CN116451794A

CN116451794A - Method, device, equipment and storage medium for estimating distillable entanglement

Info

Publication number: CN116451794A
Application number: CN202310275056.7A
Authority: CN
Inventors: 王鑫; 朱成鸿; 朱成开
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: 2023-07-18
Anticipated expiration: 2043-03-20
Also published as: CN116451794B

Abstract

The disclosure provides a method, a device, equipment and a storage medium for estimating distillatable entanglement, which relate to the field of computers, in particular 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 Wherein the target quantum state ρ _AB Representing the entangled state of the target quantum system AB containing 2n qubits; based on the target quantum state ρ _AB Generates quantum pure state |psi as the target spectrum decomposition result _ABEF >The method comprises the steps of carrying out a first treatment on the surface of the The quantum pure state |psi is processed _ABEF >Acting on a target parameterized quantum circuit to obtain an output quantum state of a total extended quantum system ABE in the target parameterized quantum circuit An adjustable parameter vector representing the target parameterized quantum circuit; using the output quantum stateObtaining the target quantum state rho _AB Is a one-way distillable entanglement estimate.

Description

Method, device, equipment and storage medium for estimating distillable entanglement

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 application, calculating quantum entanglement resources contained in any entangled state is one of the most core problems in quantum information. For example, it is important to calculate the upper bound of One-way distillable entanglement (One-way distillable entanglement) for any entanglement, which can be used to better estimate the distillable entanglement for that entanglement. How to estimate unidirectional distillable entanglement for a given entanglement state is still considered by the industry as a difficult task.

Disclosure of Invention

The present disclosure provides a method, apparatus, device and storage medium for estimating distillable entanglement.

According to an aspect of the present disclosure, there is provided a method of estimating distillable entanglement, 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 the entangled state of the target quantum system AB containing 2n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A and a second quantum system B; the first quantum system A comprises n quantum bits; the second quantum system B comprises n quantum bits; n is a positive integer greater than or equal to 1;

based on the target quantum state ρ _AB Generates quantum pure state |psi as the target spectrum decomposition result _ABEF >The method comprises the steps of carrying out a first treatment on the surface of the Wherein the target spectral decomposition result is for the target quantum state ρ _AB Carrying out spectrum decomposition to obtain the product; e represents an extended quantum system comprising k qubits for extending the target quantum system AB, F represents an auxiliary preparation of quantum pure state |ψ comprising (2n+k) qubits _ABEF >Auxiliary quantum systems of (a); k is a positive integer greater than or equal to 1;

the quantum pure state |psi is processed _ABEF Acting on a target parameterized quantum circuit to obtain an output quantum state 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 Wherein the target parameterized quantum circuit comprises 2 (2n+k) qubits;An adjustable parameter vector representing the target parameterized quantum circuit; the output quantum state->For the target quantum state ρ _AB The expansion of quantum state;

using the output quantum stateObtaining the target quantum state rho _AB Is a one-way distillable entanglement estimate.

According to another aspect of the present disclosure, there is provided a distillable entanglement estimation device 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 the entangled state of the target quantum system AB containing 2n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A and a second quantum system B; the first quantum system A comprises n quantum bits; the second quantum system B comprises n quantum bits; n is a positive integer greater than or equal to 1;

a processing unit for based on the target quantum state ρ _AB Generates quantum pure state |psi as the target spectrum decomposition result _ABEF -a >; wherein the target spectral decomposition result is for the target quantum state ρ _AB Carrying out spectrum decomposition to obtain the product; e represents a quantum system for the target containing k qubits Extended quantum system extended by system AB, F represents quantum pure state |psi which contains (2n+k) quantum bits and is used for auxiliary preparation of quantum _ABEF >Auxiliary quantum systems of (a); k is a positive integer greater than or equal to 1; the quantum pure state |psi is processed _ABEF >Acting on a target parameterized quantum circuit to obtain an output quantum state of a total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system E in the target parameterized quantum circuitWherein the target parameterized quantum circuit comprises 2 (2n+k) qubits;An adjustable parameter vector representing the target parameterized quantum circuit; the output quantum state->For the target quantum state ρ _AB The expansion of quantum state; by means of the output quantum state->Obtaining the target quantum state rho _AB Is a one-way distillable entanglement estimate.

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 The scheme utilizes less calculation resources to finish the target quantum state rho _AB The unidirectional distillable entanglement estimation 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 distillable entanglement in accordance with an embodiment of the 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 parameterized subcircuit in a specific example, according to an embodiment of the present disclosure;

FIG. 3 is a second flow diagram of an implementation of a method of estimating distillable entanglement in accordance with an embodiment of the present disclosure;

FIG. 4 is a schematic flow diagram of an implementation of a method of estimating distillable entanglement in a particular embodiment according to an embodiment of the disclosure;

FIG. 5 is a schematic illustration of the effect of a distillable entanglement estimation method in an example, according to an embodiment of the disclosure;

FIG. 6 is a schematic diagram of a construction of an estimation device that can distill entanglement in accordance with the disclosed embodiments;

FIG. 7 is a block diagram of a computing device used to implement a distillable entanglement estimation method of embodiments 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.

In order to better understand the methods provided by the embodiments of the present disclosure, the following explains related concepts related to the embodiments of the present disclosure.

Quantum states are states of motion of microscopic particles described by a plurality of quantum numbers.

Classical computers or traditional computers, computers based on the theory of classical physics as information processing. Classical computers store data or programs using the classical physical most easily implemented binary data bits, each represented by a 0 or a 1, called a bit or a bit, as the smallest unit of information. Classical computers themselves have the inevitable weakness: first, the most basic limitation of energy consumption in the calculation process. The minimum energy required for a logic element or memory cell should be several times more than kT; secondly, information entropy and heating energy consumption; thirdly, when the wiring density of the computer chip is large, the uncertainty of momentum is large when the uncertainty of the electronic position is small according to the uncertainty relation of the Hessenberg. Electrons are no longer bound and there is a quantum interference effect that can even destroy the performance of the chip.

Quantum computers (QWs) are a class of physical devices that perform high-speed mathematical and logical operations, store and process quantum information, following quantum mechanical properties, laws. When a device processes and calculates quantum information and runs a quantum algorithm, the device is a quantum computer. The quantum computer realizes a new mode of seed information processing according to the unique quantum dynamics rule. For parallel processing of computational problems, quantum computers have an absolute advantage in speed over classical computers. The transformation implemented by the quantum computer on each superposition component is equivalent to a classical calculation, all of which are completed simultaneously and are superimposed according to a certain probability amplitude to give the output result of the quantum computer, and the calculation is called quantum parallel calculation. Quantum parallel processing greatly improves the efficiency of quantum computers so that they can perform tasks that classical computers cannot do, such as factorization of a large natural number. Quantum correlation is essentially exploited in all quantum ultrafast algorithms. Therefore, quantum parallel computation with quantum state instead of classical state can reach incomparable operation speed and information processing function of classical computer, and save a large amount of operation resources.

At present, quantum computing and quantum information theory are rapidly developed, more and more quantum technologies are continuously emerging, the technology of quantum hardware is also promoted 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). Quantum entanglement is a basic component of quantum computing and quantum information processing, and is a key resource for realizing various quantum information technologies such as quantum security communication, quantum computing, quantum network and the like. The most important entanglement resource in quantum entanglement is the maximum entanglement state (Maximally entangled state), for example, for a quantum system containing two qubits, the maximum entanglement state is Bell state (Bell state); typically, bell states are allocated as resources in different sites or laboratories. Moreover, bell states are important basic resources of quantum key distribution (Quantum key distribution), quantum super-secret coding (Quantum superdense coding), quantum invisible state transfer (Quantum Teleportation) and other quantum information schemes.

Further toThe quantum operation will be described in detail; specifically, a target quantum state ρ in a two-quantum system (which may be denoted as target quantum system AB) _AB (also referred to as entangled state ρ _AB ) For example, at this time, alice and Bob have some of the qubits in the target quantum system AB in their respective laboratories, for example, a quantum system formed by some of the qubits owned by Alice may be referred to as a first quantum system (may be denoted as a), and a quantum system formed by the remaining part of the qubits owned by Bob may be referred to as a second quantum system (may be denoted as B), where the physical operations allowed by Alice and Bob are: alice and Bob perform local quantum operations and classical communication (local operations and classical communication, LOCC), which may be referred to as LOCC operations, in respective laboratories. Here, quantum operations generally refer to quantum gates and quantum measurements acting on the qubits, whereas local quantum operations mean that Alice and Bob can only quantum operate on the qubits in their respective laboratories; classical communication can then be used to communicate measurements from Alice and Bob, each performing a local quantum operation (e.g., quantum measurement).

Based on the above-described local quantum operations and classical communication (i.e., LOCC operations), unidirectional distillable entanglement describes the formation of a quantum state ρ from a given target _AB Entanglement distillation (Entanglement distillation), or entanglement purification (Entanglement purification), is carried out by unidirectional LOCC operation, such that the target quantum state ρ is obtained by distillation in the limit _AB Of the number of entangled bits of (i) that is distilled to obtain the target quantum state ρ _AB Is the maximum number of entangled bits. For example, for a d-dimensional maximum entanglement, the corresponding maximum number of entanglement bits is log ₂ d, such as the bell state of a double quantum system, the maximum entanglement bit number is 1.

Here, it should be noted that "unidirectional" in unidirectional LOCC operation means that classical communication is unidirectional, for example, all classical communication is Alice directed to Bob; alternatively, all classical communications are Bob directed to Alice; for example, unidirectional LOCC operation may specifically refer to Alice performing a local quantum operation on a qubit in its own laboratory, and notifying Bob through classical communication, so that Bob performs a local quantum operation on a qubit in its own laboratory based on a measurement result notified by Alice; alternatively, unidirectional LOCC operation may specifically refer to Bob performing a local quantum operation on a qubit in its own laboratory, and notifying Alice through classical communication, so that Alice performs a local quantum operation on a qubit in its own laboratory based on the measurement result notified by Bob.

Therefore, unidirectional distillable entanglement gives an entanglement measure of entanglement state from the perspective of quantum operation protocol, but how to calculate unidirectional distillable entanglement of given entanglement state as precisely as possible, so as to understand the quantum entanglement resources contained therein is a problem to be solved.

Based on the above, the scheme of the disclosure provides an estimation method of unidirectional distillable entanglement of entanglement, thus laying a foundation for subsequent understanding of quantum entanglement resources contained in entanglement.

Specifically, fig. 1 is a schematic diagram of an implementation flow of a method of estimating distillable entanglement 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 the entangled state of the target quantum system AB containing 2n qubits; the target quantum system AB is a double quantum system composed of a first quantum system A and a second quantum system B.

Further, the first quantum system A comprises n quantum bits; the second quantum system B comprises n quantum bits; and n is a positive integer greater than or equal to 1.

Step S102: based on the target quantum state ρ _AB Generates quantum pure state |psi as the target spectrum decomposition result _ABEF ＞。

Here, the target spectral decomposition results in the target quantum state ρ _AB Carrying out spectrum decomposition to obtain the product; e represents an extended quantum system comprising k quantum bits for extending the target quantum system AB; f represents a quantum phase containing (2n+k) qubits for assisting in the preparation of quantum pure state |ψ _ABEF >Auxiliary quantum systems of (a); and k is a positive integer greater than or equal to 1.

Step S103: the quantum pure state |psi is processed _ABEF >Acting on a target parameterized quantum circuit to obtain an output quantum state 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

Here, the target parametric quantum circuit comprises 2 (2n+k) qubits; An adjustable parameter vector representing the target parameterized quantum circuit; the output quantum state->For the target quantum state ρ _AB The expansion of the quantum state.

Here, 2n continuous qubits in the target parameterized quantum circuit correspond to the target quantum system AB; the continuous k quantum bits except the continuous 2n quantum bits in the target parameterized quantum circuit correspond to the extended quantum system E; the target parameterized quantum circuit is used for removing the residual and continuous 2n+k quanta except the continuous 2n quanta and the continuous k quanta, and corresponds to an auxiliary quantum system F.

Step S104: using the output quantum stateObtaining the target quantum state rho _AB Is a one-way distillable entanglement estimate.

In a specific example of the disclosed scheme, the target quantum state ρ _AB Is the target quantum state ρ _AB Is a unidirectional distillable entanglement upper bound. In other words, the disclosed scheme yields the target quantum state ρ _AB The estimation value of the unidirectional distillable entanglement is helpful to estimate the upper bound of the unidirectional distillable entanglement of the target quantum state, and the scheme of the present disclosure has low computational complexity and is easy to implement.

In a specific example of the disclosed scheme, the target quantum state ρ may be obtained in the following manner _AB In particular in a target quantum state ρ based _AB Generates quantum pure state |psi as the target spectrum decomposition result _ABEF >Before (i.e. before step S102 described above), the method further comprises:

obtaining the target quantum state rho _AB Is characterized by comprising a feature vector and a feature value corresponding to the feature vector;

based on the target quantum state ρ _AB And the characteristic vector and the characteristic value corresponding to the characteristic vector to obtain the target quantum state rho _AB Target spectral decomposition results of (2). For example, the target quantum state ρ _AB The target spectral decomposition results of (2) are:

here, |i>For the object ofQuantum state ρ _AB Is a characteristic vector of lambda _i For the eigenvector |i>Corresponding characteristic values.

Thus, the disclosed scheme provides a specific scheme for spectral decomposition, thus obtaining quantum pure state |ψ for subsequent preparation _ABEF >Provides support to obtain the target quantum state rho for subsequent efficient estimation _AB Lays a foundation for the maximum unidirectional distillable entanglement.

Further, in a specific example, a method for preparing the quantum pure state |ψ by using the target spectrum decomposition result is provided _ABEF >Specifically, the above is based on the target quantum state ρ _AB Generates quantum pure state |psi as the target spectrum decomposition result _ABEF >(i.e., step S102 described above), specifically includes:

determining the calculated basis i'> _EF The method comprises the steps of carrying out a first treatment on the surface of the Here, the base |i 'is calculated'> _EF Is equal to the number of target quantum states ρ _AB I' is equal to or less than the target quantum state ρ _AB A positive integer of dimensions of (2); for example, calculate the base |i'> _EF Is equal to the number of target quantum states ρ _AB Is a dimension of (2); i' has a value of 1 or more and 2 or less ²ⁿ Is a positive integer of (2);

based on the target quantum state ρ _AB Target spectral decomposition results of (2) and computing basis i'> _EF Generating quantum pure state |psi _ABEF >。

For example, the quantum pure state |ψ _ABEF >Can be calculated by the following specific expression:

here, the describedIs a tensor product operator; d, d _AB For the target quantum state ρ _AB Dimension of (d) _AB ＝2 ²ⁿ 。

Thus, the present disclosure provides a method for obtaining a target quantum state ρ using a specific spectral decomposition scheme _AB In this way, a target quantum state ρ is obtained for subsequent use of the parameterized quantum circuit _AB Expansion of the Quantum state sigma _ABE The method provides support, and further lays a foundation for the effective estimation of the unidirectional distillable entanglement of the target quantum state to be completed in a follow-up efficient manner.

In a specific example of the disclosed scheme, the target parameterized quantum circuit may be constructed in such a way that, in particular, the quantum pure state |ψ _ABEF >Before acting on the target parametric quantum circuit (i.e. before step S103 described above), the method further comprises:

creating a vector containing the adjustable parameters over successive (2n+2k) qubits in an initial quantum circuit (e.g., a blank quantum circuit)Obtaining the target parameterized quantum circuit; that is, at least part of the sub-circuits in the target parametric sub-circuit are parametric sub-circuits, e.g., the parametric sub-circuits in the target parametric sub-circuit are denoted +.>

Further, the initial quantum circuit is a blank quantum circuit containing 2 (2n+k) quantum bits. Accordingly, the preset parameterized quantum circuit is at least used for creating entanglement between at least partial qubits corresponding to the continuous (2n+2k) qubits, that is, the preset parameterized quantum circuit creates entanglement between the qubits corresponding to the continuous (2n+2k) qubits in the initial quantum circuit.

Further, the parameterized sub-circuit in the target parameterized quantum circuitCorresponding continuous (2n+2k) qubits, corresponding to extended quantum system W andan auxiliary quantum system F; the parameterized sub-circuit is removed from the target parameterized quantum circuit>The remaining 2n qubits are consecutive in addition to the corresponding consecutive 2n+2k qubits, and the remaining consecutive 2n qubits correspond to the target quantum system AB.

Further, the parameterized subcircuit of the target parameterized quantum circuitK continuous qubits corresponding to the extended quantum system E; parameterized sub-circuit of the target parameterized quantum circuit +.>The remaining consecutive 2n+k qubits, excluding the consecutive k qubits, correspond to the auxiliary quantum system F.

Further, in a specific example, 2n consecutive qubits in the target parameterized quantum circuit corresponding to the target quantum system AB are located in the first 2n qubits, or the last 2n qubits in the target parameterized quantum circuit.

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

Alternatively, in another example, the qubits corresponding to the first 2n+k consecutive qubits in the blank quantum circuit may be used as the sub-circuit corresponding to the auxiliary quantum system F, that is, 2n+k qubits correspond to the auxiliary quantum system F; further, the quantum bits corresponding to the 2n+k+1th quantum bit to the 2n+2k quantum bit are used as sub-circuits corresponding to the extended quantum system E, namely the 2n+k+1th quantum bit to the 2n+2k quantum bit, and the extended quantum system E is correspondingly extended; and taking the quantum bit corresponding to the last 2n quantum bits as a sub-circuit corresponding to the target quantum system AB, namely, the last 2n 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 previous 2n+2k consecutive qubits, to obtain a target parameterized quantum circuit.

Here, it can be appreciated that the parameterized sub-circuits in the target parameterized quantum circuitThe preset parameterized quantum circuit is obtained.

It should be noted that, in the examples shown in fig. 2 (a), fig. 2 (b) and fig. 2 (c), the target quantum system AB and the extended quantum system E may be collectively referred to as a total extended quantum system, for example, may be denoted as a total extended quantum system ABE; the extended quantum system E and the auxiliary quantum system may be collectively referred to as a total auxiliary quantum system, e.g., denoted as total auxiliary quantum system EF.

Therefore, the scheme of the disclosure provides a construction scheme of 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 the estimated value of the unidirectional distillable entanglement of the target quantum state.

Further, in a specific example, the predetermined parametric quantum circuit (i.e., parametric sub-circuit) Comprising parameters acting on qubitsThe single bit quantum gate is functionalized and a double bit quantum gate is created that entangles 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 vectorIs formed based on an adjustable rotation parameter 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 estimated value of unidirectional distillable entanglement of the target quantum state can be effectively improved.

Further, in a specific example, 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 estimated value of unidirectional distillable entanglement of the target quantum state can be effectively improved.

For example, the parameterized subcircuitComprises a D-layer sub-circuit, wherein the parameterized sub-circuitCan be specifically expressed as:

wherein the saidRepresenting the s-th layer sub-circuit in the parameterized sub-circuit. Further, an adjustable parameter vector ++>Can be specifically expressed as +.>Said->Representing layer s subcircuitsIs provided.

Here, s is a positive integer of 1 or more and D or less.

Further, assume a parameterized subcircuitThe circuit structure of each layer of sub-circuit is the same, and the adjustable parameters in each layer of sub-circuit are also the same; at this time, the s-th layer->For example, as shown in FIG. 2 (d), the +.>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 (2n+2k) adjustable rotation parameters.

Further, as shown in FIG. 2 (d), theAlso included are strong entanglement structures such as:

a CNOT gate acting on two adjacent qubits; for example, a CNOT gate controlled by the first qubit in the parameterized subcircuit and acting on the first +1st qubit; here, l is equal to or greater than 1 and equal to or less than 2n+2k-1;

a CNOT gate acting on the last qubit and the first qubit in the parameterized subcircuit; for example, the last qubit in the parameterized sub-circuit is controlled and the CNOT gate of the first qubit in the parameterized sub-circuit is acted upon.

It is necessary to say thatIt is clear that the parameterized subcircuit described aboveThe circuit structure of (a) is merely exemplary, and other structures are possible in practical application, and the scheme of the present disclosure is not limited thereto.

In a specific example of the present disclosure, fig. 3 is a schematic diagram of an implementation flow diagram of a method of estimating distillable entanglement 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. It will be appreciated that the relevant content of the method shown in fig. 1 above may also be applied to this example, and this example will not be repeated for the relevant content.

Further, the method includes at least part of the following. As shown in fig. 3, includes:

step S301: obtaining the target quantum state rho _AB 。

Further, the first quantum system A comprises n quantum bits; the second quantum system B comprises n quantum bits; n is a positive integer greater than or equal to 1;

step S302: based on the target quantum state ρ _AB Generates quantum pure state |psi as the target spectrum decomposition result _ABEF >。

Here, the relevant content of the target spectrum decomposition result may be referred to the above description, and will not be described herein.

Step S303: the quantum pure state |psi is processed _ABEF >Acting on target parameterizationSub-circuit, obtain the output quantum state of the total extended quantum system corresponding to the target quantum system AB and extended quantum system E in the said target parametric quantum circuit

Here, the relevant content of the target parametric quantum circuit may be referred to the above description, and will not be repeated here.

Step S304: obtaining a quantum state based on the output The constructed target loss function L->Is set, the objective function value of (a).

Step S305: based on the objective function value, the objective quantum state rho is obtained _AB Is a one-way distillable entanglement estimate.

Here, the target quantum state ρ _AB Is the target quantum state ρ _AB Is a unidirectional distillable entanglement upper bound.

In this way, the scheme of the disclosure utilizes the parameterized quantum circuit to estimate and obtain the estimated value of the maximum unidirectional distillable entanglement of the target quantum state, and is applicable to any quantum state, so that the scheme has strong universality.

Further, in a specific example of the disclosed approach, the objective loss function, in particular, the objective loss function, may be constructed in the following mannerIs based on the output quantum state sigma _ABE Is of coherent information of (a)The output quantum state->Degradation index eta (sigma) of (C) _A|BE The obtained product.

Here, the output quantum state σ _ABE Is of coherent information of (a)The expression of (c) may be specifically:

here, H (·) represents von neumann entropy (von Neumann entropy); sigma (sigma) _BE ＝Tr _A (σ _ABE ) Representing the output quantum state sigma _ABE A bias trace on the first quantum system a.

Further, output quantum state σ _ABE Degradation index eta (ρ) of (a) _A|BE The expression of (c) may be specifically:

here ρ _AF ＝Tr _BE (σ _ABEF ) Representing the total output quantum state sigma _ABEF Trace off on the second quantum system B and the auxiliary quantum system F; sigma (sigma) _ABE ＝Tr _F (σ _ABEF ) Representation of taking the total output quantum state sigma _ABEF A bias trace on the auxiliary quantum system F;representing a full positive guard map (completely positive trace maps, CPTP); II ₁ Representing trace norm operators; the optimization problem can be solved by a semi-positive programming method.

Thus, a concrete scheme for constructing the target loss function is provided, the scheme has strong interpretability, and the meter can be greatly reducedThe complexity of calculation can quickly obtain the target quantum state rho _AB Is a one-way distillable entanglement estimate.

Further, in a specific example, the objective loss functionThe expression of (2) is:

here the number of the elements is the number,expressed as purified output quantum state->Required dimensions

At this time, after the objective function value is obtained, the objective function value is the objective quantum state ρ _AB An estimate of unidirectional distillable entanglement of (2) and the estimate is the target quantum state ρ _AB Is a unidirectional distillable entanglement upper bound.

Thus, the scheme provides a specific scheme for constructing the target loss function, which has strong interpretability, can greatly reduce the calculation complexity and can quickly obtain the target quantum state rho _AB Is a one-way distillable entanglement estimate.

In a specific example of the disclosed approach, the objective loss function L may be derived based on the followingIs set according to the objective function value of (1); in particular, the above-mentioned derivation is based on the output quantum state +.>Constructed target loss function->Specifically, the objective function value of (1) includes:

to minimize the target loss functionFor a preset optimization target, for the target loss functionIs +.>Adjusting;

under the condition that the preset optimization condition is met is determined, obtaining a target loss functionIs set, the objective function value of (a).

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, for the target loss functionIs +.>Performing assignment, e.g. initial assignment +.>Thereby obtaining the output quantum state-based->Constructed target loss function->Function value of->The objective loss function is +.>Is +.>Making adjustments, e.g. from->Adjust to->Thus, the function value of the target loss function can be obtainedRepeating 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 an adjustable parameter vector->Target parameter value->The target parameter value +.>Corresponding objective function value->

Thus, the disclosed scheme provides a method for obtaining the target loss functionThe specific scheme of the objective function value of the (2) has strong interpretability, can greatly reduce the calculation complexity and can rapidly obtain the objective quantum state rho _AB Is a one-way distillable entanglement estimate.

The present disclosure is described in further detail below with reference to specific examples; the scheme of the disclosure provides a method for estimating unidirectional distillable entanglement of any entanglement, which obtains entanglement resources contained in the entanglement by estimating unidirectional distillable entanglement of the entanglement; specifically, the method estimates and obtains the upper bound of unidirectional distillable entanglement of any entanglement state by optimizing the adjustable parameters in the parameterized quantum circuit through machine learning, thereby making up the limitation of the existing scheme. Moreover, compared with the existing unidirectional entangled distillation upper boundary, the scheme disclosed by the invention has higher precision, and has high efficiency, practicability and universality. Here, high efficiency means that the maximum unidirectional distillable entanglement as accurate as possible can be efficiently obtained by continuous optimization by means of a machine learning method; the practicability is realized on the existing classical computer, and the estimation result can be obtained by using less calculation resources; versatility refers to the maximum unidirectional distillable entanglement that can be estimated for any given quantum state.

In a specific example, a parameterized quantum circuit used in the present disclosure 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 of the parameterized quantum circuit. Further, the optimization in the scheme disclosed by the disclosure is to optimize the parameter value of the adjustable parameter vector in the parameterized quantum circuit, so as to achieve the optimization goal.

Specifically, the present example gives a target quantum state ρ of a target quantum system AB (formed by a first quantum system a containing n qubits and a second quantum system B containing n qubits) containing 2n qubits _AB The target quantum state ρ _AB Is in an entangled state; further, the target quantum state ρ is measured _AB An important physical quantity of entanglement resources involved is unidirectional distillable entanglement, defined as: from a given target quantum state ρ by unidirectional local quantum operation and classical communication (i.e., unidirectional LOCC operation as described above) _AB The highest distillation ratio of the maximum entangled state is obtained, i.e. from a given target quantum state ρ _AB The number of entanglement bits in the limit case (i.e., the maximum number of entanglement bits) is obtained.

Based on this, unidirectional distillable entanglement, which can be noted as D _→ (ρ _AB ) The expression is as follows:

here, r is the variable to be solved; Λ represents all LOCC operations performed on the first and second quantum systems a and B;is the standard d-dimensional maximum entangled state, the d being related to the number of qubits contained in the first or second quantum system a or B, e.g. d=2 ⁿ 。

Further, the target quantum state ρ _AB Unidirectional distillable entanglement D of (2) _→ (ρ _AB ) The method can be equivalently expressed as the following formula, wherein the specific expression is as follows:

here the number of the elements is the number,pi represents all unidirectional LOCC operations, i.e. total unidirectional LOCC operations.

Here the number of the elements is the number,representing the target quantum state ρ _AB Is a function of the coherence information (coherent information); ρ _B ＝Tr _A (ρ _AB ) Representing the target quantum state ρ _AB A bias trace on the first quantum system a; h (. Cndot.) represents von Neumann entropy (von Neumann entropy).

Based on this, the first and second light sources,wherein, pi (ρ) _B )＝tr _A (∏(ρ _AB ))。

Further, for the target quantum state ρ _AB Is in a degradable state, the target quantum state ρ _AB Can be directly calculated by calculating the target quantum state rho _AB For a given positive integer k (k.gtoreq.1), the target quantum state ρ _AB Specific expressions of the unidirectional distillable entanglement are:

However, not an arbitrary target quantum state ρ _AB Are all degradable, in other words, not arbitrary target quantum state ρ _AB All have degradable properties; for target quantum states ρ without degradable properties _AB The target quantum state ρ can be estimated using approximate degradability (approximate degradable) _AB Maximum unidirectional distillable entanglement, i.e. the target quantum state ρ _AB The upper bound of unidirectional distillable entanglement of (1), namely:

wherein,,

here, η (ρ) _A|B For the target quantum state ρ _AB Degradation index (degradability parameter);representing the target quantum state ρ for purification _AB The dimensions of the quantum system required.

Further, the degradation index η (ρ) _A|B The expression of (2) is:

here ρ _AE ＝Tr _B (σ _ABE ) Representing the expansion of the quantum state sigma _ABE A bias trace on the second quantum system B;representing a full positive guard map (completely positive trace maps, CPTP); II ₁ Representing trace norm operators; in practical application, eta (rho) can be obtained by solving by a semi-positive programming method _A|B 。

Further, the present example adopts a form of adding an auxiliary system to construct an extended quantum state, and further estimates a target quantum state ρ without degradable property by using the extended quantum state _AB Is a unidirectional distillable entanglement upper bound.

Specifically, an extended quantum system E containing k quantum bits is prepared, wherein the value of k is an integer greater than or equal to 1; at the same time, an auxiliary quantum system F containing 2n+k quantum bits is prepared, and the auxiliary quantum system F is used for auxiliary generationArbitrary target quantum state ρ _AB Is of quantum pure state |psi _ABEF >The method comprises the steps of carrying out a first treatment on the surface of the And preparing a blank quantum circuit of 2 (2n+k) quantum bits.

It should be noted that, in a specific example, as shown in fig. 3, in the blank quantum circuit, the quantum bits corresponding to the first 2n consecutive quantum bits are used as the sub-circuits corresponding to the target quantum system AB, that is, the first 2n quantum bits correspond to the target quantum system AB; in the blank quantum circuit, the quantum bits corresponding to the 2n+1th quantum bit to the 2n+k th quantum bit are used as sub-circuits corresponding to the extended quantum system E, namely the 2n+1th quantum bit to the 2n+k th quantum bit, and the extended quantum system E is correspondingly extended; in the blank quantum circuit, the quantum bit corresponding to the last 2n+k quantum bits is used as a sub-circuit corresponding to the auxiliary quantum system F, namely the last 2n+k quantum bits correspond to the auxiliary quantum system F. At this time, the qubit corresponding to 2 (2n+k) qubits in the blank quantum circuit is used as a circuit corresponding to the total quantum system ABEF.

Here, the dimension of the target quantum system AB can be denoted as d _AB And d _AB ＝2 ²ⁿ The method comprises the steps of carrying out a first treatment on the surface of the The dimension of the extended quantum system E can be recorded as d _E And d _E ＝2 ^k The method comprises the steps of carrying out a first treatment on the surface of the The dimension of the auxiliary quantum system F is denoted as d _F And d is as follows _F ＝2 ^2n+k 。

Further, quantum pure state |psi is prepared by using expansion quantum system E and auxiliary quantum system F _ABEF >The method comprises the following steps: for any target quantum state ρ of input _AB Performing spectral decomposition to obtain a target quantum state rho _AB The specific expression is as follows:

here, |i > is the target quantum state ρ _AB Is lambda _i For the eigenvector |i>Corresponding characteristic values.

Preparing a calculated basis i'> _EF And based on the calculated basis i'> _EF Decomposition results with target spectrumObtaining the target quantum state rho _AB Is of the quantum state |ψ _ABEF >May also be referred to as quantum pure states; i.e. quantum pure state |ψ _ABEF >The specific expression of (2) is:

here, the base |i 'is calculated'> _EF Is equal to the number of target quantum states ρ _AB Is a dimension of (2); i' has a value of 1 or more and 2 or less ²ⁿ Is a positive integer of (a).

Further, a pre-set parameterized quantum circuit containing (2n+2k) quantum bits is prepared, and as shown in fig. 2 (b) or fig. 2 (c), the pre-set parameterized quantum circuit is applied to the extended quantum system E and the auxiliary quantum system F in the blank quantum circuit to obtain a target parameterized quantum circuit, where the parameterized sub-circuit in the target parameterized quantum circuit may be recorded as The parameterized sub-circuit->Can be specifically composed of N quantum gates, and the expression can be specifically:

here, the describedThe parameterized quantum gate acting on the total auxiliary quantum system EF is referred to as a j-th quantum gate, where j is a positive integer greater than or equal to 1 and less than or equal to N-1, α _j Represents the j quantum gate->Is provided;a quantum gate with a fixed parameter beta acting on the total auxiliary quantum system EF is shown. At this time, thenThe parameter vector composed of the adjustable parameters representing all parameterized quantum gates may be referred to as an adjustable parameter vector. />

It will be appreciated that the parameterized subcircuit described aboveThe expression form of (a) is only a specific example, in practical application, the parameter β is fixed to the quantum gate +.>The action position of (a) can be changed, for example, the expression can be specifically:

or,

in other words, the scheme of the present disclosure pairs parameterized subcircuitsIs not limited in its expression form.

In addition, the quantum gate with fixed parameter βMay refer specifically to one quantum gate, or to multiple quantum gates with fixed parameters, etc., nor is the disclosure limited thereto. It can be appreciated that if the parameter β is fixed the quantum gate +.>A plurality of quantum gates with fixed parameters are referred, and the parameter beta can be expressed by a parameter vector specifically; similarly, a parameterized quantum gate may also refer to a parameterized quantum gate, or a plurality of parameterized quantum gates, which is not limited in this disclosure; accordingly, if the quantum gate is parameterized, such as +. >Representing a plurality of parameterized quantum gates, in which case the parameter alpha is adjustable _j And may also be expressed specifically by a parameter vector.

Further, the quantum pure state |ψ prepared above is subjected to _ABEF >As the initial quantum state of the target parametric quantum circuit, the output quantum state of the total extended quantum system ABE corresponding to the target quantum system AB and the extended quantum system E in the target parametric quantum circuit is obtained(i.e., target quantum state ρ) _AB Expansion of Quantum states->) The output quantum state->The specific expression of (2) is:

here, I _AB Representing an identity matrix of the target quantum system AB; tr _F Representing a trace-off operator;representing tensor product operators.

Further, the target quantum state ρ _AB The upper bound of the unidirectional distillable entanglement of (c) can be expressed specifically as:

wherein,,

here the number of the elements is the number,to expand quantum state->Is a part of the information related to the data; sigma (sigma) _BE ＝Tr _A (σ _ABE ) Representing the expansion of the quantum state>A bias trace on the first quantum system a;Representing extended quantum states for purification>The dimensions of the desired quantum system are, for example +.>To expand quantum state->Degradation index of (c).

Here, the degradation index η (ρ) _A|BE The expression of (c) may be specifically:

wherein ρ is _AF ＝Tr _BE (σ _ABEF ) Representing the total output quantum state sigma of the total subsystem ABEF _ABEF Trace off on the second quantum system B and the auxiliary quantum system F; sigma (sigma) _ABE ＝Tr _F (σ _ABEF ) Representing the total output quantum state sigma _ABEF A bias trace on the auxiliary quantum system F;representing a CPTP map; II ₁ Representing trace norm operators.

At this time, the quantum state can be expanded through traversalObtaining the target quantum state rho _AB Upper bound of unidirectional distillable entanglement, i.e. upper bound D of unidirectional distillable entanglement _→ (ρ _AB ) The expression of (2) is further:

further, based on expanding quantum statesCoherent information and extended quantum states>Degradation index eta (sigma) of (C) _A|BE The objective loss function is constructed and can be described as +.>Namely:

here, the objective loss functionIs->Adjustable parameter vector in (a)For the variables to be optimized, the optimization objective is to minimize the objective loss function +.>For example, the objective loss function may be made +.>Minimizing to complete optimization and obtain an objective function value, and obtaining the objective quantum state ρ based on the objective function value _AB An estimate of the upper bound of unidirectional distillable entanglement.

A specific scheme for obtaining an estimate of the upper bound of the unidirectional distillable entanglement of any target quantum state using the target parametric quantum circuit is given below in conjunction with the specific figures.

Here, the inputs of this example are: target quantum state ρ of target quantum system AB containing 2n quantum bits _AB An extended quantum system E comprising k qubits, an auxiliary quantum system F comprising 2n+k qubits, a blank quantum circuit comprising 2 (2n+k) qubits, a predetermined parametric quantum circuit for acting on the extended quantum system E and the auxiliary quantum system F, and a predetermined number of computation bases i'> _EF . The output result is: target quantum state ρ _AB An estimate of the upper bound of unidirectional distillable entanglement.

As shown in fig. 4, the specific steps include:

step S401: input target quantum state ρ _AB An extended quantum system E comprising k qubits, an auxiliary quantum system F comprising 2n+k qubits, anBlank quantum circuit comprising 2 (2n+k) qubits, a preset parameterized quantum circuit comprising (2m+2k) qubits, and a computation basis i'> _EF 。

Step S402: the preset parameterized quantum circuit acts on two quantum systems corresponding to the expansion quantum system E and the auxiliary quantum system F in the blank quantum circuit to obtain a target parameterized quantum circuit, and at the moment, the parameterized sub-circuit in the target parameterized quantum circuit can be recorded as At the same time, an adjustable parameter vector is initialized>Is provided.

In a specific example, the sub-circuits are parameterizedThe method comprises the following steps:

at this time, alpha can be initialized ₁ ,α ₂ ,…α _N-1 。

Step S403: for the target quantum state ρ _AB Performing spectrum decomposition to obtain target spectrum decomposition result, namely |i>For the target quantum state ρ _AB Is lambda _i For the eigenvector |i>Corresponding characteristic values.

Step S404: based on the target spectral decomposition result and the calculated basis i'> _EF Obtaining the target quantum state rho _AB Is of quantum pure state |psi _ABEF >I.e.

It can be appreciated that quantum pure state |ψ is obtained _ABEF >The steps of (i.e., step S403 and step S404) and the step of obtaining the target parametric quantum circuit (i.e., step S402) may be exchanged, which is not limited by the scheme of the present disclosure.

Step S405: the quantum pure state |psi is processed _ABEF >As the input quantum state of the target parameterized quantum circuit, obtaining the output quantum state of the total expansion quantum system ABE corresponding to the expansion quantum system E and the target quantum system AB in the target parameterized quantum circuitTarget quantum state ρ _AB Expansion of Quantum states->The specific expression is as follows:

step S406: constructing an objective loss functionThe expression is as follows:

step S407: by gradient descent optimization or other optimization methods, for the adjustable parameter vector Adjustment is made to minimize the target loss function +.>In determining the target loss functionCount->Under the condition that the function value of (a) reaches the minimum value, an adjustable parameter vector is obtained>Can be described as the optimum parameter vector +.>At the same time, the minimum function value is obtained>(i.e., objective function values).

Step S408: outputting the minimum function valueThe minimum function value->Namely the target quantum state rho _AB An estimate of the upper bound of unidirectional distillable entanglement.

In summary, the following advantages exist in the solution of the present disclosure:

according to the scheme, the parameterized quantum circuit idea can be used, the adjustable parameters of the parameterized quantum gate are determined through a machine learning method, and further the estimated value of the upper bound of unidirectional distillable entanglement of a given entanglement state is estimated.

The second, this disclosure scheme has commonality; compared with the prior art, the method can estimate any entangled state, is not limited to a specific state or needs to construct a specific structure, and is high in universality.

Thirdly, the scheme disclosed by the invention has high efficiency; the scheme can obtain the upper bound of unidirectional distillable entanglement through machine learning optimization, and has higher accuracy. The scheme of the present disclosure achieves better effects than the existing scheme in a low noise entangled state scene.

Fourth, this disclosure scheme has the practicality, because this disclosure scheme has adopted parameterized quantum circuit, has had by a wide margin with the help of parameterized quantum circuit's power of calculation, need not artifical construction or split special structure, can estimate the upper bound that obtains one-way distillable entanglement, consequently, has stronger practicality.

Application presentation

This example performs entanglement distillation on 2-qubit Werner State. In particular, the specific form of the target quantum state used is

Wherein the parameters p e [ -1,1], d=4, v have the matrix form:

by utilizing the scheme disclosed by the invention, the estimated value of the unidirectional distillable entanglement upper bound can be obtained. As shown in fig. 5, I _c Coherent information representing the target quantum state, D, being a known lower bound _R Represents the unidirectional distillable entanglement boundary obtained by the prior scheme, D _→,PQC Representing the estimated unidirectional distillable entanglement upper bound of the disclosed solution, it can be seen from fig. 5 that the estimated value of the disclosed solution is closer to the existing lower bound, in other words, the disclosed solution is more accurate, than the existing solution.

The present disclosure also provides an estimation device for distillable entanglement, as shown in fig. 6, comprising:

an obtaining unit 601 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 the entangled state of the target quantum system AB containing 2n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A and a second quantum system B; the first quantum system A comprises n quantum bits; the second quantum system B comprisesThere are n qubits; n is a positive integer greater than or equal to 1;

a processing unit 602 for based on the target quantum state ρ _AB Generates quantum pure state |psi as the target spectrum decomposition result _ABEF >The method comprises the steps of carrying out a first treatment on the surface of the Wherein the target spectral decomposition result is for the target quantum state ρ _AB Carrying out spectrum decomposition to obtain the product; e represents an extended quantum system comprising k qubits for extending the target quantum system AB, F represents an auxiliary preparation of quantum pure state |ψ comprising (2n+k) qubits _ABEF >Auxiliary quantum systems of (a); k is a positive integer greater than or equal to 1; the quantum pure state |psi is processed _ABEF >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 Wherein the target parameterized quantum circuit comprises 2 (2n+k) qubits; / >An adjustable parameter vector representing the target parameterized quantum circuit; the output quantum state->For the target quantum state ρ _AB The expansion of quantum state; by means of the output quantum state->Obtaining the target quantum state rho _AB Is a one-way distillable entanglement estimate.

In a specific example of the disclosed scheme, the target quantum state ρ _AB Is the target quantum state ρ _AB Is a unidirectional distillable entanglement upper bound.

In a specific example of the present disclosure, the processing unit 602 is further configured to:

based on the target quantum state ρ _AB And the characteristic vector and the characteristic value corresponding to the characteristic vector to obtain the target quantum state rho _AB Target spectral decomposition results of (2).

In a specific example of the present disclosure, the processing unit 602 is specifically configured to:

determining the calculated basis i'> _EF The method comprises the steps of carrying out a first treatment on the surface of the Wherein, calculate the base |i'> _EF Is equal to the number of target quantum states ρ _AB Is related to the dimension of (a); i' is less than or equal to the target quantum state ρ _AB A positive integer of dimensions of (2);

based on the target quantum state ρ _AB Target spectral decomposition results of (2) and computing basis i'> _EF Generating quantum pure state |psi _ABEF 。

creating a vector containing the tunable parameters over successive (2n+2k) qubits in an initial quantum circuitObtaining the target parameterized quantum circuit; wherein at least part of the sub-circuits in the target parameterized quantum circuit are parameterized sub-circuits +.>

Wherein the initial quantum circuit is a blank quantum circuit containing 2 (2n+k) quantum bits;

the preset parameterized quantum circuit is at least used for establishing entanglement among at least partial qubits corresponding to continuous (2n+2k) qubits;

parameterized sub-circuits in the target parameterized quantum circuitCorresponding continuous (2n+2k) qubits, and corresponding expansion quantum system E and auxiliary quantum system F; the parameterized sub-circuit is removed from the target parameterized quantum circuit>The remaining 2n qubits are continuous except for the corresponding continuous 2n+2k qubits, and the remaining continuous 2n qubits correspond to the target quantum system AB;

parameterized subcircuit of the target parameterized quantum circuitK continuous qubits corresponding to the extended quantum system E; parameterized sub-circuit of the target parameterized quantum circuit +. >The remaining consecutive 2n+k qubits, excluding the consecutive k qubits, correspond to the auxiliary quantum system F.

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 vectorIs formed based on an adjustable rotation parameter in a parameterized single-bit quantum gate;

and/or the number of the groups of groups,

the two-bit quantum gate is a controlled NOT gate or a controlled unitary gate.

obtaining a quantum state based on the outputConstructed target loss function->Is set according to the objective function value of (1);

based on the objective function value, the objective quantum state rho is obtained _AB Is a one-way distillable entanglement estimate.

In a specific example of the disclosed solution, the objective loss functionBased on the output quantum state->Coherent information of- >The output quantum state->Degradation index eta (sigma) of (C) _A|BE The obtained product.

In a specific example of the disclosed solution, the objective loss functionThe expression of (2) is:

wherein,,expressed as purified output quantum state->The required dimensions.

under the condition that the preset optimization condition is met is determined, obtaining a target loss functionIs set, the objective function value of (a). />

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. 7 illustrates a schematic block diagram of an example computing device 700 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. 7, the apparatus 700 includes a computing unit 701 that can perform various appropriate actions and processes according to a computer program stored in a Read Only Memory (ROM) 702 or a computer program loaded from a storage unit 708 into a Random Access Memory (RAM) 703. In the RAM 703, various programs and data required for the operation of the device 700 may also be stored. The computing unit 701, the ROM 702, and the RAM 703 are connected to each other through a bus 704. An input/output (I/O) interface 705 is also connected to bus 704.

Various components in device 700 are connected to I/O interface 705, including: an input unit 706 such as a keyboard, a mouse, etc.; an output unit 707 such as various types of displays, speakers, and the like; a storage unit 708 such as a magnetic disk, an optical disk, or the like; and a communication unit 709 such as a network card, modem, wireless communication transceiver, etc. The communication unit 709 allows the device 700 to exchange information/data with other devices via a computer network, such as the internet, and/or various telecommunication networks.

The computing unit 701 may be a variety of general and/or special purpose processing components having processing and computing capabilities. Some examples of computing unit 701 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 701 performs the respective methods and processes described above, for example, a distillable entanglement estimation method. For example, in some embodiments, the distillable entanglement estimation method may be implemented as a computer software program tangibly embodied on a machine-readable medium, such as storage unit 708. In some embodiments, part or all of the computer program may be loaded and/or installed onto device 700 via ROM 702 and/or communication unit 709. When the computer program is loaded into RAM 703 and executed by the computing unit 701, one or more steps of the distillable entanglement estimation method described above may be performed. Alternatively, in other embodiments, the computing unit 701 may be configured to perform the distillable entanglement 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 distillable entanglement, comprising:

the quantum pure state |psi is processed _ABEF >Acting on a target parameterized quantum circuit to obtain an output quantum state of a total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system E in the target parameterized quantum circuitWherein the target parameterized quantum circuit comprises 2 (2n+k) qubits;Representing the target parameterTransforming an adjustable parameter vector of the quantum circuit; the output quantum state->For the target quantum state ρ _AB The expansion of quantum state;

2. The method of claim 1, wherein the target quantum state ρ _AB Is the target quantum state ρ _AB Is a unidirectional distillable entanglement upper bound.

3. The method of claim 1 or 2, further comprising:

4. A method according to claim 3, wherein the target quantum state ρ is based on _AB Generates quantum pure state |psi as the target spectrum decomposition result _ABEF >Comprising:

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

creating a vector containing the tunable parameters over successive (2n+2k) qubits in an initial quantum circuitObtaining the target parameterized quantum circuit; wherein at least part of the sub-circuits in the target parameterized quantum circuit are parameterized sub-circuits +. >

parameterized sub-circuits in the target parameterized quantum circuitCorresponding continuous (2n+2k) qubits, and corresponding expansion quantum system E and auxiliary quantum system F; removing the parameterized subcircuit from the target parameterized quantum circuitThe remaining 2n qubits are continuous except for the corresponding continuous 2n+2k qubits, and the remaining continuous 2n qubits correspond to the target quantum system AB;

parameterized subcircuit of the target parameterized quantum circuitK continuous qubits corresponding to the extended quantum system E; parameterized sub-circuit of the target parameterized quantum circuit +.>The remaining consecutive 2n+k qubits, excluding the consecutive k qubits, correspond to the auxiliary quantum system F.

6. The method of claim 5, 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.

7. The method of claim 6, wherein the parameterized single-bit quantum gate is a turngate comprising at least one adjustable rotation parameter; wherein the adjustable parameter vectorIs formed based on an adjustable rotation parameter in a parameterized single-bit quantum gate;

and/or the number of the groups of groups,

the two-bit quantum gate is a controlled NOT gate or a controlled unitary gate.

8. The method of any of claims 1-7, wherein the utilizing the output quantum stateObtaining the target quantum state rho _AB An estimate of unidirectional distillable entanglement comprising:

based on the objective function value, the objective is obtainedTarget sub-state ρ _AB Is a one-way distillable entanglement estimate.

9. The method of claim 8, wherein the objective loss functionBased on the output quantum state->Coherent information of->The output quantum state->Degradation index eta (sigma) of (C) _A|BE The obtained product.

10. The method of claim 9, wherein the objective loss functionThe expression of (2) is:

wherein,,expressed as purified output quantum state->The required dimensions.

11. The method of any of claims 8-10, wherein the deriving is based on the output quantum state Constructed target loss function->Comprises:

12. A distillable entanglement estimation device comprising:

a processing unit for based on the target quantum state ρ _AB Generates quantum pure state |psi as the target spectrum decomposition result _ABEF >The method comprises the steps of carrying out a first treatment on the surface of the Wherein the target spectral decomposition result is for the purposeTarget sub-state ρ _AB Carrying out spectrum decomposition to obtain the product; e represents an extended quantum system comprising k qubits for extending the target quantum system AB, F represents an auxiliary preparation of quantum pure state |ψ comprising (2n+k) qubits _ABEF >Auxiliary quantum systems of (a); k is a positive integer greater than or equal to 1; the quantum pure state |psi is processed _ABEF >Acting on a target parameterized quantum circuit to obtain an output quantum state of a total expansion quantum system corresponding to the target quantum system AB and the expansion quantum system E in the target parameterized quantum circuitWherein the target parameterized quantum circuit comprises 2 (2n+k) qubits;An adjustable parameter vector representing the target parameterized quantum circuit; the output quantum state->For the target quantum state ρ _AB The expansion of quantum state; by means of the output quantum state->Obtaining the target quantum state rho _AB Is a one-way distillable entanglement estimate.

13. The apparatus of claim 12, wherein the target quantum state ρ _AB Is the target quantum state ρ _AB Is a unidirectional distillable entanglement upper bound.

14. The apparatus of claim 12 or 13, wherein the processing unit is further configured to:

obtaining the target quantum state rho _AB Feature vector of (2), and feature corresponding to the feature vectorA value;

15. The apparatus of claim 14, wherein the processing unit is specifically configured to:

16. The apparatus of any of claims 12-15, wherein the processing unit is further to:

parameterized sub-circuits in the target parameterized quantum circuitCorresponding continuous (2n+2k) qubits, and corresponding expansion quantum system E and auxiliary quantum system F; removing the parameterized subcircuit from the target parameterized quantum circuit The remaining 2n qubits are continuous except for the corresponding continuous 2n+2k qubits, and the remaining continuous 2n qubits correspond to the target quantum system AB;

17. The apparatus of claim 16, 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.

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

and/or the number of the groups of groups,

the two-bit quantum gate is a controlled NOT gate or a controlled unitary gate.

19. The apparatus according to any of claims 12-18, wherein the processing unit is specifically configured to:

20. The apparatus of claim 19, wherein the objective loss functionBased on the output quantum state->Coherent information of->The output quantum state->Degradation index eta (sigma) of (C) _A|BE The obtained product.

21. The apparatus of claim 20, wherein the objective loss functionThe expression of (2) is:

wherein,,expressed as purified output quantum state->The required dimensions.

22. The apparatus according to any one of claims 19-21, wherein the processing unit is specifically configured to:

23. 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 11;

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 1-11.

24. 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 11;

alternatively, the computer instructions are for causing the computer to perform the method according to any one of claims 1-11.

25. A computer program product comprising a computer program which, when executed by at least one quantum processing unit, implements the method according to any of claims 1-11;

or the computer program, when executed by a processor, implements the method according to any of claims 1-11.