CN116346334B

CN116346334B - Distillable key estimation method, apparatus, device and storage medium

Info

Publication number: CN116346334B
Application number: CN202310275119.9A
Authority: CN
Inventors: 刘耕; 王鑫
Original assignee: Beijing Baidu Netcom Science and Technology Co Ltd
Current assignee: Beijing Baidu Netcom Science and Technology Co Ltd
Priority date: 2023-03-20
Filing date: 2023-03-20
Publication date: 2024-02-02
Anticipated expiration: 2043-03-20
Also published as: CN116346334A

Abstract

The disclosure provides a method, a device, equipment and a storage medium for estimating a distilled key, relates to the technical field of computers, and particularly relates to the field of quantum computing. The specific implementation scheme is as follows: obtaining the target quantum state rho ^AB The method comprises the steps of carrying out a first treatment on the surface of the Based on the target quantum state ρ ^AB Generating quantum pure state rho ^ABEE' The method comprises the steps of carrying out a first treatment on the surface of the E represents an extended quantum system comprising m qubits, E' represents an auxiliary quantum system comprising (m+n) qubits; -incorporating said quantum pure state ρ ^ABEE' Acting on a target parameterized quantum circuit to obtain an output quantum state sigma of a total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system E in the target parameterized quantum circuit ^ABE (θ); using the output quantum state sigma ^ABE (θ) to obtain the target quantum state ρ ^AB Is an estimate of the compression entanglement of the target quantum state ρ ^AB Is used to estimate the target quantum state ρ ^AB Is provided.

Description

Distillable key estimation method, apparatus, device and storage medium

Technical Field

The present disclosure relates to the field of computer technology, and in particular, to the field of quantum computing technology.

Background

In practical applications, quantum keys may be subject to errors due to noise or eavesdroppers. Thus, some additional operations are required to ensure that the quantum key can be securely obtained. At this point, the act of obtaining a secure quantum key from the error condition, through only the trusted classical communication channel (authentic classical communication channel), is called key distillation (secret key distillation). However, currently, the calculation of distillable keys for one quantum state is extremely difficult.

Disclosure of Invention

The present disclosure provides an estimation method, apparatus, device and storage medium for distillable keys.

According to an aspect of the present disclosure, there is provided a method of estimating a distillable key, including:

obtaining the target quantum state rho ^AB The method comprises the steps of carrying out a first treatment on the surface of the Wherein the target quantum state ρ ^AB Representing an object comprising n qubitsLabeling entangled state of subsystem AB; the target quantum system AB is a double quantum system consisting of a first quantum system A and a second quantum system B;

based on the target quantum state ρ ^AB Generating quantum pure state rho ^ABEE’ The method comprises the steps of carrying out a first treatment on the surface of the Wherein E represents an extended quantum system comprising m quantum bits for extending the target quantum system AB, and E' represents a pure state ρ comprising (m+n) quantum bits for auxiliary preparation of quantum ^ABEE’ Auxiliary quantum systems of (a); n is a positive integer greater than or equal to 2, and m is a positive integer greater than or equal to 1;

-incorporating said quantum pure state ρ ^ABEE’ Acting on a target parameterized quantum circuit to obtain an output quantum state sigma of a total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system E in the target parameterized quantum circuit ^ABE (θ); wherein the target parameterized quantum circuit comprises 2 (n+m) quantum bits, and θ represents an adjustable parameter vector of the target parameterized quantum circuit;

using the output quantum state sigma ^ABE (θ) to obtain the target quantum state ρ ^AB Wherein the target quantum state ρ is ^AB Is used to estimate the target quantum state ρ ^AB Is provided.

According to another aspect of the present disclosure, there is provided an apparatus for estimating a distillable key, comprising:

an acquisition unit for obtaining the target quantum state ρ ^AB The method comprises the steps of carrying out a first treatment on the surface of the Wherein the target quantum state ρ ^AB Representing an entangled state of a target quantum system AB comprising n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A and a second quantum system B;

a processing unit for based on the target quantum state ρ ^AB Generating quantum pure state rho ^ABEE' The method comprises the steps of carrying out a first treatment on the surface of the Wherein E represents an extended quantum system for extending the target quantum system AB, which contains m quantum bits, and E' represents an auxiliary preparation amount, which contains (m+n) quantum bitsSub-pure state ρ ^ABEE’ Auxiliary quantum systems of (a); n is a positive integer greater than or equal to 2, and m is a positive integer greater than or equal to 1; -incorporating said quantum pure state ρ ^ABEE’ Acting on a target parameterized quantum circuit to obtain an output quantum state sigma of a total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system e in the target parameterized quantum circuit ^ABE (θ); wherein the target parameterized quantum circuit comprises 2 (n+m) quantum bits, and θ represents an adjustable parameter vector of the target parameterized quantum circuit; using the output quantum state sigma ^ABE (θ) to obtain the target quantum state ρ ^AB Wherein the target quantum state ρ is ^AB Is used to estimate the target quantum state ρ ^AB Is provided.

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

at least one quantum processing unit QPU;

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

The instructions are executed by the at least one QPU to enable the at least one QPU to perform the method described above;

alternatively, it includes:

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 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 described above;

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

According to a further 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 executed by a processor implements the method described above.

In this way, the scheme of the disclosure utilizes the extended quantum system E of the target quantum system AB to estimate and obtain the target quantum state ρ ^AB For estimating the target quantum state ρ ^AB The scheme utilizes less computing resources to finish the target quantum state rho ^AB The compression entanglement estimation of the method has high efficiency, and the scheme disclosed by the invention has lower calculation complexity and is easy to implement.

It should be understood that the description in this section is not intended to identify key or critical features of the embodiments of the disclosure, nor is it intended to be used to limit the scope of the disclosure. Other features of the present disclosure will become apparent from the following specification.

Drawings

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

FIG. 1 is a schematic diagram of an implementation flow of a method of estimating a distillable key according to an embodiment of the present disclosure;

FIGS. 2 (a) through 2 (c) are schematic structural diagrams of a target parametric quantum circuit in a specific example according to an embodiment of the present disclosure;

FIG. 2 (d) is a schematic diagram of the structure of a pre-set parameterized quantum circuit in a specific example according to an embodiment of the present disclosure;

FIG. 3 is a flow diagram of an implementation of a method of distillable key estimation in a particular embodiment in accordance with an embodiment of the present disclosure;

FIG. 4 is a schematic diagram of a construction of a distillable key estimation apparatus according to a disclosed embodiment;

fig. 5 is a block diagram of a computing device used to implement a method of distillable key estimation of an embodiment of the present disclosure.

Detailed Description

Exemplary embodiments of the present disclosure are described below in conjunction with the accompanying drawings, which include various details of the embodiments of the present disclosure to facilitate understanding, and should be considered as merely exemplary. Accordingly, one 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 of the present disclosure. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.

The term "and/or" is herein merely an association relationship describing an associated object, meaning that there may be three relationships, e.g., a and/or B, may represent: a exists alone, A and B exist together, and B exists alone. The term "at least one" herein means any one of a plurality or any combination of at least two of a plurality, e.g., including at least one of A, B, C, may mean including any one or more elements selected from the group consisting of A, B and C. The terms "first" and "second" herein mean a plurality of similar technical terms and distinguishes them, and does not limit the meaning of the order, or only two, for example, a first feature and a second feature, which means that there are two types/classes of features, the first feature may be one or more, and the second feature may be one or more.

In addition, numerous specific details are set forth in the following detailed description in order to provide a better understanding of the present disclosure. It will be appreciated by one 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 well known to those skilled in the art have not been described in detail in order not to obscure the present disclosure.

The recent development of the quantum computing field is rapid, and the quantum computing field from quantum algorithm and quantum hardware equipment to quantum soft and hard integrated platform is advancing towards large-scale and practical stable steps. More and more quantum technologies are continuously emerging, the technology of quantum hardware is also improved year by year, and quantum communication and quantum internet are also continuously developed.

One of the most important resources in quantum technology is quantum entanglement (Quantum entanglement), which is a basic component of quantum computing and quantum information processing, and plays a vital role in the scenes of quantum security communication, distributed quantum computing and the like. For example, for information transmission existing in aspects of social production and life, researchers are studying how to handle information security tasks using quantum technology, wherein one important resource used is quantum entanglement.

Quantum entanglement is a phenomenon peculiar to quantum mechanics, and when several particles interact with each other, since the characteristics possessed by each particle are integrated into an integral property, the respective properties cannot be described alone, and only the properties of the entire system (which may be referred to as a quantum system) formed by the several particles can be described, and this phenomenon is called quantum entanglement. Among them, the quantum state of the quantum system having quantum entanglement characteristics may be referred to as a quantum entanglement state.

Based on quantum entanglement, one important application is quantum cryptography communication and quantum key distribution. In classical cryptography, a key (secret key) refers to a string of bits of the same length as the information to be encrypted. Encryption of the information can be achieved by adding the information to be encrypted to the key; in quantum cryptography, similar keys and encryption processes are also owned.

Quantum key (quantum secret key) in quantum cryptography is based on quantum mechanical mechanisms with quantum bits as keys. Specifically, by utilizing the uncertainty principle of quantum mechanics, an eavesdropper cannot accurately obtain the quantum key under the condition of not interfering the system, so that the safety of the quantum key is ensured.

In practical applications, quantum keys may be subject to errors due to noise or eavesdroppers. Thus, some additional operations are required to ensure that the quantum key can be securely obtained. At this point, the act of obtaining a secure quantum key from the error condition, through only the trusted classical communication channel (authentic classical communication channel), is called key distillation (secret key distillation).

Specifically, the density matrix ρ of the target quantum states (i.e., target quantum entangled states, all abbreviated as target quantum states in the present disclosure) is given ^AB In the case of (a), the distillable key K _D (ρ ^AB ) Specifically, the following formula can be used to give:

here, the target quantum state represents a quantum state corresponding to a dual system (i.e., the target quantum system AB) formed by the first quantum system a (may also be simply referred to as a system a) and the second quantum system B (may also be simply referred to as a system B), and may be used in the density matrix ρ ^AB Representation, i.e., the present disclosure scheme may be embodied as a target quantum state ρ ^AB . The Λ represents a local quantum operation and common classical communication protocol (Local Operations and Public Communication, LOPC), the δ represents the trace distance; the said Representing n target quantum states ρ ^AB Quantum states consisting of tensor products of (2); said->A proprietary CCQ (classification-Quantum) of length m may be expressed in the following specific expression:

here, E represents an extended quantum system containing m qubits.

As can be seen from the above, the key K can be distilled _D (ρ ^AB ) Mainly quantifying a given target quantum state ρ ^AB In the limit, distilled quantum keys.

In practical situations, the calculation of a distillable key in a quantum state is extremely difficult, because of the difficulty of optimizing a limit case scheme, so how to efficiently estimate the distillable key is of great significance for quantum encryption and communication.

Based on the above, the scheme of the disclosure provides a method for estimating a quantum distillable key, so as to estimate the quantum distillable key efficiently and accurately. It should be noted that the reasons for the proposal of the present disclosure and the importance thereof are represented in the following three aspects:

first, quantum key distribution is one of the most important applications of quantum cryptography, and based on the characteristics of quantum mechanics, the effect that classical cryptography cannot reach can be achieved.

The distillable key of the second, quantum state characterizes the maximum ratio by which a quantum state can be used to generate a secure quantum key, and estimating this value can know how much secure quantum key the quantum state can generate in different scenarios.

Third, computing distillable keys for quantum states is a difficult task, requiring estimation of distillable keys for quantum states by compression entanglement. However, direct computation of compression entanglement remains a difficult problem, and therefore, it is desirable to find an efficient method to estimate compression entanglement.

Specifically, fig. 1 is a schematic diagram of an implementation flow of a method for estimating a distillable key according to an embodiment of the present disclosure; the method is optionally applied to a quantum computing device with classical computing capability, and also can be applied to a classical computing device with classical computing capability, or directly applied to an electronic device with classical computing capability, such as a personal computer, a server cluster, and the like, or directly applied to a quantum computer, and the scheme of the disclosure is not limited to this.

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

step S101: obtaining the target quantum state rho ^AB 。

Here, the target quantum state ρ ^AB Representing an entangled state of a target quantum system AB comprising n qubits; the target quantum system ABIs a double quantum system composed of a first quantum system A and a second quantum system B.

Step S102: based on the target quantum state ρ ^AB Generating quantum pure state rho ^ABEE’ 。

Here, E represents an extended quantum system for extending the target quantum system AB, which includes m qubits, and E' represents a quantum pure state σ for assisting in preparation of quantum pure state σ, which includes (m+n) qubits ^ABEE’ Auxiliary quantum systems of (a); and n is a positive integer greater than or equal to 2, and m is a positive integer greater than or equal to 1.

Step S103: -incorporating said quantum pure state ρ ^ABEE’ Acting on a target parameterized quantum circuit to obtain an output quantum state sigma of a total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system E in the target parameterized quantum circuit ^ABE (θ)。

Here, the target parametric quantum circuit includes 2 (n+m) quantum bits, θ represents an adjustable parameter vector of the target parametric quantum circuit.

Here, n continuous qubits in the target parameterized quantum circuit correspond to the target quantum system AB; the target parameterized quantum circuit is provided with continuous m quantum bits except for continuous n quantum bits, and corresponds to the extended quantum system E; the target parameterized quantum circuit is provided with the rest m+n qubits except for the n continuous qubits and the m continuous qubits, and corresponds to an auxiliary quantum system E'.

Step S104: using the output quantum state sigma ^ABE (θ) to obtain the target quantum state ρ ^AB Is used to compress entangled estimates.

Here, the target quantum state ρ ^AB Is used to estimate the target quantum state ρ ^AB Is provided.

In a specific example of the disclosed scheme, the target quantum state ρ ^AB Is the target quantum state ρ ^AB Is the upper bound of distillable keys. In other words, the method and the device for obtaining the estimated value of the compression entanglement of the target quantum state help to obtain the distillable key of the target quantum state in an estimated manner, and are low in computational complexity and easy to implement.

In a specific example of the disclosed scheme, the target quantum state ρ may be obtained as follows ^AB Is a compressed entangled estimate of (1); specifically, the above uses the output quantum state σ ^ABE (θ) to obtain the target quantum state ρ ^AB Specifically, the compression entanglement estimation value of (1) includes:

obtaining sigma based on output quantum state ^ABE An objective function value of the objective loss function C (θ) constructed by (θ);

based on the objective function value, the objective quantum state rho is obtained ^AB Is used to compress entangled estimates.

That is, the disclosed scheme is capable of utilizing the output quantum state σ ^ABE The objective function value of the objective loss function C (theta) is obtained by constructing the objective loss function C (theta), and the objective quantum state ρ can be obtained by using the objective function value ^AB In this way, the target quantum state ρ can be obtained rapidly by classical optimization ^AB Is used to compress entangled estimates.

In a specific example of the disclosed approach, the target loss function may be constructed in such a way that, in particular, the target loss function C (θ) is based on the output quantum state σ ^ABE And (θ) conditional mutual information I (A; b|E).

Thus, a concrete scheme for constructing the target loss function is provided, and the scheme has strong interpretationIn addition, the computational complexity can be greatly reduced, and the target quantum state rho can be rapidly obtained ^AB Is used to compress entangled estimates.

For example, in one example, the output quantum state σ may be directly outputted ^ABE The conditional mutual information I (A; b|E) of (θ) is taken as the target loss function C (θ), and the specific expression of the target loss function C (θ) is as follows:

C(θ)＝I(A；B|E)＝S(AE)+S(BE)-S(ABE)-S(E)；

here, the S (AE) =s (σ ^AE )＝-Tr[σ ^AE log ₂ σ ^AE ]Representing the output quantum state sigma on two quantum systems AE composed of a first quantum system A and an extended quantum system E ^AE Von neumann entropy of (c); s (BE) =s (σ ^BE )＝-Tr[σ ^BE log ₂ σ ^BE ]Representing the output quantum state sigma on a two-quantum system BE consisting of a second quantum system B and an extended quantum system E ^BE Von neumann entropy of (c); the S (ABE) =s (σ ^ABE )＝-Tr[σ ^ABE log ₂ σ ^ABE ]Representing the output quantum state sigma on the total extended quantum system ABE composed of the target quantum system AB and the extended quantum system E ^ABE Von neumann entropy of (c); the S (E) =s (σ ^E )＝-Tr[σ ^E log ₂ σ ^E ]Representing the output quantum state sigma on an extended quantum system E ^E Von neumann entropy of (c); the Tr is a trace operator. At this time, half of the objective function value of the objective loss function C (θ) is the objective quantum state ρ ^AB Is used to compress entangled estimates.

Further, in another example, σ may be based on the output quantum state ^ABE The conditional mutual information I (A; b|E) of (theta) obtains the target loss function C (theta), and the specific expression of the target loss function C (theta) is as follows:

C(θ)＝αI(A；B|E)＝α(S(AE)+S(BE)-S(ABE)-S(E))；

Wherein α is a constant greater than 0 and less than 1.

Further, for example, the quantum state σ will be output ^ABE Half of the conditional mutual information I (A; b|E) (i.e) As the target loss function C (θ), at this time, the target loss function C (θ) has a specific expression of:

the meaning of each sub-item may refer to the above description, and will not be repeated here. At this time, the objective function value of the objective loss function C (θ) is the objective quantum state ρ ^AB Is used to compress entangled estimates.

In a specific example of the disclosed scheme, the objective function value of the objective loss function C (θ) may be obtained based on the following manner; specifically, the above-described derivation is based on the output quantum state σ ^ABE The objective function value of the objective loss function C (θ) constructed by (θ) specifically includes:

taking the minimized target loss function C (theta) as a preset optimization target, and adjusting an adjustable parameter vector theta in the target loss function C (theta);

and under the condition that the preset optimization condition is met, obtaining the objective function value of the objective loss function C (theta).

It should be noted that, the gradient descent optimization method or other optimization methods may be used to complete the preset optimization objective; further, the preset optimization condition is that the objective function value of the objective loss function converges to a minimum value, that is, the difference between the objective function value obtained in the current optimization process and the objective function value obtained in the last optimization process is less than or equal to a preset threshold, where the preset threshold is a tested value, and can be set according to actual requirements, which is not limited in the scheme of the disclosure. Or, the preset optimization condition may specifically be that the preset optimization iteration number is reached, that is, the preset optimization condition may be determined to be satisfied when the current iteration number reaches the preset optimization iteration number.

For example, an adjustable parameter vector θ in the target loss function C (θ) is assignedValues, e.g. initially assigned as θ ₀ Thereby obtaining sigma based on the output quantum state ^ABE (θ ₀ ) The function value C (theta) of the objective loss function C (theta) is constructed ₀ ) The method comprises the steps of carrying out a first treatment on the surface of the Adjusting the adjustable parameter vector θ in the objective loss function C (θ) by gradient descent optimization method, such as from θ ₀ Adjusted to theta ₁ Thus, the function value C (θ) of the target loss function can be obtained ₁ ) The method comprises the steps of carrying out a first treatment on the surface of the Repeating the optimization process until the objective function value of the objective loss function converges to the minimum value or the actual optimization frequency reaches the preset optimization iteration frequency, and obtaining the objective parameter value theta of the adjustable parameter vector theta at the moment ^* And the target parameter value theta ^* Corresponding objective function value C (θ ^* )。

Thus, the present disclosure provides a specific solution for obtaining the objective function value of the objective loss function C (θ), which has a strong interpretability, and can also greatly reduce the computational complexity, and can rapidly obtain the objective quantum state ρ ^AB Is used to compress entangled estimates.

In a specific example of the disclosed scheme, the target parametric quantum circuit may be constructed in such a way that, in particular, when the quantum pure state ρ is to be ^ABEE’ Before acting on the target parametric quantum circuit, the method further comprises:

creating a preset parameterized quantum circuit containing the adjustable parameter vector theta on 2+n continuous qubits in the initial quantum circuit to obtain the target parameterized quantum circuit;

here, the initial quantum circuit is a blank quantum circuit containing 2 (n+m) quantum bits; the preset parameterized quantum circuit is at least used for establishing entanglement among at least partial qubits corresponding to the continuous 2m+n qubits.

Further, m continuous qubits in a preset parameterized quantum circuit of the target parameterized quantum circuit correspond to the extended quantum system E; the rest m+n continuous qubits except the continuous m qubits in the preset parameterized quantum circuit of the target parameterized quantum circuit correspond to the auxiliary quantum system e'; and n quanta bits which are remained in the target parameterized quantum circuit except for continuous 2m+n quanta bits corresponding to a preset parameterized quantum circuit correspond to the target quantum system AB.

Further, in a specific example, the remaining n qubits in the target parameterized quantum circuit, excluding the consecutive 2m+n qubits, are consecutive, wherein n consecutive qubits are located in the first n qubits, or the last n qubits, in the target parameterized quantum circuit.

For example, in one example, as shown in fig. 2 (a), the qubits corresponding to the first n consecutive qubits in the blank quantum circuit may be used as the sub-circuits corresponding to the target quantum system AB, that is, the first n qubits correspond to the target quantum system AB; further, the quantum bit corresponding to the n+1th quantum bit to the n+mth quantum bit is used as a sub-circuit corresponding to the extended quantum system E, namely the n+1th quantum bit to the n+mth quantum bit, and corresponds to the extended quantum system E; and taking the quantum bit corresponding to the last m+n quantum bits as a sub-circuit corresponding to the auxiliary quantum system E ', namely, the last m+n quantum bits correspond to the auxiliary quantum system E'. At this time, as shown in fig. 2 (b), a preset parameterized quantum circuit is created on the qubit corresponding to the n+1st to 2 nd (n+m) th consecutive qubits, to obtain a target parameterized quantum circuit.

Or in another example, the quantum bits corresponding to the first m continuous quantum bits in the blank quantum circuit can be used as a sub-circuit corresponding to the extended quantum system E, that is, the first m quantum bits correspond to the extended quantum system E; further, the quantum bits corresponding to the m+1th to 2m+n quantum bits are used as sub-circuits corresponding to the auxiliary quantum system E ', namely the m+1th to 2m+n quantum bits, and correspond to the auxiliary quantum system E'; and taking the quantum bit corresponding to the last n quantum bits as a sub-circuit corresponding to the target quantum system AB, namely the last n quantum bits correspond to the target quantum system AB. At this time, as shown in fig. 2 (c), a preset parameterized quantum circuit is created on the qubit corresponding to the 1 st to 2m+n th consecutive qubits, to obtain a target parameterized quantum circuit.

Therefore, the scheme of the present disclosure provides a scheme for designing the target parameterized quantum circuit, so that training efficiency is effectively improved, meanwhile, calculation complexity is reduced, the scheme is easier to implement, and a foundation is laid for subsequently obtaining an estimated value of compression entanglement of a target quantum state.

Further, in a specific example, the pre-set parameterized quantum circuit includes a parameterized single-bit quantum gate acting on the qubits, and a two-bit quantum gate that causes entanglement between the two qubits.

It should be noted that, in order to enhance the expression capability of the preset parameterized quantum circuit and further enhance the training efficiency, the preset parameterized quantum circuit may further include a D (a positive integer greater than or equal to 1) layer, where each layer may specifically include a parameterized single-bit quantum gate acting on a qubit, and a double-bit quantum gate that makes entanglement between two qubits occur; here, the value of D may affect the expressive power and training efficiency of the preset parameterized quantum circuit, and may be selected based on actual requirements.

Further, it should be noted that, in the case that the preset parameterized quantum circuit includes multiple layers, the circuit structures of the different layers of sub-circuits may be the same or different, and the scheme of the disclosure is not limited thereto, for example, a circuit template may be provided, and the different sub-circuits include at least part of the structures in the circuit template, where the circuit structures of the different sub-circuits may be different, but all the structures in the circuit template, in other words, the circuit structures of the different sub-circuits are similar; moreover, the adjustable parameters in the different layer sub-circuits may be the same or different, and the present disclosure is not limited in this regard.

Like this, this disclosed scheme has further refined the circuit structure of target parameterization quantum circuit, and this circuit structure's expression ability is strong, has lower circuit degree of depth, and then can effectively promote training efficiency, moreover, can also greatly reduce computational complexity.

Further, in a specific example, the parameterized single-bit quantum gate is a turngate comprising at least one adjustable rotation parameter; wherein the adjustable parameter vector θ is formed based on adjustable rotation parameters in a parameterized single bit quantum gate. For example, the parameterized single-bit quantum gate is a single-bit rotary gate, such as a u3 gate, and the u3 gate includes three independent adjustable rotation parameters, such as a rotation angle X, a rotation angle Y, and a rotation angle Z. Therefore, the circuit structure of the target parameterized quantum circuit is further refined, the circuit structure is easy to implement and high in expression capacity, training efficiency can be effectively improved, and the accuracy of the compression entangled estimated value of the target quantum state can be effectively improved.

In a specific example of the disclosed scheme, the two-bit quantum gate is a controlled not gate (CNOT gate), or a controlled unitary gate. Therefore, the circuit structure of the target parameterized quantum circuit is further refined, the circuit structure is easy to implement and high in expression capacity, training efficiency can be effectively improved, and the accuracy of the compression entangled estimated value of the target quantum state can be effectively improved.

For example, the predetermined parametric quantum circuit U (θ) includes a D-layer sub-circuit, where the predetermined parametric quantum circuit U (θ) may be specifically expressed as:

U(θ)＝(u ₁ (θ ⁽¹⁾ ),U ₂ (θ ⁽²⁾ ),…,U _k (θ ^(k) ),…,U _D (θ ^(D) ))；

wherein the U is _k (θ ^(k) ) Representing a kth layer sub-circuit in the preset parameterized quantum circuit. Further, the adjustable parameter vector θ may be specifically expressed as θ= (θ) ⁽¹⁾ ,θ ⁽²⁾ ,…,θ ^(k) ,…,θ ^(D) ) The θ is ^(k) Representing a k-th layer sub-circuit U _k (θ ^(k) ) Is provided.

Further, it is assumed that the circuit structure of each layer of sub-circuit in the preset parameterized quantum circuit U (θ) is the same, and the adjustable parameters in each layer of sub-circuit are also the same; at this time, the k-th layer U _k (θ ^(k) ) For example, as shown in FIG. 2 (d), the U _k (θ ^(k) ) Layer(s)The sub-circuit comprises:

the single qubit rotation gate acting on each qubit is, for example, a u3 gate, and the u3 gate includes three independent adjustable rotation parameters, such as a rotation angle X, a rotation angle Y and a rotation angle Z. Based on this, the target parametric quantum circuit comprises 3D (2m+n) adjustable rotation parameters.

Further, as shown in FIG. 2 (d), the U _k (θ ^(k) ) The layer sub-circuit further comprises:

a CNOT gate acting on two adjacent qubits; for example, CNOT gate controlled by the first quantum bit in the preset parameterized quantum circuit and acting on the first +1th quantum bit; here, l is 1 or more and 2m+n-1 or less;

A CNOT gate acting on the last and first qubits in a preset parameterized quantum circuit; for example, the last qubit in the preset parameterized quantum circuit is controlled and acts as a CNOT gate for the first qubit in the preset parameterized quantum circuit.

The present disclosure is described in further detail below with reference to specific examples; the scheme of the disclosure provides a method for estimating a distillable secret key, which realizes the estimation of the distillable secret key by estimating compression entanglement of a target quantum state; specifically, the method optimizes tunable parameters in a parameterized quantum circuit (Parameterized Quantum Circuit, PQC) by implementing the parameterized quantum circuit on a quantum computer or simulating the parameterized quantum circuit on a classical computer, and optimizes extended quantum states (e.g., ρ) for a given extended quantum system (e.g., extended quantum system E) size using machine learning ^ABE ) Searching is performed to obtain an estimated value of the compression entanglement of the target quantum state, i.e. the upper bound of the distillable key of the target quantum state.

The parameterized quantum circuit in this example may be composed of several single-qubit rotation gates and a controlled inverse gate (CNOT gate), where the rotation angles of the several single-qubit rotation gates constitute an adjustable parameter vector θ of the parameterized quantum circuit. The optimization in the scheme disclosed by the disclosure is to optimize the parameter value of the adjustable parameter vector theta, so as to realize the optimization target.

It should be noted that, as an entanglement measure of broad interest, the compression entanglement (squashed entanglement) has many excellent properties and has been proved to be an upper bound of a distillable key, and thus, obtaining an estimated value of the compression entanglement of a target quantum state helps to estimate a distillable key of the target quantum state, in other words, the method for estimating a distillable key according to the present disclosure is realized by estimating the compression entanglement of the target quantum state. Specifically, given a target quantum state ρ of one target quantum system AB (formed by a first quantum system (may be denoted as A) and a second quantum system (may be denoted as B) ^AB (the target Quantum state ρ) ^AB An entangled quantum state), then the target quantum state ρ ^AB Compression entanglement of (c) may be defined as:

wherein said ρ is ^ABE Representing the target quantum state ρ ^AB An extended quantum state of (2), the extended quantum state ρ ^ABE The collapsed state on the target quantum system AB is ρ ^AB Mathematically, the extended quantum state ρ ^ABE A density matrix representation of extended quantum states may be used; further, the Tr _E Representing taking a partial trace on an extended quantum system E, wherein the extended quantum system E represents a quantum system consisting of m quantum bits; i (A; b|E) represents the extended quantum state ρ ^ABE The quantum condition mutual information of (a) can be specifically expressed as:

I(A；B|E)＝S(AE)+S(BE)-S(ABE)-S(E)；

wherein S (·) =s (ρ) ^· )＝-Tr[ρ ^· log ₂ ρ ^· ]Representing the quantum state ρ ^· Von neumann entropy (Von Neumann entropy).

Further, the scheme of the present disclosure eliminates the estimation of compression entanglement by using methods such as semi-orthographic programming in the conventional scheme, and instead uses parameterized quantum circuits for a given expansion dimensionExtended quantum states (e.g. ρ ^ABE ) Traversing, optimizing the target loss function by using a machine learning method, so as to find the minimum function value of the target loss function under a given expansion dimension, and further realizing the estimation of compression entanglement of the target quantum state.

It should be noted that, under a given expansion dimension, the present disclosure may theoretically reach an optimal estimation of compression entanglement, and in a process in which the expansion dimension gradually increases, the present disclosure may gradually approach a theoretical value of compression entanglement.

For the present example, one or more of the target quantum states ρ described above are given ^AB And giving an extended quantum system E containing m quantum bits, generating the target quantum state rho ^AB P of the purified quantum state (i.e. quantum pure state) ^ABEE’ Here, the quantum pure state ρ ^ABEE’ The system quantum state corresponding to the total subsystem containing 2 (m+n) quantum bits; e' represents a quantum system comprising (m+n) qubits for assisting in the preparation of quantum pure states ρ ^ABEE’ May be referred to simply as an auxiliary quantum system. Also, in this example, a blank quantum circuit containing 2 (m+n) quantum bits is prepared.

Further, in the blank quantum circuit, a D layer of preset parameterized quantum circuit U (theta) is created on the sub-circuits corresponding to the extended quantum system E and the auxiliary quantum system E', so as to obtain a target parameterized quantum circuit containing 2 (m+n) quantum bits; and the quantum pure state rho is processed ^ABEE’ As the initial quantum state of the target parametric quantum circuit, the output quantum state of the total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system in the target parametric quantum circuit is obtainedAt this time, the parameterized output quantum state sigma can be obtained ^ABE Half of the conditional mutual information I (A; b|E) of (θ) is used as a target loss function, and the adjustable parameter vector θ in the target parameterized quantum circuit is further optimized until the target loss function value convergesThus, the extended quantum state with minimum mutual information under the condition of the given extended dimension m is obtained.

A specific scheme for obtaining an estimate of compression entanglement for a given target quantum state using a target parametric quantum circuit is given below in connection with the specific figures.

Here, the inputs of this example are: target quantum state ρ of target quantum system AB containing n quantum bits ^AB An extended quantum system E comprising m qubits, and a blank quantum circuit comprising 2 (n+m) qubits. The output result is: target quantum state ρ ^AB An estimated value of compression entanglement in a given expansion dimension, wherein the estimated value of compression entanglement is the target quantum state rho ^AB Is the upper bound of distillable keys.

As shown in fig. 3, the specific steps include:

step S301: inputting a target quantum state ρ of a target quantum system AB containing n quantum bits ^AB And an extended quantum system E containing m qubits and based on a target quantum state ρ ^AB And expanding the quantum system E to generate a target quantum state rho ^AB Is any one of the quantum pure states ρ ^ABEE’ 。

Step S302: preparing a blank quantum circuit containing 2 (n+m) quantum bits, and creating a preset parameterized quantum circuit U (theta) containing a D layer sub-circuit on 2m+n quantum bits with continuous quantum bits in the blank quantum circuit to obtain the target parameterized quantum circuit.

Here, it should be noted that n qubits are left in the target parameterized quantum circuit in addition to 2m+n qubits to which the preset parameterized quantum circuit U (θ) acts, and at this time, the qubits of the remaining n qubits are also continuous.

For example, as shown in fig. 2 (a), the qubits corresponding to the first n consecutive qubits in the blank quantum circuit may be used as the sub-circuit corresponding to the target quantum system AB, that is, the first n qubits correspond to the target quantum system; further, the quantum bit corresponding to the n+1th quantum bit to the n+mth quantum bit is used as a sub-circuit corresponding to the extended quantum system E, namely the n+1th quantum bit to the n+mth quantum bit, and corresponds to the extended quantum system E; and taking the quantum bit corresponding to the last m+n quantum bits as a sub-circuit corresponding to the auxiliary quantum system E ', namely, the last m+n quantum bits correspond to the auxiliary quantum system E'. At this time, as shown in fig. 2 (b), a preset parameterized quantum circuit is created on the qubit corresponding to the n+1st to 2 nd (n+m) th consecutive qubits, to obtain a target parameterized quantum circuit.

Furthermore, the quantum bits corresponding to the first m continuous quantum bits in the blank quantum circuit can be used as a sub-circuit corresponding to the extended quantum system E, namely the first m quantum bits correspond to the extended quantum system E; further, the quantum bits corresponding to the m+1th to 2m+n quantum bits are used as sub-circuits corresponding to the auxiliary quantum system E ', namely the m+1th to 2m+n quantum bits, and correspond to the auxiliary quantum system E'; and taking the quantum bit corresponding to the last n quantum bits as a sub-circuit corresponding to the target quantum system AB, namely the last n quantum bits correspond to the target quantum system AB. At this time, as shown in fig. 2 (c), a preset parameterized quantum circuit is created on the qubit corresponding to the 1 st to 2m+n th consecutive qubits, to obtain a target parameterized quantum circuit.

It should be noted that, as shown in fig. 2 (b) and fig. 2 (c), the preset parameterized quantum circuit U (θ) includes a D-layer sub-circuit, where the U (θ) may be specifically expressed as (U) ₁ (θ ⁽¹⁾ ),U ₂ (θ ⁽²⁾ ),…,U _k (θ ^(k) ),…,U _D (θ ^(D) ) And, wherein the U _k (θ ^(k) ) Representing a kth layer sub-circuit in the preset parameterized quantum circuit. Further, the adjustable parameter vector θ may be specifically expressed as (θ ⁽¹⁾ ,θ ⁽²⁾ ,…,θ ^(k) ,…,θ ^(D) ) The θ is ^(k) Representing a k-th layer sub-circuit U _k (θ ^(k) ) Is provided.

Here, k is a positive integer of 1 or more and D or less. And D is a positive integer greater than or equal to 1. It should be noted that, the value of D may affect the expression capability and training efficiency of the preset parameterized quantum circuit, that is, the value of D may affect the expression capability and training efficiency of the target parameterized quantum circuit, so the value may be selected based on the actual requirement.

It should be noted that the circuit structures of the different layers of sub-circuits may be the same or different, and the scheme of the disclosure is not limited thereto, for example, a circuit template may be provided, and the different sub-circuits include at least part of the structures in the circuit template, where the circuit structures of the different sub-circuits may be different, but all are the structures in the circuit template, in other words, the circuit structures of the different sub-circuits are similar; moreover, the adjustable parameters in the different layer sub-circuits may be the same or different, and the present disclosure is not limited in this regard.

Further, the circuit structure of the preset parameterized quantum circuit is described in detail below; it should be noted that, the circuit structures given in this example are only used to explain the scheme of the present disclosure, and other circuit structures may also be in the actual scenario, and the scheme of the present disclosure is not limited thereto.

Specifically, in this example, the circuit structure of each layer of sub-circuit in the preset parameterized quantum circuit U (θ) is the same, and the adjustable parameters in each layer of sub-circuit are also the same; for example, in the kth layer U _k (θ ^(k) ) For example, at this time, as shown in FIG. 2 (d), the U _k (θ ^(k) ) Comprising the following steps: the single qubit rotation gate acting on each qubit is, for example, a u3 gate, and the u3 gate includes three independent adjustable rotation parameters, such as a rotation angle X, a rotation angle Y and a rotation angle Z. Based on this, the target parametric quantum circuit comprises 3D (2m+n) adjustable rotation parameters.

Further, as shown in FIG. 2 (d), the U _k (θ ^(k) ) Also included are strong entanglement structures such as in particular:

For example, for a target parameterized quantum circuit as shown in FIG. 2 (b), the k-th layer sub-circuit U _k (θ ^(k) ) The method specifically comprises the following steps:

controlled by first in target parametric quantum circuit ₁ The first qubit and act on ₁ A CNOT gate of +1 qubits; here, l ₁ N+1 or more and 2 (m+n) -1 or less;

is controlled by the 2 (m+n) th quantum bit in the target parameterized quantum circuit and acts as a CNOT gate of the n+1 th quantum bit in the target parameterized quantum circuit.

For another example, for a target parameterized quantum circuit as shown in FIG. 2 (c), the k-th layer sub-circuit U _k (θ ^(k) ) The method specifically comprises the following steps:

controlled by first in target parametric quantum circuit ₂ The first qubit and act on ₂ A CNOT gate of +1 qubits; here, l ₂ Is equal to or more than 1 and equal to or less than 2m+n-1;

controlled by 2m+n quantum bits in the target parametric quantum circuit, and acts as a CNOT gate for 1 st quantum bit in the target parametric quantum circuit.

Step S303: -incorporating said quantum pure state ρ ^ABEE’ As the initial quantum state of the target parametric quantum circuit, the output quantum state of the total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system in the target parametric quantum circuit is obtained

Step S304: will output quantum state sigma ^ABE Half of the conditional mutual information I (A; b|E) of (θ) is taken as a target loss function, where the target loss function can be denoted as C (θ), in which case the target loss function C (θ) is expressed specificallyThe formula is:

wherein the S (AE) =s (σ ^AE )＝-Tr[σ ^AE log ₂ σ ^AE ]Representing the output quantum state sigma on two quantum systems AE composed of a first quantum system A and an extended quantum system E ^AE Von neumann entropy of (c); s (BE) =s (σ ^BE )＝-Tr[σ ^BE log ₂ σ ^BE ]Representing the output quantum state sigma on a two-quantum system BE consisting of a second quantum system B and an extended quantum system E ^BE Von neumann entropy of (c); the S (ABE) =s (σ ^ABE )＝-Tr[σ ^ABE log ₂ σ ^ABE ]Representing the output quantum state sigma on the total extended quantum system ABE composed of the target quantum system AB and the extended quantum system E ^ABE Von neumann entropy of (c); the S (E) =s (σ ^E )＝-Tr[σ ^E log ₂ σ ^E ]Representing the output quantum state sigma on an extended quantum system E ^E Von neumann entropy of (c); the Tr is a trace operator.

Step S305: the adjustable parameter vector θ is adjusted using a gradient descent optimization method or other optimization method to minimize the target loss function C (θ). When the function value of the objective loss function C (theta) reaches the minimum value, the optimal parameter value of the adjustable parameter vector theta is obtained and can be recorded as the optimal parameter vector theta ^* . At the same time, the minimum function value C (θ) ^* ) (i.e., the objective function values described above).

Correspondingly, the target output quantum state of the total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system in the target parameterized quantum circuitThe quantum state is the extended quantum state with the minimum condition mutual information under the given extended dimension.

Step S306: output minimum function value C (θ) ^* ) The minimum function value C (θ ^* ) Namely, isGiven an extended quantum system E comprising m qubits, a target quantum state ρ ^AB Is also an estimate of the compression entanglement of (2), and is also the target quantum state ρ ^AB To facilitate benchmarking for distillable keys.

Case display

The effect of estimating the compressive entanglement of the isotropic state using the scheme of the present disclosure is shown below.

The isotropic state is a common two-way quantum state whose density matrix can be written as:

wherein d is the dimension of a single party,is the noise figure>Is the maximum entangled state. In the experiment, d=2 was set. Further, the isotropic states of the noise coefficients a=0.1, 0.3,0.5,0.7 were estimated for compression entanglement on a specific platform, respectively, to obtain the results shown in the following table. Here, the table below specifically shows the result of comparing the estimated value of the scheme of the present disclosure with the trivial upper bound given that the extended quantum system is a 2-qubit.

a	0.1	0.3	0.5	0.7
					Estimated values of the disclosed scheme	0.0019	0.013	0.126	0.387
The trivial upper bound	0.010	0.085	0.226	0.437
					The scheme of the disclosure runs time (seconds)	86	83	87	90

From experimental results, it can be seen that there is a significant improvement in the estimated value of the disclosed solution over the trivial upper bound, sufficient to demonstrate the effectiveness of the disclosed solution. Moreover, the scheme of the present disclosure can obtain an accurate estimated value, and at the same time, it takes little time, and has high efficiency.

It should be noted that, the solution of the present disclosure uses the target parameterized quantum circuit to directly generate the extended quantum states, and theoretically, traverses all the extended quantum states under the given scale of the extended quantum system, thereby realizing effective estimation of compression entanglement.

Moreover, the scheme of the disclosure utilizes a mature machine learning optimization method, so that estimation of the general quantum state compression entanglement can be effectively completed by using less computing resources, and the scheme also has high efficiency.

In addition, the target parameterized quantum circuit adopted by the scheme disclosed by the invention is flexible enough to generate an extended quantum state of the target quantum state and optimize the extended quantum state, and has no limit on the input target quantum state. That is, for any quantum channel, the disclosed scheme can be implemented and gives an estimate of its compression entanglement, and therefore, is more friendly, practical and versatile for general quantum states.

The present disclosure also provides a device for estimating a distillable key, as shown in fig. 4, including:

an acquisition unit 401 for obtaining a target quantum state ρ ^AB The method comprises the steps of carrying out a first treatment on the surface of the Wherein the target quantum state ρ ^AB Representing an entangled state of a target quantum system AB comprising n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A and a second quantum system B;

a processing unit 402 for based on the target quantum state ρ ^AB Generating quantum pure state rho ^ABEE' The method comprises the steps of carrying out a first treatment on the surface of the Wherein E represents an extended quantum system comprising m quantum bits for extending the target quantum system AB, and E' represents a pure state ρ comprising (m+n) quantum bits for auxiliary preparation of quantum ^ABEE’ Auxiliary quantum systems of (a); n is a positive integer greater than or equal to 2, and m is a positive integer greater than or equal to 1; -incorporating said quantum pure state ρ ^ABEE’ Acting on a target parameterized quantum circuit to obtain an output quantum state sigma of a total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system E in the target parameterized quantum circuit ^ABE (θ); wherein the target parameterized quantum circuit comprises 2 (n+m) quantum bits, and θ represents an adjustable parameter vector of the target parameterized quantum circuit; using the output quantum state sigma ^ABE (E) Obtaining the target quantum state rho ^AB Wherein the target quantum state ρ is ^AB Is used to estimate the target quantum state ρ ^AB Is provided.

In a specific example of the disclosed scheme, the target quantum state ρ ^AB Is the target quantum state ρ ^AB Is the upper bound of distillable keys.

In a specific example of the solution of the present disclosure, the processing unit 402 is specifically configured to:

In a specific example of the disclosed scheme, the target loss function C (θ) is based on the output quantum state σ ^ABE And (θ) conditional mutual information I (A; b|E).

and under the condition that the preset optimization condition is met, obtaining an objective function value of the objective loss function C (theta).

In a specific example of the present disclosure, the processing unit 402 is further configured to:

wherein the initial quantum circuit is a blank quantum circuit containing 2 (n+m) quantum bits; the preset parameterized quantum circuit is at least used for establishing entanglement among at least part of qubits corresponding to continuous 2m+n qubits;

the m continuous qubits in the preset parameterized quantum circuit of the target parameterized quantum circuit correspond to the extended quantum system E; the rest m+n continuous qubits except the continuous m qubits in the preset parameterized quantum circuit of the target parameterized quantum circuit correspond to the auxiliary quantum system E'; and n quanta bits which are remained in the target parameterized quantum circuit except for continuous 2m+n quanta bits corresponding to a preset parameterized quantum circuit correspond to the target quantum system AB.

In a specific example of the disclosed scheme, the remaining n qubits in the target parameterized quantum circuit, excluding the consecutive 2m+n qubits, are consecutive, wherein n consecutive qubits are located in the first n qubits, or the last n qubits, in the target parameterized quantum circuit.

In a specific example of the disclosed scheme, the preset parameterized quantum circuit includes a parameterized single-bit quantum gate acting on the qubits, and a two-bit quantum gate that causes entanglement between the two qubits.

In a specific example of the disclosed solution, the parameterized single-bit quantum gate is a turngate comprising at least one adjustable rotation parameter; wherein the adjustable parameter vector θ is formed based on adjustable rotation parameters in a parameterized single bit quantum gate.

In a specific example of the disclosed scheme, the two-bit quantum gate is a controlled NOT gate, or a controlled unitary gate.

Descriptions of specific functions and examples of each unit of the apparatus in the embodiments of the present disclosure may refer to related descriptions of corresponding steps in the foregoing method embodiments, which are not repeated herein.

The present disclosure also provides 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 above method of applying a 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 described for application to a quantum computing device.

The present disclosure also provides a computing device comprising:

at least one quantum processing unit (quantum processing unit, QPU);

the instructions are executed by the at least one QPU to enable the at least one QPU to perform the method applied to the quantum computing device.

It will be appreciated that the QPU elements used in the present disclosure may also be referred to as quantum processors or quantum chips, may relate to physical chips comprising a plurality of qubits interconnected in a particular manner.

Moreover, it is to be understood that the qubits described in the present disclosure may refer to the basic information units of a quantum computing device. Qubits are contained in QPUs and the concept of classical digital bits is generalized.

Further, in accordance with embodiments of the present disclosure, the present disclosure also provides a computing device, a readable storage medium, and a computer program product.

FIG. 5 illustrates a schematic block diagram of an example computing device 500 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. Computing devices may also represent various forms of mobile apparatuses, such as personal digital assistants, cellular telephones, smartphones, wearable devices, and other similar computing apparatuses. The components shown herein, their connections and relationships, and their functions, are meant to be exemplary only, and are not meant to limit implementations of the disclosure described and/or claimed herein.

As shown in fig. 5, the apparatus 500 includes a computing unit 501 that can perform various suitable actions and processes according to a computer program stored in a Read Only Memory (ROM) 502 or a computer program loaded from a storage unit 508 into a Random Access Memory (RAM) 503. In the RAM 503, various programs and data required for the operation of the device 500 can also be stored. The computing unit 501, ROM 502, and RAM 503 are connected to each other by a bus 504. An input/output (I/O) interface 505 is also connected to bus 504.

Various components in the device 500 are connected to the I/O interface 505, including: an input unit 506 such as a keyboard, a mouse, etc.; an output unit 507 such as various types of displays, speakers, and the like; a storage unit 508 such as a magnetic disk, an optical disk, or the like; and a communication unit 509 such as a network card, modem, wireless communication transceiver, etc. The communication unit 509 allows the device 500 to exchange information/data with other devices via a computer network such as the internet and/or various telecommunication networks.

The computing unit 501 may be a variety of general and/or special purpose processing components having processing and computing capabilities. Some examples of computing unit 501 include, but are not limited to, a Central Processing Unit (CPU), a Graphics Processing Unit (GPU), various specialized Artificial Intelligence (AI) computing chips, various computing units running machine learning model algorithms, a Digital Signal Processor (DSP), and any suitable processor, controller, microcontroller, etc. The calculation unit 501 performs the respective methods and processes described above, for example, a distillable key estimation method. For example, in some embodiments, the method of estimating a distillable key may be implemented as a computer software program tangibly embodied on a machine-readable medium, such as storage unit 508. In some embodiments, part or all of the computer program may be loaded and/or installed onto the device 500 via the ROM 502 and/or the communication unit 509. When a computer program is loaded into RAM 503 and executed by computing unit 501, one or more steps of the distillable key estimation method described above may be performed. Alternatively, in other embodiments, the computing unit 501 may be configured to perform the distillable key estimation method by any other suitable means (e.g. by means of firmware).

Various implementations of the systems and techniques described here above may be implemented in digital electronic circuitry, integrated circuit systems, field Programmable Gate Arrays (FPGAs), application Specific Integrated Circuits (ASICs), application Specific Standard Products (ASSPs), systems On Chip (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and/or combinations thereof. These various embodiments may include: implemented in one or more computer programs, the one or more computer programs may be executed and/or interpreted on a programmable system including at least one programmable processor, which may be a special purpose or general-purpose programmable processor, that may receive data and instructions from, and transmit data and instructions to, a storage system, at least one input device, and at least one output device.

Program code for carrying out methods of the present disclosure may be written in any combination of one or more programming languages. These program code 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 code, when executed by the processor or controller, causes the functions/operations specified in the flowchart and/or block diagram to be implemented. 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. The 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 portable 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 pointing device (e.g., a mouse or trackball) by which a user can 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 may 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 input, speech input, or tactile input.

The systems and techniques described here can be implemented in a computing system that includes a background 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 background, 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 a client and a server. The client and server are typically 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 incorporating a blockchain.

It should be appreciated that various forms of the flows shown above may be used to reorder, add, or delete steps. For example, the steps recited in the present disclosure may be performed in parallel, sequentially, or in a different order, provided that the desired results of the disclosed aspects are achieved, and are not limited herein.

The above detailed description should not be taken as limiting the scope of the present disclosure. It will be apparent to those skilled in the art that various modifications, combinations, sub-combinations and alternatives are possible, depending on design requirements and other factors. Any modifications, equivalent substitutions, improvements, etc. that are within the principles of the present disclosure are intended to be included within the scope of the present disclosure.

Claims

1. A method of estimating a distillable key, comprising:

obtaining the target quantum state rho ^AB The method comprises the steps of carrying out a first treatment on the surface of the Wherein the target quantum state ρ ^AB Representing an entangled state of a target quantum system AB comprising n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A and a second quantum system B;

based on the target quantum state ρ ^AB Generating quantum pure state rho ^ABEE′ The method comprises the steps of carrying out a first treatment on the surface of the Wherein E represents an extended quantum system comprising m quantum bits for extending the target quantum system AB, and E' represents a pure state ρ comprising (m+n) quantum bits for auxiliary preparation of quantum ^ABEE′ Auxiliary quantum systems of (a); n is a positive integer greater than or equal to 2, and m is a positive integer greater than or equal to 1;

-incorporating said quantum pure state ρ ^ABEE′ Acting on a target parameterized quantum circuit to obtain an output quantum state sigma of a total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system E in the target parameterized quantum circuit ^ABE (θ); wherein the target parameterized quantum circuit comprises 2 (n+m) quantum bits, and θ represents an adjustable parameter vector of the target parameterized quantum circuit;

by adjusting the output quantum state sigma ^ABE An adjustable parameter vector theta in (theta) to obtain the target quantum state rho ^AB Wherein the target quantum state ρ is ^AB Is used for the compression entangled estimation value of (2)Estimating the target quantum state ρ ^AB Is a distillable key of (a); the target quantum state ρ ^AB Is the target quantum state ρ ^AB Is the upper bound of distillable keys.

2. The method of claim 1, wherein the outputting of the quantum state σ is performed by adjusting ^ABE An adjustable parameter vector theta in (theta) to obtain the target quantum state rho ^AB Is provided, comprising:

3. The method of claim 2, wherein the target loss function C (θ) is based on the output quantum state σ ^ABE And (θ) conditional mutual information I (A; b|E).

4. The method of claim 2, wherein the deriving is based on an output quantum state σ ^ABE The objective function value of the objective loss function C (θ) constructed by (θ) includes:

5. The method of any of claims 1-4, further comprising:

wherein the initial quantum circuit is a blank quantum circuit containing 2 (n+m) quantum bits; the preset parameterized quantum circuit is at least used for establishing entanglement among at least part of qubits corresponding to continuous 2m+n qubits; the m continuous qubits in the preset parameterized quantum circuit of the target parameterized quantum circuit correspond to the extended quantum system E; the rest m+n continuous qubits except the continuous m qubits in the preset parameterized quantum circuit of the target parameterized quantum circuit correspond to the auxiliary quantum system E'; and n quanta bits which are remained in the target parameterized quantum circuit except for continuous 2m+n quanta bits corresponding to a preset parameterized quantum circuit correspond to the target quantum system AB.

6. The method of claim 5, wherein the remaining n qubits in the target parameterized quantum circuit, excluding the consecutive 2m+n qubits, are consecutive, wherein n consecutive qubits are located in the first n qubits, or the last n qubits, in the target parameterized quantum circuit.

7. The method of claim 6, wherein the pre-set parameterized quantum circuit comprises a parameterized single-bit quantum gate acting on the qubits and a two-bit quantum gate that causes entanglement between the two qubits.

8. The method of claim 7, wherein the parameterized single-bit quantum gate is a turngate comprising at least one adjustable rotation parameter; wherein the adjustable parameter vector θ is formed based on adjustable rotation parameters in a parameterized single bit quantum gate.

9. The method of claim 7, wherein the two-bit quantum gate is a controlled not gate, or a controlled unitary gate.

10. An apparatus for estimating a distillable key, comprising:

an acquisition unit for obtaining the target quantum state ρ ^AB The method comprises the steps of carrying out a first treatment on the surface of the Wherein the target quantumState ρ ^AB Representing an entangled state of a target quantum system AB comprising n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A and a second quantum system B;

A processing unit for based on the target quantum state ρ ^AB Generating quantum pure state rho ^ABEE′ The method comprises the steps of carrying out a first treatment on the surface of the Wherein E represents an extended quantum system comprising m quantum bits for extending the target quantum system AB, and E' represents a quantum pure state sigma comprising (m+n) quantum bits for assisting in preparation of quantum pure state sigma ^ABEE′ Auxiliary quantum systems of (a); n is a positive integer greater than or equal to 2, and m is a positive integer greater than or equal to 1; -incorporating said quantum pure state ρ ^ABEE′ Acting on a target parameterized quantum circuit to obtain an output quantum state sigma of a total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system E in the target parameterized quantum circuit ^ABE (θ); wherein the target parameterized quantum circuit comprises 2 (n+m) quantum bits, and θ represents an adjustable parameter vector of the target parameterized quantum circuit; by adjusting the output quantum state sigma ^ABE An adjustable parameter vector theta in (theta) to obtain the target quantum state rho ^AB Wherein the target quantum state ρ is ^AB Is used to estimate the target quantum state ρ ^AB Is a distillable key of (a); the target quantum state ρ ^AB Is the target quantum state ρ ^AB Is the upper bound of distillable keys.

11. The apparatus of claim 10, wherein the processing unit is specifically configured to:

12. The apparatus of claim 11, wherein the targetThe loss function C (θ) is based on the output quantum state σ ^ABE And (θ) conditional mutual information I (A; b|E).

13. The apparatus of claim 11, wherein the processing unit is specifically configured to:

14. The apparatus of any of claims 10-13, wherein the processing unit is further to:

15. The apparatus of claim 14, wherein the remaining n qubits in the target parameterized quantum circuit, excluding the consecutive 2m+n qubits, are consecutive, wherein n consecutive qubits are located in the first n qubits, or the last n qubits, in the target parameterized quantum circuit.

16. The apparatus of claim 15, wherein the pre-set parameterized quantum circuit comprises a parameterized single-bit quantum gate acting on a qubit and a two-bit quantum gate that causes entanglement between two qubits.

17. The apparatus of claim 16, wherein the parameterized single-bit quantum gate is a turngate comprising at least one adjustable rotation parameter; wherein the adjustable parameter vector θ is formed based on adjustable rotation parameters in a parameterized single bit quantum gate.

18. The apparatus of claim 16, wherein the two-bit quantum gate is a controlled not gate, or a controlled unitary gate.

19. A computing device, comprising:

at least one quantum processing unit QPU;

the instructions being executable by the at least one QPU to enable the at least one QPU to perform the method of any one of claims 1 to 9;

alternatively, it includes:

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 1-9.

20. A non-transitory computer-readable storage medium storing computer instructions which, 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 to 9;

Alternatively, the computer instructions are for causing the computer to perform the method according to any one of claims 1-9.