention has high efficiency, practicability and expansibility.

In a specific example, a function analysis method may also be adopted to obtain a target parameter value of the target adjustable parameter; specifically, a target fourier series F (x) of the objective function is obtained, wherein the target fourier series F (x) is a fourier series that approximates the objective function within the target definition domain. Further, other Fourier series, such as other Fourier series P (x) and Q (x), are derived based on the target Fourier series F (x), wherein,

based on a preset relational expression, obtaining a target parameter value of the target adjustable parameter; for example, for the target quantum circuit shown in fig. 4 (c) (the target quantum circuit will be described later, and will not be described again), the preset relation may specifically be:

here, the Q ^* (x) Is the complex conjugate of Q (x), P ^* (x) Is the complex conjugate of P (x).

Therefore, the calculation amount can be effectively reduced, and a foundation is laid for efficiently estimating and obtaining the Rayleigh entropy corresponding to the first quantum state.

It is understood that, in practical applications, any trigonometric polynomial that can approximate the objective function with a certain precision may also be used to optimize the optimal parameter value of the target adjustable parameter, and the disclosure is not limited thereto.

Two ways are given below for constructing the pre-parameterized quantum circuit, including:

the first mode is as follows:

in this way, the preset parameterized quantum circuit comprises L training layers; l is an even number greater than or equal to 2, and the value of L is related to the first error condition;

at least two of the L training layers include:

the target revolving door is used for carrying out a revolving operation on a first angle by the revolving parameter x;

the first rotating gate is used for rotating a second angle and acts on a quantum bit in the preset parameterized quantum circuit;

a second revolving gate for revolving the third angle and acting on the qubit in the preset parameterized quantum circuit;

and the rotation angle phi of the first revolving door and the rotation angle theta of the second revolving door are the target adjustable parameters.

Here, the first target revolving door and the second target revolving door are target revolving doors in different training levels; that is, target revolving gates of different training layers in the preset parameterized quantum circuit are replaced by different controlled unitary gates, for example, a target revolving gate (which may be referred to as a first target revolving gate for convenience of description) in one training layer in the preset parameterized quantum circuit is replaced by a first controlled unitary gate, and a target revolving gate (which may be referred to as a second target revolving gate for convenience of description) in another training layer in the preset parameterized quantum circuit is replaced by a second controlled unitary gate, so as to obtain the target quantum circuit.

It should be noted that, in practical applications, the types and the numbers of the revolving doors included in different training levels of the L training levels may be the same, for example, the revolving doors described above are all included; alternatively, the number of the training layers may be different, for example, some other training layers include at least one of the above-mentioned revolving doors, and some other training layers include other quantum doors, and the like.

In a specific example, the preset parameterized quantum circuit includes a qubit, and in this case, the target revolving gate, the first revolving gate, and the second revolving gate are all single-qubit revolving gates acting on the qubit.

Further, in another example, the predetermined parameterized quantum circuit includes a qubit, and each of the L training layers includes a target revolving gate, a first revolving gate, and the second revolving gate, that is, the target revolving gate, the first revolving gate, and the second revolving gate of each training layer are single-qubit revolving gates acting on the qubit.

The second mode is as follows:

in this way, the preset parameterized quantum circuit includes L training layers; l is an even number greater than or equal to 2, and the value of L is related to the first error condition;

at least two of the L training layers include:

the target revolving door is used for carrying out a revolving operation on a first angle by the revolving parameter x; the first target revolving door and the second target revolving door are target revolving doors in different training layers;

and the rotation angle theta of the second revolving door is the target adjustable parameter.

That is, in the second mode, the first revolving door is not included in the training floor of the at least two training floors, as compared to the first mode. It is understood that the above description of the first mode, except for the first swing door, is also applicable to the second mode, and the description thereof is omitted.

Therefore, the scheme effectively improves the expression capacity of the preset parameterized quantum circuit, and meanwhile, the used quantum gates are small in variety and number, so that a foundation is laid for efficiently estimating and obtaining the Rayleigh entropy corresponding to the quantum state.

Further, in a specific example of the disclosed solution, each angle satisfies one of the following conditions:

the first angle is an angle corresponding to the z axis;

the second angle is an angle corresponding to the z axis;

the third angle is an angle corresponding to the y-axis.

That is, in one example, the first angle is an angle corresponding to the z-axis; in another example, the second angle is an angle corresponding to the z-axis; in yet another example, the third angle is an angle corresponding to the y-axis; alternatively, any two of the above conditions are satisfied, for example, the first angle and the second angle are both angles corresponding to the z-axis. Or, the three conditions are simultaneously satisfied, that is, the first angle and the second angle are both angles corresponding to the z-axis, and the third angle is an angle corresponding to the y-axis.

For example, in a specific example, at least two of the L training layers include:

the rotation parameter x of the target revolving door is used for rotating the angle corresponding to the z axis;

the first rotating door is used for rotating the angle corresponding to the z axis;

and the second rotating door is used for rotating the angle corresponding to the y axis.

Or, in another example, at least two of the L training layers include:

Further, in another specific example, the preset parameterized quantum circuit includes a qubit, and in this case, the target revolving gate, the first revolving gate, and the second revolving gate are all single-qubit revolving gates acting on the qubit.

Further, each of the L training layers includes:

the target revolving door, the rotation parameter x is used for rotating the angle corresponding to the z axis;

and the second revolving door is used for carrying out rotating operation on the angle corresponding to the y axis.

Or, each of the L training layers includes:

Therefore, the expression capacity of the preset parameterized quantum circuit is effectively improved, the types and the number of the quantum gates used are small, the number of the target adjustable parameters to be trained is small, and therefore a foundation is laid for efficiently estimating and obtaining the Rayleigh entropy corresponding to the first quantum state.

Further, in another specific example of the disclosure, when any one of the L training levels includes the target revolving door, the first revolving door, and the second revolving door, the order of actions of the revolving doors is as follows:

the first revolving door, the second revolving door and the target revolving door.

Or, in another specific example, when any one of the L training layers includes the target revolving door and the second revolving door, the order of actions of the revolving doors is as follows: a second revolving door and a target revolving door.

That is to say, in a specific example, the target revolving door, the first revolving door and the second revolving door included in each of at least two of the L training levels sequentially include, in order of action of the revolving door:

the second rotating door is used for rotating the angle corresponding to the y axis;

the target revolving door.

Or, in another specific example, the target revolving door and the second revolving door included in each of at least two of the L training levels sequentially include, according to an action sequence of the revolving doors:

the target revolving door.

For example, taking the example that the preset parameterized quantum circuit includes a qubit, and correspondingly, the target revolving gate, the first revolving gate, and the second revolving gate are all single-qubit revolving gates acting on the qubit, as shown in fig. 3 (a), one of at least two training layers of the L training layers, for example, an ith training layer of the L training layers, sequentially includes, according to an acting sequence:

angle of rotation phi _i At an angle corresponding to the z-axisFirst revolving door R _Z (φ _i )；

Angle of rotation theta _i The second revolving door R is an angle corresponding to the y axis _Y (θ _i )；

Rotation parameter x _j A target revolving door R with an angle corresponding to the z-axis _Z (x _j )。

Here, the first rotating door R _Z (φ _i ) Angle of rotation phi _i And a second revolving door R _Y (θ _i ) Angle of rotation theta of _i And setting a target adjustable parameter in the ith training layer, wherein i is an integer which is greater than or equal to 1 and less than or equal to L. It is understood that, in this example, the other training layer of the at least two training layers of the L training layers has a structure as shown in fig. 3 (a). And will not be described in detail herein.

Further, in another specific example, each of the training layers in the L training layers has a structure as shown in fig. 3 (a), and details thereof are not repeated here.

For another example, taking the example that the preset parameterized quantum circuit includes a qubit, and correspondingly, the target revolving gate and the second revolving gate are both single-qubit revolving gates acting on the qubit, as shown in fig. 3 (d), one of at least two training layers of the L training layers, for example, an ith training layer of the L training layers, sequentially includes, according to an acting sequence:

angle of rotation theta _i A second revolving door R with the angle corresponding to the y axis _Y (θ _i )；

Here, the second rotary gate R _Y (θ _i ) Angle of rotation of theta _i And setting a target adjustable parameter in the ith training layer, wherein i is an integer which is greater than or equal to 1 and less than or equal to L. It is understood that, in this example, the other training layer of the at least two training layers of the L training layers has a structure as shown in fig. 3 (d). And will not be described in detail herein.

Further, in another specific example, each of the training layers in the L training layers has a structure as shown in fig. 3 (d), and details are not repeated here.

Therefore, the expression capacity of the preset parameterized quantum circuit is effectively improved, the types and the number of the quantum gates used are small, the number of the target adjustable parameters to be trained is small, and therefore a foundation is laid for efficiently estimating and obtaining the Rayleigh entropy corresponding to the quantum state.

Further, in another specific example, after the L training layers of the preset parameterized quantum circuit, another revolving gate is further included.

In a specific example, after presetting the L training layers of the parameterized quantum circuit, the method further includes:

a third revolving gate for revolving a fourth angle and acting on a quantum bit in the preset parameterized quantum circuit;

a fourth rotating gate used for rotating the fifth angle and acting on the quantum bit in the preset parameterized quantum circuit;

wherein a rotation angle phi of the third rotary door ₀ And a rotation angle theta of the fourth rotary door ₀ And adjusting the parameters for the target.

In a specific example, the preset parameterized quantum circuit includes a qubit, and in this case, the third rotating gate and the fourth rotating gate are both single-qubit rotating gates that act on the qubit.

For example, in an example, as shown in fig. 3 (b), the preset parameterized quantum circuit further includes, after the L training layers:

angle of rotation phi ₀ A third revolving door R with an angle corresponding to the z-axis _Z (φ ₀ )；

Angle of rotation theta ₀ A fourth revolving door R with the angle corresponding to the y axis _Y (θ ₀ )。

Here, the rotation angle phi ₀ And a rotation angle theta ₀ Also the target adjustable parameter.

Based on this, the mathematical expression of the pre-set parameterized quantum circuit as shown in fig. 3 (b) can be specifically:

in a specific example, after the L training layers of the preset parameterized quantum circuit, another revolving gate is further included:

a third revolving gate for revolving the fourth angle and acting on the quantum bit in the preset parameterized quantum circuit;

a fifth revolving gate used for rotating the sixth degree and acting on the quantum bit in the preset parameterized quantum circuit;

wherein a rotation angle phi of the third rotary door ₀ And a rotation angle theta of the fourth rotary door ₀ Is the target adjustable parameter; the rotation angle beta of the fifth revolving door is a fixed parameter, namely a parameter which does not participate in training. Or, the rotation angle phi of the third revolving door ₀ A rotation angle theta of the fourth revolving door ₀ And the rotation angle beta of the fifth revolving door is the target adjustable parameter.

In a specific example, the preset parameterized quantum circuit includes a qubit, and in this case, the third revolving gate, the fourth revolving gate, and the fifth revolving gate are all single-qubit revolving gates acting on the qubit.

For example, in another example, as shown in fig. 3 (c), the preset parameterized quantum circuit further includes, after the L training layers:

Angle of rotation theta ₀ A fourth revolving door R with an angle corresponding to the y-axis _Y (θ ₀ )；

And a fifth revolving door R with a rotation angle beta corresponding to the z-axis _Z (β)。

Here, the rotation angle phi ₀ Angle of rotation theta ₀ And the rotation angle beta are target adjustable parameters.

Based on this, the mathematical expression of the pre-set parameterized quantum circuit as shown in fig. 3 (c) may be specifically:

or, the rotation angle phi ₀ And a rotation angle theta ₀ All are target adjustable parameters, and the rotation angle beta is a fixed parameter and does not participate in training.

or, in another example, after the L training layers of the preset parameterized quantum circuit, the method further includes:

a fourth rotation gate for rotating the fifth angle and acting on the qubit in the preset parameterized quantum circuit;

wherein a rotation angle θ of the fourth rotary door ₀ And adjusting the parameters for the target.

It should be noted that, for the related content of the fourth revolving door, reference may be made to the above description, and details are not described herein again. That is, in this example, as shown in fig. 3 (e), the L training levels are followed by the fourth revolving door, and the third revolving door is not included, compared to the structure shown in fig. 3 (b).

Or, in yet another example, after the L training layers of the preset parameterized quantum circuit, another revolving gate is further included:

wherein a rotation angle θ of the fourth rotary door ₀ Is the target adjustable parameter; the rotation angle beta of the fifth revolving door is a fixed parameter, namely a parameter which does not participate in training. Or, the rotation angle phi of the third revolving door ₀ A rotation angle theta of the fourth rotary door ₀ And the rotation angle beta of the fifth revolving door is the target adjustable parameter.

It should be noted that, for the related contents of the fourth revolving door and the fifth revolving door, reference may be made to the above description, and details are not described herein again. That is, compared to the structure shown in fig. 3 (c), in this example, as shown in fig. 3 (f), the L training levels are followed by the fourth and fifth revolving doors, and the third revolving door is not included.

Therefore, the scheme effectively improves the expression capability of the preset parameterized quantum circuit, and meanwhile, the types and the number of the used quantum gates are small, and the number of the target adjustable parameters to be trained is small, so that the basis is laid for efficiently estimating and obtaining the Rayleigh entropy corresponding to the quantum state, and the basis is laid for improving the accuracy of the result.

In a specific example of the disclosure, the target quantum circuit includes M layers, where M is a positive integer greater than or equal to 1 and less than or equal to L/2;

at least one of the M layers is based on:

replacing a first controlled unitary gate with a first target revolving gate of a first training layer in the two training layers, and replacing a second controlled unitary gate with a second target revolving gate of a second training layer in the two training layers; wherein the two training layers are any two training layers of the L training layers.

It is to be understood that this example applies to the first and second ways described above.

Here, since the target quantum circuit is obtained by expanding the preset parameterized quantum circuit, and two target revolving gates of different layers in the preset parameterized quantum circuit are respectively replaced by the first controlled unitary gate and the second controlled unitary gate, the target quantum circuit at most comprises L/2 layers.

Further, in the case that each training layer in the pre-parameterized quantum circuit includes a target revolving gate, for example, each training layer includes a revolving gate of the first type, i.e., a revolving gate shown in fig. 3 (a), or each training layer includes a revolving gate of the second type, i.e., a revolving gate shown in fig. 3 (d), in this case, the target quantum circuit includes L/2 layers.

In a specific example, at least two training layers of the L training layers (for example, the ith training layer and the (i + 1) (or i +2, etc., which are only exemplary, and may be other layers) training layers) include: the target spin gate, the first spin gate, the second spin gate, where there is one layer in the target quantum circuit, such as

Layer (A)

For rounding up the symbol), the target revolving gate (i.e. the first target revolving gate) of the (i + 1) th training layer (which may correspond to the above-mentioned first training layer) is replaced by the first controlled unitary gate, and the target revolving gate (i.e. the second target revolving gate) of the (i) th training layer (the second training layer) is replaced by the second controlled unitary gate.

Further, since at least one of the M layers is based on two training layers in the pre-set parameterized quantum circuit, in one example, at least one of the M layers includes:

two first revolving doors;

two second revolving doors;

a first controlled unitary gate;

a second controlled unitary gate.

Further, in another example, at least one of the M layers comprises, in order of quantum gate action:

a first revolving door;

a second revolving door;

a first controlled unitary gate;

a first revolving door;

a second revolving door;

a second controlled unitary gate.

Or, in another example, at least one of the M layers comprises:

two second revolving doors;

a first controlled unitary gate;

a second controlled unitary gate.

a second revolving door;

a first controlled unitary gate;

a second revolving door;

a second controlled unitary gate;

here, the related description of the quantum gate in this example can be according to the above description, and is not described here again.

Therefore, in the process of constructing the target quantum circuit on the basis of the preset parameterized quantum circuit, the expression capacity of the target quantum circuit is effectively improved, the types and the number of the used quantum gates are small, the number of target adjustable parameters to be trained is small, the foundation is laid for efficiently estimating and obtaining the Rayleigh entropy corresponding to the quantum state, and the foundation is laid for improving the accuracy of the result.

Moreover, different construction modes can be adopted in the process of constructing the target quantum circuit based on the preset parameterized quantum circuit, so that the scheme disclosed by the invention has strong expansibility.

In a specific example of the present disclosure, the two training layers are any two adjacent training layers of the L training layers. That is, at least one of the M layers is based on two adjacent training layers in the pre-set parameterized quantum circuit.

In a specific example, each of any two adjacent training layers (e.g., the ith training layer and the (i + 1) th training layer) of the L training layers includes: the target revolving gate, the first revolving gate, the second revolving gate, in which case there is one layer in the target quantum circuit, such as the first

The layers are obtained by replacing the target revolving door (i.e. the first target revolving door) of the (i + 1) th training layer (i.e. the first training layer) with the first controlled unitary door, and replacing the target revolving door (i.e. the second target revolving door) of the (i) th training layer (the second training layer) with the second controlled unitary door.

Further, in an example, each of the layers of the target quantum circuit is obtained based on two adjacent training layers of a preset parameterized quantum circuit, for example, each of the layers is obtained by replacing a first target revolving gate of a first training layer of the two adjacent training layers of the preset parameterized quantum circuit with a first controlled unitary gate, and replacing a second target revolving gate of a second training layer of the two training layers with a second controlled unitary gate. At this time, the number of the first controlled unitary gates and the number of the second controlled unitary gates in the target quantum circuit are both half of the number of the target revolving gates in the preset parameterized quantum circuit.

Specifically, in the case that each training layer in the preset parameterized quantum circuit includes the target revolving gate, the first revolving gate and the second revolving gate, and the sequence of actions of the revolving gates is as shown in fig. 3 (a), the second revolving gate in the L/2 layer of the target quantum circuit

The layers are based on the following:

the method comprises the steps of replacing a target revolving door (namely a first target revolving door) in an (i + 1) th training layer with the first controlled unitary door, and replacing the target revolving door (namely a second target revolving door) in the ith training layer with the second controlled unitary door.

Specifically, as shown in FIG. 4 (a), the second one in the target quantum circuit

Layers (i taking values from 1 to L) comprising, in the order of action of the quantum gates:

angle of rotation phi _i+1 A first revolving door R with an angle corresponding to the z-axis _Z (φ _i+1 )；

Angle of rotation theta _i+1 A second revolving door R with the angle corresponding to the y axis _Y (θ _i+1 )；

A first controlled unitary gate;

angle of rotation phi _i A first revolving door R with an angle corresponding to the z-axis _Z (φ _i )；

A second controlled unitary gate.

Or, in the case that each training layer in the preset parameterized quantum circuit comprises the target revolving gate and the second revolving gate, and the action sequence of each revolving gate is as shown in fig. 3 (d), the second of the L/2 layers of the target quantum circuit

The layers are based on the following:

the target revolving door (namely the first target revolving door) in the (i + 1) th training layer is replaced by the first controlled unitary door, and the target revolving door (namely the second target revolving door) in the (i) th training layer is replaced by the second controlled unitary door.

Specifically, as shown in FIG. 4 (b), the second in the target quantum circuit

A first controlled unitary gate;

A second controlled unitary gate.

It should be noted that the auxiliary registers acting on different layers in the target quantum circuit are the same; also, the master registers acted upon by the unused layers are the same. That is to say, in practical application, the quantum bit in the preset parameterized quantum circuit may be used as an auxiliary register, and after the main register is expanded, the target revolving gate in each training layer in the preset parameterized quantum circuit may be replaced by a target controlled unitary gate, so that each layer shares the same auxiliary register and main register.

Therefore, the target quantum circuit is constructed on the basis of the preset parameterized quantum circuit, the process is low in consumption, the unitary operator can be controlled through the auxiliary register, the state information of the auxiliary register is obtained through measurement, and the Rayleigh entropy corresponding to the first quantum state is obtained.

In addition, in the scheme of the present disclosure, as shown in fig. 4 (a) or fig. 4 (b), when the quantum state of the auxiliary register is |0>In the case of (2), activating a controlled unitary gate with a hollow core in the target quantum circuit

I.e. a second controlled unitary gate. When the quantum state of the auxiliary register is |1>In this case, a controlled unitary gate U with a solid core, i.e. the first controlled unitary gate, is activated. In practical applications, that is, in the case of the determination of the current quantum state of the auxiliary register, the first controlled unitary gate operates,or a second controlled unitary gate, rather than both. Therefore, the unitary operator can be controlled through the auxiliary register, the state information of the auxiliary register is obtained through measurement, and then the Rayleigh entropy corresponding to the first quantum state is obtained through estimation. Moreover, the scheme disclosed by the invention is suitable for any quantum state and has rich application scenes.

In a specific example of the disclosure, the target parameter value of the target adjustable parameter in the sub-circuit is obtained by a training method, that is, a preset parameterized quantum circuit (constructed in a first manner or a second manner) is trained in the following manner, and the training is performed to obtain the target parameter value of the target adjustable parameter; specifically, as shown in fig. 5, the method further includes:

step S501: taking the value of the rotation parameter x of the preset parameterized quantum circuit as any data point x in the N data points _j Under the condition of (3), acquiring an actual output result y of the preset parameterized quantum circuit _j 。

Here, the actual output result y _j Outputting a result of the preset parameterized quantum circuit for the target adjustable parameter in the preset parameterized quantum circuit under a current parameter value; n is a positive integer which is more than or equal to 1, and j is a positive integer which is more than or equal to 1 and less than or equal to N; the rotation parameter x includes the first rotation parameter and the second rotation parameter.

It is understood that in the structure shown in fig. 4 (a), the rotation parameters corresponding to the target revolving door in different layers may be collectively referred to as rotation parameters.

Step S502: obtaining N actual output results y _j 。

That is, under the condition that j takes values from 1 to N, N actual output results y can be obtained _j 。

Step S503: determining whether an iteration termination condition is satisfied; in a case where it is determined that the iteration termination condition is satisfied, executing step S504; otherwise, step S505 is executed.

Here, the iteration termination condition includes at least one of:

the method I comprises the following steps: based on the N actual output results y _j And N target output results

Determining that the loss value of a preset loss function meets a convergence condition; the target output result

Here, in the case where the order α is preset to be a rational number greater than 1, y (x) _j ) Is based on a predetermined order alpha and an independent variable x _j Obtaining; in the case that the preset order alpha is a rational number which is more than 0 and less than 1, y (x) _j ) Based on a predetermined order α, a predetermined threshold γ and an argument x _j Obtaining; or in the case of presetting a rational number with the order alpha being more than 0 and less than 1, y (x) _j ) Based on a predetermined order alpha, a normalization coefficient c and an independent variable x _j Thus, the compound was obtained.

The second method comprises the following steps: and the current iteration times reach the preset times.

In practical application, as long as one of the above conditions is satisfied, the iteration termination condition can be satisfied.

Step S504: and taking the current parameter value of the target adjustable parameter as the target parameter value of the target adjustable parameter in the preset parameterized quantum circuit after training.

Step S505: adjusting the parameter values of the target adjustable parameter, and returning to step S501 to obtain N actual output results y after the parameter values are adjusted _j And re-determining whether the iteration termination condition is satisfied until the iteration termination condition is satisfied.

Thus, the target parameter value of the target adjustable parameter of the sub-circuit is obtained by training other parameterized quantum circuits; here, because the preset parameterized quantum circuit has a simple circuit structure compared with a target quantum circuit, the calculation amount can be effectively reduced by training the preset parameterized quantum circuit to obtain the target parameter value of the target adjustable parameter, and a foundation is laid for efficiently determining and obtaining the rayleigh entropy corresponding to the first quantum state.

In a specific example of the disclosed scheme, the unitary operator can be embodied in the following two forms:

the first form: unitary operator U = e ^iρ . In particular, the amount of the solvent to be used,

in the case that the unitary operator U is obtained based on the first quantum system, an equivalent circuit of the first controlled unitary gate in the target quantum circuit is the unitary operator U = e ^iρ And the equivalent circuit of the second controlled unitary gate in the target quantum circuit is the conjugate transpose of the unitary operator U

An equivalent circuit of (1); wherein the ρ represents the first quantum state.

In the first form, in the case of presetting a rational number with the order α greater than 1 (namely, α > 1), the objective function

In the case where the predetermined order α is a rational number greater than 0 and less than 1 (i.e., 0 < α < 1), the objective function

Here, α is the above-described preset order, and γ is the above-described preset threshold.

Here, it should be noted that the selection of the objective function y (x) is not unique; in practical applications, the objective function may be transformed, for example, to

At this time, the normalization requirement can be satisfied, that is, the value of x is [ - π, π]In the case of (a) the (b),

is of the value of [ -1,1]In between.

That is, in a specific example, the unitary operator U is obtained based on the first quantum system, such as the unitary operator U: = e ^iρ Conjugate transpose of the unitary operator U

At this time, as shown in fig. 4 (a) or fig. 4 (b), the number of qubits contained in the master register in the target quantum circuit is equal to the number of qubits contained in the first quantum system, for example, equal to n; at this time, the first controlled unitary gate (for convenience of description, the first controlled unitary gate may also be represented by U) is a unitary operator U: = e ^iρ Said second controlled unitary gate (the first controlled unitary gate, too, may be used)

To represent) is

Equivalent circuit of (2).

It should be noted that, in the first form, a first input state of the auxiliary register of the target quantum circuit is a preset initial state, and a second input state of the main register is the first quantum state.

The second form: unitary operator U = RE. In particular, the amount of the solvent to be used,

when the unitary operator U is obtained based on the total subsystem corresponding to the first quantum system, the equivalent circuit of the first controlled unitary gate in the target quantum circuit is the equivalent circuit of the unitary operator U = RE, and the equivalent circuit of the second controlled unitary gate in the target quantum circuit is the conjugate transpose of the unitary operator U

The equivalent circuit of (a); wherein E represents a block encoding of the first quantum state; the R represents a subsystem based on the total amountConstructed reflection operators.

In the second form, in the case of presetting a rational number with the order α greater than 1 (namely, α > 1), the objective function

In the case of a rational number with a predetermined order α greater than 0 and less than 1 (i.e. 0 < α < 1), the objective function

Here, α is the above-mentioned preset order, c is the above-mentioned normalization coefficient, and the value of c is related to the preset threshold γ. It should be noted that the selection of the objective function y (x) is not unique; in practical application, the objective function can be transformed as long as normalization is required, that is, the value of x is [ -pi, pi [ -pi ])]In the case of (2), y (x) is a value of [ -1,1]In the meantime.

That is, in another specific example, the unitary operator U is obtained based on a total quantum system corresponding to the first quantum system, for example, for the total quantum system formed by the first quantum system a and the second quantum system B, and the binary quantum state of the total quantum system is | ψ>For the scenario of (1), the unitary operator U = RE, the conjugate transpose of the unitary operator U

At this time, the objective function

Or an objective function

Correspondingly, the first controlled unitary gate is an equivalent circuit of the unitary operator U = RE, and the second controlled unitary gate is

An equivalent circuit of (1).

Further, in this example, the number of qubits included in the main register in the target quantum circuit = the number of qubits included in the first quantum system a (for example, n) + the number of qubits included in the quantum subsystem (for example, n + n '), where n' is the number of qubits included in the second quantum system B in the quantum subsystem, that is, the number of qubits corresponding to the second quantum state. Based on this, in a specific example, the number of main quantum bits contained in the main register is: 2n + n'.

Here, E is a Block encoding (Block encoding) of a first quantum state, and is expressed in the form of:

i.e. the block code E is a unitary operator with the density matrix p of the first quantum state of the first quantum system a in the upper left corner.

Further, configured to generate the binary quantum state | ψ>The operator of (c), may be referred to as a V operator for short (i.e. the target state generation operator, for this example, the target state is the binary quantum state | ψ>) The V operator satisfies V |0 ^n+n′ >＝|ψ>. As shown in fig. 4 (d), the equivalent circuit of the block code E (in the order of the quantum gates) includes:

a V operator acting on the first set of qubits and the second set of qubits;

a Swap gate acting on the second set of qubits and the third set of qubits;

conjugate transpose of V operator acting on first and second sets of qubits

Here, the number of qubits included in the first set of qubits is related to the number of qubits corresponding to the second quantum state (i.e. included in the second quantum system), for example, equal to the number n' of qubits included in the second quantum system B; the number of qubits comprised by the second set of qubits is related to the number of qubits corresponding to the first quantum state (i.e. comprised by the first quantum system a), for example, equal to the number n of qubits corresponding to the first quantum state; the number of qubits comprised by the third set of qubits is related to the number of qubits corresponding to the first quantum state (i.e. comprised by the first quantum system a), for example also equal to the number n of qubits corresponding to the first quantum state.

It should be noted that, in this example, the first set of qubits, the second set of qubits, and the third set of qubits may all be collectively referred to as a master register.

Further, a reflection operator R (Reflector) of the form:

R＝2|0 ^n+n′ ><0 ^n+n′ |-I

here, I is a cell matrix.

Further, an equivalent circuit of the first controlled unitary gate U = RE can be constructed based on the block code E and the reflection operator R, and the second controlled unitary gate

An equivalent circuit of (2).

Specifically, as shown in fig. 4 (e), the second in the target quantum circuit

The equivalent circuit of the first controlled unitary gate U = RE in the layer comprises the following components according to the action sequence of the quantum gate:

a V operator acting on the first set of qubits and the second set of qubits;

a Swap gate controlled by the auxiliary register and acting on the second set of qubits and the third set of qubits;

conjugate transpose of V operator acting on first and second sets of qubits

A reflection operator R controlled by the auxiliary register and acting on the first and second groups of qubits.

Further, in the target quantum circuit

Said second controlled unitary gate in a layer

The equivalent circuit of (2) comprises the following components in the action sequence of the quantum gate:

a reflection operator R controlled by the auxiliary register and acting on the first and second groups of qubits;

a V operator acting on the first set of qubits and the second set of qubits;

conjugate transpose of V operator acting on first and second sets of qubits

It is to be understood that, similarly to fig. 4 (b), in this example, as shown in fig. 4 (f), all of the first turnstiles R in fig. 4 (e) may also be deleted _Z (φ _i ) (ii) a Further, a third rotary gate R is included in the target quantum circuit _Z (φ ₀ ) In the case of (3), the third revolving door R may be also deleted _Z (φ ₀ ) And the target quantum circuit obtained based on the expansion of fig. 3 (d) and 3 (e) is obtained, or the target quantum circuit obtained based on the expansion of fig. 3 (d) and 3 (f) is obtained, so that an even function is simulated, and the circuit depth can be further reduced by half while the same effect is achieved.

It should be noted that, in the scheme of the present disclosure, as shown in fig. 4 (e) or fig. 4 (f), when the quantum state of the auxiliary register is |0>, the reflection operator R with an empty core and the Swap gate with an empty core in the second controlled unitary gate of the target quantum circuit are activated. And in the case that the quantum state of the auxiliary register is |1>, activating a reflection operator R with solid and a Swap gate with solid in a first controlled unitary gate of the target quantum circuit. That is, in practical applications, the reflection operator R and Swap gate in the first controlled unitary gate or the reflection operator R and Swap gate in the second controlled unitary gate work with the current quantum state determination of the auxiliary register.

Thus, the present disclosure provides a concrete expression form of unitary operator, which is convenient to be realized by an equivalent circuit, and greatly improves the practicability on medium-scale noisy quantum equipment, and has strong expandability.

Based on this, the scheme of this disclosure has the following advantages:

first, the disclosed solution requires a smaller width of the target quantum circuit. Compared with the quantity of auxiliary quantum bits required by the existing scheme, the quantity of the auxiliary quantum bits in the target quantum circuit of the scheme can be one, so that compared with the existing scheme, the width of the target quantum circuit used by the scheme is minimum, a foundation is laid for effectively reducing the calculated amount and improving the processing efficiency, and meanwhile, the precision is high.

Secondly, the scheme of the disclosure is easier to realize. Compared with the existing scheme, the scheme disclosed by the invention has the advantages that the number and the types of quantum gates used in the target quantum circuit are less in the complexity and the number of the quantum gates, for example, single-quantum-bit-controlled unitary gates such as a first controlled unitary gate and a second controlled unitary gate can be used, so that the required quantum computing resources are reduced, and meanwhile, the feasibility of implementation in a medium-scale quantum computing device is increased.

Thirdly, the practicability is stronger. The target quantum circuit constructed by the scheme is simple, low in cost and high in practicability.

The following describes the disclosed embodiments in further detail with reference to specific examples; in particular, the Quantum state (Quantum state) of a Quantum system can be used to its densityDegree matrix (Density matrix) and is marked as a mathematical symbol rho; for the present example, the character ρ represents a first quantum state, which may also be referred to herein as ρ for ease of subsequent description _A 。

Further, rayleigh entropy R corresponding to the first quantum state ρ _α (ρ) is defined as:

(i.e. the

)。

Here, tr denotes a Trace (Trace), ln denotes a natural logarithm, and α denotes a preset order, which is a rational number greater than 0 and not 1, i.e., α ∈ (0, 1) · (1, ∞).

It will be appreciated that for the Rayleigh entropy R described above _α For the formula of (p), the base can be changed to other positive numbers, and in this case, only the corresponding transformation needs to be performed on the formula, for example,

wherein a is more than 0. This example calculates primarily rayleigh entropy with base e, and due to the aforementioned characteristics, the disclosed solution is still applicable even if the base of the logarithm is changed.

Based on the formula, rayleigh entropy R is calculated _α The core of (ρ) is to acquire the alpha trace of the first quantum state ρ, namely tr (ρ) ^α )。

In practical application, the first quantum state ρ _A Can be prepared by a Quantum circuit (Quantum circuit) (such as the target Quantum circuit of the present disclosure), for example, the first Quantum state ρ is prepared as denoted by E _A Quantum circuit of (E), then quantum circuit E and first quantum state ρ _A The relationship of (c) is then:

E|0> _AB ＝|ψ> _AB and tr _B (|ψ><ψ| _AB )＝ρ _A 。

Here, AB denotes a system comprising two subsystems (i.e., a first quantity)A total subsystem of subsystem a and a second quantum system B); i0> _AB Represents the zero state, i.e., the initial quantum state of the quantum system; phi> _AB Indicating the output quantum state of the quantum subsystem after acting on quantum circuit E, | ψ><ψ| _AB A density matrix representing the total subsystem as a pure state; at this time, tr is for the sum subsystem AB _B Representing the Partial trace, i.e. the quantum state of the first quantum system A, i.e. the first quantum state p _A 。

Based on this, the quantum entropy estimation task can then be described as: for a first quantum state p _A How to design a target quantum circuit to obtain Rayleigh entropy R meeting precision requirements _α An estimate of (ρ).

In particular, it is an object of the disclosed solution to present a practical and efficient quantum rayleigh entropy estimation scheme. Essentially divided into two parts, the first part, simulating an objective function based on quantum signal processing or quantum neural networks, e.g.

Or

The part can construct a preset parameterized quantum circuit and train the preset parameterized quantum circuit, so that the preset parameterized quantum circuit can simulate the target function y (x); and the second part is used for realizing a target quantum circuit by using the target parameter value obtained in the first part so as to estimate alpha-order Rayleigh entropy corresponding to the first quantum state.

Here, the solution of the present disclosure utilizes the capability of the quantum revolving gate sequence to simulate an arbitrary square integrable function (i.e., y (x)), and combines the extraction capability of the trigonometric polynomial to efficiently solve the rayleigh entropy estimation problem by obtaining an expected value through quantum measurement.

The first part, program one, is mainly used to calculate or optimize the target adjustable parameters of the revolving door on the auxiliary register, and the program one is a subroutine called by program two (i.e. main program).

Step 11: inputting a preset order alpha, a preset threshold gamma and an error tolerance value epsilon (namely the first error condition).

Here, α ∈ (0, 1) — (1, ∞) is a constant; the preset threshold gamma is a constant smaller than a non-zero eigenvalue corresponding to the first quantum state; the error tolerance value epsilon can constrain the difference degree between an actual output result and a target output result output by a preset parameterized quantum circuit for simulating the target function y (x), so that the accuracy of the Rayleigh entropy obtained by estimation is constrained.

It should be noted that, the value of the preset threshold γ may also be used to constrain the accuracy of the finally obtained rayleigh entropy. In other words, in practical applications, the preset threshold γ and the error tolerance value e can jointly constrain the accuracy of the obtained rayleigh entropy.

Step 12: constructing a preset parameterized quantum circuit to be trained, and determining the number of training layers of the preset parameterized quantum circuit to be trained according to the error tolerance value E, wherein the preset parameterized quantum circuit to be trained comprises L training layers; further, the number N of training data sets may also be determined based on the error tolerance value e. Here, L is an even number of 2 or more; and N is a positive integer greater than or equal to 1.

Here, in this example, the preset parameterized quantum circuit is a parameterized circuit including one quantum bit (which may be referred to as an auxiliary quantum bit or an auxiliary register in this example).

It should be noted that, in practical applications, a preset parameterized quantum circuit including two or more qubits may be further configured to simulate the target function y (x), and the preset parameterized quantum circuit is within the protection range of the present disclosure as long as the target function can be simulated and the target parameterized quantum circuit capable of solving the rayleigh entropy is obtained by expansion.

In this example, each of the L training layers of the preset parameterized quantum circuit includes a quantum revolving gate sequence, and the quantum revolving gate sequences in each training layer are the same.

It should be noted that, in practical applications, quantum revolving gate sequences included in different training layers in the L training layers may be the same or different, or quantum revolving gate sequences included in some training layers are the same, quantum revolving gate sequences included in other training layers are different, and the like, which is not limited in this disclosure.

Further, in this example, a quantum rotation gate sequence included in the ith training layer of the L training layers is taken as an example for explanation. As shown in fig. 3 (a), based on the order of the action of the revolving gates in the quantum revolving gate sequence, the quantum revolving gate sequence included in the i-th training layer sequentially includes:

angle of rotation phi _i The first revolving door R is the angle corresponding to the z-axis _Z (φ _i )；

Here, the first rotating door R _Z (φ _i ) Angle of rotation phi _i And a second revolving door R _Y (θ _i ) Angle of rotation of theta _i And setting a target adjustable parameter in the ith training layer, wherein i is an integer which is greater than or equal to 1 and less than or equal to L.

Further, in this example, after the L training layers in the preset parameterized quantum circuit, other revolving gates are further included.

Specifically, in an example, as shown in fig. 3 (b), the preset parameterized quantum circuit further includes, after L training layers:

Angle of rotation theta ₀ A fourth revolving door R with an angle corresponding to the y-axis _Y (θ ₀ )。

or, in another example, as shown in fig. 3 (c), the preset parameterized quantum circuit further includes, after the L training layers:

And a fifth revolving door R of which the rotating angle beta is the angle corresponding to the z-axis _Z (β)。

Here, the rotation angle phi ₀ Angle of rotation theta ₀ And the rotation angle beta are both target adjustable parameters.

Based on this, the mathematical expression of the pre-set parameterized quantum circuit as shown in fig. 3 (c) can be specifically:

note that, the circuit configuration of each of the L training layers may refer to the configuration shown in fig. 3 (a), which is not shown in fig. 3 (b) and 3 (c).

It should be noted that, since the preset parameterized quantum circuit includes a qubit, the operation and the expected value of the preset parameterized quantum circuit can be effectively and accurately simulated by using classical computing equipment, that is, no quantum computing resource is consumed, so that the quantum computing resource is saved, and the processing cost is also reduced.

Further, it can be understood that, in practical applications, when the number of qubits included in the preset parameterized quantum circuit is small (for example, 20-30 qubits), the target parameter value of the target adjustable parameter can be calculated in a classical calculation device by means of an analog circuit, so that the consumption of quantum calculation resources is avoided to the maximum extent within the allowable range of calculation efficiency.

Step 13: preparing a training data set; for example, N training data points are prepared

For training the above-described preset parameterized quantum circuit.

The example is described by taking a preset parameterized quantum circuit shown in fig. 3 (c) as an example, and the rotation angle β is a target adjustable parameter to participate in a subsequent training process. Accordingly, the target quantum circuit is extended based on the pre-set parameterized quantum circuit shown in fig. 3 (c), as shown in fig. 4 (c).

Step 14: l +1 parameter values θ, and L +1 parameter values Φ, and 1 parameter value β are randomly generated.

Here, the L +1 parameter values θ may be respectively written as θ ₀ And

(i is a positive integer of 1 to L). Vectors may also be used for ease of recording

I.e. θ = { θ = { θ ₀ ，θ ₁ ，…，θ _i ，…，θ _L }。

Similarly, L +1 parameter values

Can be respectively recorded as phi ₀ And

(i is a positive integer of 1 to L). For ease of recording, it can also be expressed using a vector φ, i.e., φ = { φ = ++ ₀ ，φ ₁ ，…，φ _i ，…φ _L }。

At this time, the preset parameterized quantum circuit may be represented as U _x (β，θ，φ)。

Step 15: for each rotation parameter x _j And j is more than or equal to 1 and less than or equal to N, the following operations are carried out:

(a) Simulation of the above-described pre-set parameterized quantum circuit U comprising single quantum bits using a classical simulator (i.e. on a classical computing device) _x (β, θ, φ); also, for each x _j The preset parameterized quantum circuit can be obtained

(b) Inputting a predetermined initial state, e.g. |0>The expected value of the observable Z is obtained by using the classical simulator simulation, namely the actual output result of the auxiliary register is obtained and marked as y _j 。

For each x _j After all the operations are executed, namely the operations are finished, a group of actual output results are obtained

And N in total.

Step 16: will actually output the result

And target output result

The 2-norm therebetween as a loss function, i.e., the loss function L (β, θ, Φ) is:

wherein, in the case that the preset order alpha is known, the preset order alpha can be based on

Obtaining a target output result

Here, it is understood that, in practical applications, the loss function may also be any other metric function describing the distance, such as a commonly used mean absolute error function, a mean square error function, a cross entropy function, and the like. An appropriate loss function may be selected according to factors such as data size, hardware environment, learning accuracy, or convergence speed, which is not particularly limited in the present disclosure.

And step 17: calculating a loss value based on the loss function L (beta, theta, phi), and optimizing, for example, by a gradient descent method, the target adjustable parameters beta, theta and phi are adjusted to minimize L (beta, theta, phi);

wherein the target adjustable parameter theta comprises theta ₀ And

that is, θ = { θ = ₀ ，θ ₁ ，…，θ _i ，…，θ _L The target adjustable parameter phi comprises phi ₀ And

i.e., = { phi = + ₀ ，φ ₁ ，…，φ _i ，…φ _L }。

In practical application, on a classical computing device, a common gradient descent method can be used, and other more scientific and effective optimization methods can also be used for adjusting parameters of a target

And target adjustable parameter phi ₀ And

optimization is performed such that the loss value of the loss function is minimized, and the disclosed solution does not limit the specific optimization manner.

Step 18: after the target adjustable parameters are adjusted, repeating the steps 15-17 until the loss function L (beta, theta, phi) converges or the iteration number is reached, obtaining the optimal parameter value (namely the target parameter value) of each target adjustable parameter, wherein the optimal parameter value is respectively the target parameter value

And

here, ,

it will be appreciated that the above optimization process is repeated to minimize the loss value of the loss function or to reach a convergence state, or to reach the number of iterations, at which point the actual output y may be considered to be the actual output _j Output result approaching target

Current parameter value of target adjustable parameter

And

i.e. the optimum parameter value.

Step 19: outputs an optimum parameter value (i.e. a target parameter value),

and

total 2L + 3.

It is understood that, in practical applications, the program may be executed in a classical computing device or a quantum computing device without considering the computation cost, and the present disclosure is not particularly limited thereto.

In practical applications, the implementation of the first procedure is not unique, for example, in the process of initializing the target adjustable parameters (for example, in step 14), the intrinsic properties of the target adjustable parameters may be utilized, or the initial values of the target adjustable parameters may be set, so as to improve the optimization efficiency; or, a function analysis method can be used to directly obtain the optimal parameter value of the target adjustable parameter. In other words, in practical applications, a suitable implementation may be selected based on factors such as a specific application scenario and a hardware environment.

For example, the calculating the target adjustable angle by using the function analysis method specifically includes:

the input objective function y (x), can be abbreviated as f. And calculating to obtain a target Fourier series F (x) which can approximate the target function F in the target definition domain. Calculating to obtain other Fourier series P (x) and Q (x); wherein,

and recursively calculating the optimal parameter values of the target adjustable parameters beta, theta and phi according to the following equation:

here, the Q ^* (x) Is the complex conjugate of Q (x), P ^* (x) Is the complex conjugate of P (x). Finally, outputting the optimal parameter value

And

in practical applications, any trigonometric polynomial capable of approximating the objective function with a certain accuracy may be used to optimize the optimal parameter value of the target adjustable parameter.

The second part is a program II which is a main program and is mainly used for estimating and obtaining the Rayleigh entropy corresponding to the first quantum state.

It is understood that, in practical applications, the second program may also be executed in a classical computing device and may also be executed in a quantum computing device without considering the computation cost, and the present disclosure is not particularly limited thereto.

Specifically, as shown in fig. 6, the specific steps of the main routine include:

step 21: and expanding the preset parameterized quantum circuit into a target quantum circuit with n +1 quantum bits, so that the target quantum circuit can estimate the Rayleigh entropy corresponding to the first quantum state. Taking the target quantum circuit shown in fig. 4 (c) as an example, n newly added or expanded quantum bits are main quantum bits, and the n main quantum bits may be collectively referred to as a main register.

That is, the target quantum circuit includes an auxiliary register and a main register; wherein the auxiliary register comprises an auxiliary qubit; the master register includes n master quantum bits. Here, n is determined based on the number of qubits corresponding to the first quantum state (i.e. the number of qubits included in the first quantum system), for example, n is the number of qubits included in the first quantum system. In other words, the number of primary qubits comprised by the primary register is the same as the number of qubits comprised by the first quantum system.

Specifically, the target quantum circuit is based on the following: and using the quantum bit in the preset parameterized quantum circuit as an auxiliary register, expanding a main register containing n quantum bits, and simultaneously replacing a first target revolving gate acting on the auxiliary register in the preset parameterized quantum circuit with the first controlled unitary gate and replacing a second target revolving gate acting on the auxiliary register in the preset parameterized quantum circuit with the second controlled unitary gate.

Further, the first target revolving door and the second target revolving door are target revolving doors in different training levels; that is, target revolving gates of different training layers in the preset parameterized quantum circuit are replaced by different controlled unitary gates, for example, a target revolving gate (which may be referred to as a first target revolving gate for convenience of description) in one training layer in the preset parameterized quantum circuit is replaced by a first controlled unitary gate, and a target revolving gate (which may be referred to as a second target revolving gate for convenience of description) in another training layer in the preset parameterized quantum circuit is replaced by a second controlled unitary gate, so as to obtain the target quantum circuit.

It can be understood that, since the target quantum circuit is obtained by expanding the preset parameterized quantum circuit, and two target revolving gates of different layers in the preset parameterized quantum circuit are respectively replaced by the first controlled unitary gate and the second controlled unitary gate, in the case that the preset parameterized quantum circuit includes L layers, the target quantum circuit includes at most L/2 layers.

Specifically, a main register containing n main quantum bits is expanded from the preset parameterized quantum circuit, and meanwhile, target revolving gates in two adjacent training layers of the preset parameterized quantum circuit are respectively replaced with a first controlled unitary gate and a second controlled unitary gate, for example, the target revolving gate of the (i + 1) th training layer is replaced with the first controlled unitary gate, and the target revolving gate of the i-th training layer is replaced with the second controlled unitary gate, so as to obtain a second controlled unitary gate in the target quantum circuit shown in fig. 4 (a)

A structural view of a layer, the first

The layer specifically comprises the following components in the action sequence of each quantum gate:

angle of rotation phi _i+1 At an angle corresponding to the z-axisFirst revolving door R _Z (φ _i+1 )；

Angle of rotation theta _i+1 The second revolving door R is an angle corresponding to the y axis _Y (θ _i+1 )；

A first controlled unitary gate;

A second controlled unitary gate.

Here, for convenience of description, the related parameterized quantum circuit acting on the auxiliary qubit in the target quantum circuit may be referred to as a sub-circuit of the target quantum circuit. It will be appreciated that the sub-circuit also includes an L/2 layer. Further, as shown in fig. 4 (a), each layer in the sub-circuit includes a target tunable parameter; by a first of the sub-circuits

Layers are examples, including:

Here, the rotation angle phi _i+1 Angle of rotation theta _i+1 And a rotation angle phi _i And a rotation angle theta _i Is a target adjustable parameter of the current layer.

It can be understood that, since the target quantum circuit is obtained by expanding on the basis of the preset parameterized quantum circuit, the target quantum circuit further includes other rotating gates after the L/2 layer, similar to the preset parameterized quantum circuit.

Specifically, in one example, after the L/2 layer in the target quantum circuit, a third rotating gate R shown in fig. 3 (b) is further included _Z (φ ₀ ) And a fourth revolving door R _Y (θ ₀ ). Here, the rotation angle phi ₀ And a rotation angle theta ₀ Are all target adjustable parameters.

Or, in another example, after the L/2 layer in the target quantum circuit, a third rotating gate R as shown in fig. 3 (c) is further included _Z (φ ₀ ) And a fourth revolving door R _Y (θ ₀ ) And a fifth revolving door R _Z (beta.) in the presence of a catalyst. Here, the rotation angle phi ₀ And a rotation angle theta ₀ Are all target adjustable parameters; and the rotation angle beta is a fixed value. Or, the rotation angle phi ₀ Angle of rotation theta ₀ And the rotation angle beta is a target adjustable parameter. For details, reference is made to the above statements, which are not described in detail here.

Step 22: setting an error tolerance value E larger than 0, presetting an order alpha, presetting a threshold value gamma larger than 0, and setting a first input state of an auxiliary register in the target quantum circuit to be a preset initial state, such as |0>Or |1>(ii) a Setting the second input state of the main register in the target quantum circuit to the first quantum state ρ (i.e., ρ as described above) _A )。

Here, it can be understood that the first controlled unitary gate in the target quantum circuit is an equivalent circuit of a unitary operator U, and as shown in fig. 4 (a), the first controlled unitary gate can also be represented by a character U for convenience of description. Further, a second controlled unitary gate in the target quantum circuit is a transpose of a unitary operator U

The second controlled unitary gate may also use a character for convenience of description

And (4) showing.

Further, in oneIn a specific example, when the quantum state of the auxiliary register is |0>In the case of (3), activating a controlled unitary gate with a hollow in the target quantum circuit

I.e. a second controlled unitary gate. When the quantum state of the auxiliary register is |1>In this case, a controlled unitary gate U with a solid core, i.e. the first controlled unitary gate, is activated. That is, in practical applications, the first controlled unitary gate operates or the second controlled unitary gate operates with the current quantum state determination of the auxiliary register, but not both.

Step 23: inputting a preset order alpha, a preset threshold gamma and an error tolerance value epsilon into a program I, operating the program I, and acquiring an output optimal parameter value (namely a target parameter value):

and

here, i.e.

Step 24: as shown in FIG. 4 (c), the optimum parameter values are input

And

and a target quantum circuit for applying the unitary operator U to the n +1 qubits, namely a first controlled unitary gate equivalent to U, and

an equivalent second controlled unitary gate acts on the target quantum circuit on the n +1 qubits.

As shown in fig. 4 (a) to 4 (c), the first controlled unitary gate may also use words for convenience of descriptionDenoted by the symbol U. Further, a second controlled unitary gate in the target quantum circuit is a transpose of a unitary operator U

And (4) showing. Further, in this example, the unitary operator U is obtained based on the first quantum state ρ, for example, U: = e ^iρ At this time, the first controlled unitary gate U is e ^iρ The equivalent circuit of (a); said second controlled unitary gate

Is e ^-iρ Equivalent circuit of

Step 25: obtaining observables for a target quantum circuit

Expected value of<Z>。

Here, observables

In particular, the measurement operator Z is applied to the auxiliary register, while the remaining qubits (i.e. the main register) are not operated on, where I denotes the identity matrix. Specifically, the expected value is obtained as follows:

(a) Setting the number of quantum measurements to

(b) Measuring the auxiliary register by using a Paglie Z operator, and counting the occurrence times of 0 and 1;

(c) Based on the statistical results, computing observables

Desired value of (c):

step 26: output-based observables

Expected value of<Z>Estimating to obtain Rayleigh entropy R corresponding to the first quantum state rho _α (ρ), i.e.:

when the alpha is greater than 1, the alpha is,

when the alpha is less than 1, the alpha is more than 1,

at this time, the Rayleigh entropy R is obtained _α (ρ) is an estimated value, i.e., an estimated value of the rayleigh entropy corresponding to the first quantum state ρ.

It should be noted that the objective function simulated by the scheme of the present disclosure

In practical application, can also be respectively paired

And

making corresponding changes, e.g. selection

And

as an objective function, i.e. an objective function

Where b is any constant greater than 0 and less than 1, provided that normalization can be satisfiedThe chemical requirements are satisfied, namely, the value of x is [ -pi, pi]In the case of (2), y (x) is a value of [ -1,1]In the meantime.

It should be noted that the objective function y (x) in this example may also be embodied in other forms, such as, for example,

and c is the normalization coefficient, and the value of c is related to a preset threshold gamma. At this time, the target quantum circuit expanded based on the preset parameterized quantum circuit may be the structure shown in fig. 4 (e) or fig. 4 (f); furthermore, the input state of the first set of qubits is a predetermined initial state, such as |0>Or |1>The input state of the second set of qubits is also a predetermined initial state, e.g. |0>Or |1>And the input state of the third group of qubits is the first quantum state ρ.

Expansion scheme

Since the logarithmic function of the simulation has a definition only between (0, + ∞) and (one ∞, 0)]There is no definition within the interval (a). Therefore, the method can expand the logarithmic function definition domain through the piecewise function so as to define an even function as the target function in the first program. For example, all of the first spin gates R in the target quantum circuit shown in FIG. 3 (a) in "program one" and "program two" may be deleted _Z (φ _i ) And a third revolving door R as shown in FIG. 3 (c) _Z (φ ₀ ) The structure shown in fig. 3 (d) and 3 (e) or fig. 3 (d) and 3 (f) is obtained, so as to simulate an even function, and the circuit depth can be further reduced by half while the same effect is achieved.

Case display

The following demonstrates the disclosed aspects by specific examples.

In this case, a quantum state of a single qubit is selected as a first quantum state ρ, where the first quantum state ρ is a mixed state and the predetermined order α =2. By operating the scheme disclosed by the invention, the estimation value of the Rayleigh entropy of the 2 th order of the first quantum state rho is obtained. Specifically, the matrix expression of the first quantum state ρ is:

a target quantum circuit shown in fig. 4 (c) was used, and L =50 was set. At this time, the objective of the experiment is to estimate the rayleigh entropy of order 2 corresponding to the first quantum state ρ.

Here, the error between the estimated rayleigh entropy of the 2 nd order 0.34272675 corresponding to the first quantum state ρ obtained by numerical simulation based on the scheme of the present disclosure and the actual value 0.38566248 is very small.

In conclusion, the scheme disclosed by the invention can adapt to recent quantum computers and has the following characteristics:

first, the scheme of the present disclosure can solve to obtain the estimated value of the rayleigh entropy of the quantum state by using only one auxiliary qubit.

Second, the disclosed scheme can control unitary operators using a single ancillary qubit, thus reducing the required quantum computing resources while enhancing the feasibility of medium-scale quantum computing device implementations. Moreover, since the disclosed solution relies on the minimum non-zero eigenvalue but non-scale of the quantum state, the requirements on the target quantum circuit are lower and more practical on a medium-scale quantum computing device.

Thirdly, the scheme disclosed by the invention is suitable for any scenes of the unitary operator and the controlled quantum gate thereof which can be effectively prepared, and alpha is not required to be limited to be a positive integer, so that the application range is wider, the application scenes are rich, and the universality is stronger.

Fourthly, the scheme disclosed by the invention has practicability, high efficiency, certainty, expansibility and innovativeness; in particular, utility means that the disclosed scheme can be implemented on a near-term quantum computer, without the need for quantum fourier transforms; high efficiency means that the disclosed scheme can construct quantum circuits with low consumption, and output estimated values with low consumption; the certainty means that the scheme of the present disclosure can obtain an estimated value satisfying the precision requirement with a very high probability; scalability means that the disclosed scheme is applicable to large-scale quantum states (here, since the disclosed scheme mainly relies on the minimum non-zero eigenvalue of the first quantum state rather than the scale of the first quantum state, the disclosed scheme is more suitable for large-scale quantum states, has wider applicability, and is more scalable); innovativeness means that the disclosed scheme provides a novel quantum circuit to achieve quantum entropy estimation.

The present disclosure also provides a quantum entropy determination apparatus, as shown in fig. 7, including:

a parameter processing unit 701, configured to determine a target parameter value of a target adjustable parameter in a sub-circuit of a target quantum circuit; wherein the target parameter value satisfies a first error condition; the target quantum circuit comprises an auxiliary register and a main register, and the sub-circuit acts on the auxiliary register; the target quantum circuit also comprises a target controlled unitary gate which is controlled by the auxiliary register and acts on the main register, the target controlled unitary gate is used for estimating Rayleigh entropy corresponding to a first quantum state, and the Rayleigh entropy is used for measuring the chaos degree of a total subsystem corresponding to the first quantum state; the target controlled unitary gate comprises a first controlled unitary gate equivalent to unitary operator U and a transpose to the unitary operator U

a measuring unit 702, configured to obtain state information of the auxiliary register in the target quantum circuit when the target adjustable parameter is the target parameter value, the first input state of the auxiliary register is a preset initial state, and the second input state of the main register at least includes the first quantum state; and

an output unit 703 is configured to estimate, based on the state information of the auxiliary register, a rayleigh entropy corresponding to the first quantum state under the first error condition.

In a specific example of the present disclosure, the parameter processing unit 701 is specifically configured to:

taking the target parameter value of the target adjustable parameter in the trained preset parameterized quantum circuit as the target parameter value of the target adjustable parameter in the sub-circuit; the trained preset parameterized quantum circuit is used for simulating an objective function y (x);

wherein the objective function y (x) satisfies the following requirements:

under the condition that the preset order alpha is a rational number larger than 1, the objective function y (x) is used for representing the incidence relation between the preset order alpha and the independent variable x;

under the condition that the preset order alpha is a rational number which is larger than 0 and smaller than 1, the objective function y (x) is used for representing the association relationship among the preset order alpha, the preset threshold gamma and the independent variable x; or, under the condition that a preset order α is a rational number greater than 0 and less than 1, the objective function y (x) is used for representing an association relationship among the preset order α, a normalization coefficient c and an argument x, where the normalization coefficient c is related to the preset threshold γ, and the preset threshold γ is a constant less than a non-zero eigenvalue corresponding to the first quantum state;

wherein, the target quantum circuit is obtained by the following method:

taking quantum bits in the preset parameterized quantum circuit as an auxiliary register, expanding a main register, replacing a first target revolving gate acting on the auxiliary register in the preset parameterized quantum circuit with the first controlled unitary gate, and replacing a second target revolving gate acting on the auxiliary register in the preset parameterized quantum circuit with the second controlled unitary gate;

wherein the first rotation parameter of the first target revolving door and the second rotation parameter of the second target revolving door are both independent variables x of the objective function y (x); the sub-circuit comprises at least part of the circuit except the first target revolving gate and the second target revolving gate in the preset parameterized quantum circuit.

In a specific example of the present disclosure, the parameter processing unit 701 is further configured to:

taking the value of the rotation parameter x of the preset parameterized quantum circuit as any data point x in the N data points _j Under the condition of (3), acquiring an actual output result y of the preset parameterized quantum circuit _j (ii) a The actual output result y _j Outputting a result of the preset parameterized quantum circuit for the target adjustable parameter in the preset parameterized quantum circuit under a current parameter value; n is a positive integer greater than or equal to 1, and j is a positive integer greater than or equal to 1 and less than or equal to N; the rotation parameter x comprises the first rotation parameter and the second rotation parameter;

obtaining N actual output results y _j ；

Under the condition that the iteration termination condition is determined to be met, taking the current parameter value of the target adjustable parameter as the target parameter value of the target adjustable parameter in the preset parameterized quantum circuit after training is finished;

wherein the iteration termination condition comprises at least one of:

based on the N actual output results y _j And N target output results

Wherein, in the case that the preset order alpha is a rational number larger than 1, the y (x) _j ) Is based on a predetermined order α and an independent variable x _j Obtaining; in the case that the preset order alpha is a rational number which is greater than 0 and less than 1, y (x) _j ) Is based on a predetermined order alpha, a predetermined threshold gamma and an independent variable x _j Obtaining; or, in the case that the preset order alpha is a rational number greater than 0 and less than 1, the y (x) _j ) Based on a predetermined order alpha, a normalization coefficient c and an independent variable x _j Obtaining;

and the current iteration times reach the preset times.

under the condition that the iteration termination condition is determined not to be met, adjusting the parameter value of the target adjustable parameter;

re-dereferencing the rotation parameter x of the preset parameterized quantum circuit to be any data point x in the N data points _j Under the condition of (3), acquiring an actual output result y of the preset parameterized quantum circuit _j ；

N actual output results y are obtained again _j Until the iteration termination condition is satisfied.

In a specific example of the present disclosure, the preset parameterized quantum circuit includes L training layers; l is an even number greater than or equal to 2, and the value of L is related to the first error condition;

at least two of the L training layers comprise:

the target revolving door is used for carrying out a revolving operation on a first angle by the revolving parameter x; the first target revolving door and the second target revolving door are target revolving doors in different training levels;

the rotation angle phi of the first revolving door and the rotation angle theta of the second revolving door are the target adjustable parameters;

or,

at least two of the L training layers include:

In a specific example of the disclosed approach, at least one of the following is also satisfied:

the first angle is an angle corresponding to the z axis;

the second angle is an angle corresponding to the z axis;

the third angle is an angle corresponding to the y-axis.

In a specific example of the present disclosure, when any one of the L training layers includes the target revolving door, the first revolving door, and the second revolving door, an action sequence of each revolving door is as follows:

the first revolving door, the second revolving door and the target revolving door;

or,

under the condition that any training layer of the L training layers comprises the target revolving door and the second revolving door, the action sequence of each revolving door is as follows: a second revolving door and a target revolving door.

In a specific example of the present disclosure, after the L training layers of the preset parameterized quantum circuit, another revolving gate is further included.

at least one of the M layers is based on:

replacing a first controlled unitary gate by a first target revolving gate of a first training layer in the two training layers, and replacing a second controlled unitary gate by a second target revolving gate of a second training layer in the two training layers; wherein the two training layers are any two of the L training layers.

In a specific example of the present disclosure, the two training layers are any two adjacent training layers of the L training layers.

In a specific example of the disclosed solution, in a case where the unitary operator U is obtained based on the first quantum system, an equivalent circuit of the first controlled unitary gate in the target quantum circuit is the unitary operator U = e ^iρ And the equivalent circuit of the second controlled unitary gate in the target quantum circuit is the conjugate transpose of the unitary operator U

An equivalent circuit of (1); wherein the ρ represents the first quantum state;

or,

in a case that the unitary operator U is obtained based on a total quantum system corresponding to the first quantum system, an equivalent circuit of the first controlled unitary gate in the target quantum circuit is an equivalent circuit of the unitary operator U = RE, and an equivalent circuit of the second controlled unitary gate in the target quantum circuit is a conjugate transpose of the unitary operator U

An equivalent circuit of (1); wherein E represents a block encoding of the first quantum state; the R represents a reflection operator constructed based on the total amount subsystem.

For a description of specific functions and examples of each unit of the apparatus in the embodiment of the present disclosure, reference may be made to the related description of the corresponding steps in the foregoing method embodiments, and details are not repeated here.

The present disclosure also provides a non-transitory computer readable storage medium having stored thereon computer instructions that, when executed by at least one quantum processing unit, cause the at least one quantum processing unit to perform the method of the above application quantum computing device.

The present disclosure also provides a computer program product comprising a computer program which, when executed by at least one quantum processing unit, implements the method as applied to a quantum computing device.

The present disclosure also provides a computing device, including:

at least one quantum processing unit;

the instructions are executable by the at least one quantum processing unit to enable the at least one quantum processing unit to perform the method as applied to a quantum computing device.

It is to be understood that a Quantum Processing Unit (QPU), also referred to as a quantum processor or quantum chip, used in the aspects of the present disclosure may refer to a physical chip comprising a plurality of qubits interconnected in a specific manner.

Moreover, it is understood that a qubit in accordance with aspects of the present disclosure may refer to a fundamental unit of information of a quantum computing device. Qubits are contained in QPUs and generalize the concept of classical digital bits.

Further, according to an embodiment of the present disclosure, the present disclosure also provides a computing device, a readable storage medium, and a computer program product.

FIG. 8 illustrates a schematic block diagram of an example computing device 800 that may be used to implement embodiments of the present disclosure. Computing devices are intended to represent various forms of digital computers, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. The computing device may also represent various forms of mobile devices, such as personal digital assistants, cellular telephones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions, are meant to be examples only, and are not meant to limit implementations of the disclosure described and/or claimed herein.

As shown in fig. 8, the apparatus 800 includes a computing unit 801 that can perform various appropriate actions and processes according to a computer program stored in a Read Only Memory (ROM) 802 or a computer program loaded from a storage unit 808 into a Random Access Memory (RAM) 803. In the RAM803, various programs and data necessary for the operation of the device 800 can also be stored. The calculation unit 801, the ROM802, and the RAM803 are connected to each other by a bus 804. An input/output (I/O) interface 805 is also connected to bus 804.

A number of components in the device 800 are connected to the I/O interface 805, including: an input unit 806 such as a keyboard, a mouse, or the like; an output unit 807 such as various types of displays, speakers, and the like; a storage unit 808, such as a magnetic disk, optical disk, or the like; and a communication unit 809 such as a network card, modem, wireless communication transceiver, etc. The communication unit 809 allows the device 800 to exchange information/data with other devices via a computer network such as the internet and/or various telecommunication networks.

Computing unit 801 may be a variety of general and/or special purpose processing components with processing and computing capabilities. Some examples of the computing unit 801 include, but are not limited to, a Central Processing Unit (CPU), a Graphics Processing Unit (GPU), various dedicated Artificial Intelligence (AI) computing chips, various computing units running machine learning model algorithms, a Digital Signal Processor (DSP), and any suitable processor, controller, microcontroller, and the like. The calculation unit 801 executes the respective methods and processes described above, such as the quantum entropy determination method. For example, in some embodiments, the quantum entropy determination method may be implemented as a computer software program tangibly embodied in a machine-readable medium, such as storage unit 808. In some embodiments, part or all of a computer program may be loaded onto and/or installed onto device 800 via ROM802 and/or communications unit 809. When a computer program is loaded into RAM803 and executed by computing unit 801, one or more steps of the quantum entropy determination method described above may be performed. Alternatively, in other embodiments, the computing unit 801 may be configured to perform the quantum entropy determination method in any other suitable manner (e.g., by way of firmware).

Various implementations of the systems and techniques described here above may be implemented in digital electronic circuitry, integrated circuitry, field Programmable Gate Arrays (FPGAs), application Specific Integrated Circuits (ASICs), application Specific Standard Products (ASSPs), system on a chip (SOCs), complex Programmable Logic Devices (CPLDs), computer hardware, firmware, software, and/or combinations thereof. These various embodiments may include: implemented in one or more computer programs that are executable and/or interpretable on a programmable system including at least one programmable processor, which may be special or general purpose, receiving data and instructions from, and transmitting data and instructions to, a storage system, at least one input device, and at least one output device.

Program code for implementing the methods of the present disclosure may be written in any combination of one or more programming languages. These program codes may be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus, such that the program codes, when executed by the processor or controller, cause the functions/operations specified in the flowchart and/or block diagram to be performed. The program code may execute entirely on the machine, partly on the machine, as a stand-alone software package partly on the machine and partly on a remote machine or entirely on the remote machine or server.

In the context of this disclosure, a machine-readable medium may be a tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. The machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

To provide for interaction with a user, the systems and techniques described here can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to a user; and a keyboard and a pointing device (e.g., a mouse or a trackball) by which a user may provide input to the computer. Other kinds of devices may also be used to provide for interaction with a user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form, including acoustic, speech, or tactile input.

The systems and techniques described here can be implemented in a computing system that includes a back-end component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front-end component (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with an implementation of the systems and techniques described here), or any combination of such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: local Area Networks (LANs), wide Area Networks (WANs), and the Internet.

The computer system may include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. The server may be a cloud server, a server of a distributed system, or a server with a combined blockchain.

It should be understood that various forms of the flows shown above may be used, with steps reordered, added, or deleted. For example, the steps described in the present disclosure may be executed in parallel, sequentially or in different orders, and are not limited herein as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved.

The above detailed description should not be construed as limiting the scope of the disclosure. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions may be made in accordance with design requirements and other factors. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present disclosure should be included in the scope of protection of the present disclosure.

Claims

1. A quantum entropy determination method, comprising:

determining a target parameter value of a target adjustable parameter in a sub-circuit of a target quantum circuit; wherein the target parameter value satisfies a first error condition; the target quantum circuit comprises an auxiliary register and a main register, and the sub-circuit acts on the auxiliary register; the target quantum circuit also comprises a target controlled unitary gate which is controlled by the auxiliary register and acts on the main register, the target controlled unitary gate is used for estimating Rayleigh entropy corresponding to a first quantum state, and the Rayleigh entropy is used for measuring the chaos degree of a total subsystem corresponding to the first quantum state; the target controlled unitary gate comprises a first controlled unitary gate equivalent to a unitary operator U and a transpose of the unitary operator U

2. The method of claim 1, wherein the rayleigh entropy associated with the first quantum state is: and alpha-order Rayleigh entropy corresponding to the first quantum state, wherein alpha is a preset order.

3. The method of claim 1, wherein the determining a target parameter value for a target adjustable parameter in a sub-circuit of a target quantum circuit comprises:

wherein the objective function y (x) satisfies the following requirements:

wherein the target quantum circuit is obtained by:

taking a quantum bit in the preset parameterized quantum circuit as an auxiliary register, expanding a main register, replacing a first target revolving gate acting on the auxiliary register in the preset parameterized quantum circuit with the first controlled unitary gate, and replacing a second target revolving gate acting on the auxiliary register in the preset parameterized quantum circuit with the second controlled unitary gate;

wherein the first rotation parameter of the first target revolving door and the second rotation parameter of the second target revolving door are both independent variables x of the objective function y (x); the sub-circuit comprises at least part of the circuit except the first target rotating gate and the second target rotating gate in the preset parameterized quantum circuit.

4. The method of claim 3, further comprising:

obtaining N actual output results y _j ；

Under the condition that the iteration termination condition is determined to be met, taking the current parameter value of the target adjustable parameter as the target parameter value of the target adjustable parameter in the preset parameterized quantum circuit after training is completed;

wherein the iteration termination condition comprises at least one of:

based on the N actual output results y _j And N target output results

Wherein, in the case that the preset order alpha is a rational number larger than 1, the y (x) _j ) Is based on a predetermined order alpha and an independent variable x _j Obtaining; in the case that the preset order alpha is a rational number which is more than 0 and less than 1, y (x) _j ) Is based on a predetermined order alpha, a predetermined threshold gamma and an independent variable x _j Obtaining; or in the case of presetting a rational number with the order alpha being more than 0 and less than 1, y (x) _j ) Based on a predetermined order alpha, a normalization coefficient c and an independent variable x _j Obtaining;

and the current iteration times reach the preset times.

5. The method of claim 4, further comprising:

adjusting the parameter value of the target adjustable parameter under the condition that the iteration termination condition is determined not to be met;

6. The method of any of claims 3-5, wherein the pre-set parameterized quantum circuit comprises L training layers; l is an even number greater than or equal to 2, and the value of L is related to the first error condition;

at least two of the L training layers include:

or,

at least two of the L training layers include:

7. The method of claim 6, wherein at least one of:

the first angle is an angle corresponding to the z axis;

the second angle is an angle corresponding to the z axis;

the third angle is an angle corresponding to the y-axis.

8. The method of claim 6, wherein,

under the condition that any training layer of the L training layers comprises the target revolving door, the first revolving door and the second revolving door, the action sequence of each revolving door is as follows:

or,

9. The method of claim 6, wherein the L training layers of the pre-set parameterized quantum circuit are followed by additional turning gates.

10. The method of claim 6, wherein the target quantum circuit comprises M layers, wherein M is a positive integer greater than or equal to 1 and less than or equal to L/2;

at least one of the M layers is based on:

replacing a first controlled unitary gate by a first target revolving gate of a first training layer in the two training layers, and replacing a second controlled unitary gate by a second target revolving gate of a second training layer in the two training layers; wherein the two training layers are any two training layers of the L training layers.

11. The method of claim 10, wherein the two training layers are any adjacent two of the L training layers.

12. The method of claim 10, wherein,

The equivalent circuit of (a); wherein the ρ represents the first quantum state;

or,

under the condition that the unitary operator U is obtained based on the total subsystem corresponding to the first quantum system, the equivalent circuit of the first controlled unitary gate in the target quantum circuit is the equivalent circuit of the unitary operator U = RE, and the target quantum circuitThe equivalent circuit of the second controlled unitary gate in the scalar subcircuit is the conjugate transpose of the unitary operator U

13. A quantum entropy determination device, comprising:

14. The apparatus of claim 13, wherein the rayleigh entropy associated with the first quantum state is: and the alpha-order Rayleigh entropy corresponding to the first quantum state, wherein alpha is a preset order.

15. The apparatus according to claim 13, wherein the parameter processing unit is specifically configured to:

wherein the objective function y (x) satisfies the following requirements:

wherein, the target quantum circuit is obtained by the following method:

16. The apparatus of claim 15, wherein the parameter processing unit is further configured to:

obtaining N actual output results y _j ；

wherein the iteration termination condition comprises at least one of:

based on the N actual output results y _j And N target output results

Wherein y (x) is a rational number with a preset order alpha larger than 1 _j ) Is based on a predetermined order alpha and an independent variable x _j Obtaining; in advance ofWhen the order alpha is a rational number larger than 0 and smaller than 1, the y (x) _j ) Based on a predetermined order α, a predetermined threshold γ and an argument x _j Obtaining; or, in the case that the preset order alpha is a rational number greater than 0 and less than 1, the y (x) _j ) Based on a predetermined order alpha, a normalization coefficient c and an independent variable x _j Obtaining;

and the current iteration times reach the preset times.

17. The apparatus of claim 16, wherein the parameter processing unit is further configured to:

18. The apparatus of any one of claims 15-17, wherein the pre-defined parameterized quantum circuit includes L training layers; l is an even number greater than or equal to 2, and the value of L is related to the first error condition;

at least two of the L training layers include:

or,

at least two of the L training layers comprise:

the second rotating gate is used for rotating the third angle and acts on the quantum bit in the preset parameterized quantum circuit;

19. The apparatus of claim 18, wherein at least one of:

the first angle is an angle corresponding to the z axis;

the second angle is an angle corresponding to the z axis;

the third angle is an angle corresponding to the y axis.

20. The apparatus of claim 18, wherein,

when any one of the L training layers includes the target revolving door, the first revolving door, and the second revolving door, the order of actions of the revolving doors is as follows:

or,

21. The apparatus of claim 18, wherein the L training layers of the pre-set parameterized quantum circuit are followed by additional turning gates.

22. The device of claim 18, wherein the target quantum circuit comprises M layers, wherein M is a positive integer greater than or equal to 1 and less than or equal to L/2;

at least one of the M layers is based on:

23. The apparatus of claim 22, wherein the two training layers are any two adjacent training layers of the L training layers.

24. The apparatus of claim 22, wherein,

or,

The equivalent circuit of (a); wherein E represents a block encoding of the first quantum state; the R represents a reflection operator constructed based on the total amount subsystem.

25. A computing device, comprising:

at least one quantum processing unit;

the instructions are executable by the at least one quantum processing unit to enable the at least one quantum processing unit to perform the method of any one of claims 1-12;

alternatively, it comprises:

at least one processor; and

a memory communicatively coupled to the at least one processor; wherein,

the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-12.

26. A non-transitory computer readable storage medium storing computer instructions that, when executed by at least one quantum processing unit, cause the at least one quantum processing unit to perform the method of any one of claims 1-12;

alternatively, the computer instructions are for causing the computer to perform the method of any of claims 1-12.

27. A computer program product comprising a computer program which, when executed by at least one quantum processing unit, implements the method according to any one of claims 1-12;

or which computer program, when being executed by a processor, carries out the method according to any one of the claims 1-12.