CN116484965A

CN116484965A - Method, device, equipment and storage medium for estimating distillable entanglement

Info

Publication number: CN116484965A
Application number: CN202310272675.0A
Authority: CN
Inventors: 朱成开; 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: 2023-07-25

Abstract

The present disclosure provides methods, apparatus, devices, and storage media for estimating distillable entanglement, relating to the field of computers, and in particular to the field of quantum computing. The specific implementation scheme is as follows: obtaining k target quantum states rho _AB The method comprises the steps of carrying out a first treatment on the surface of 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 containing n quantum bits and a second quantum system B containing n quantum bits; k is a given positive integer; obtaining quantum-classical information obtained after total unidirectional LOCC operation on k first quantum systems AUsing the quantum-classical informationEstimating to obtain the target quantum state rho _AB An estimate of unidirectional distillable entanglement of (c), said estimate being used to estimate said target quantum state ρ _AB Is a unidirectional distillable entanglement lower bound.

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 lower bound of One-way distillable entanglement (One-way distillable entanglement) for any entangled state, which can be used to better estimate the distillable entanglement for that entangled state. 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 k target quantum states rho _AB The method comprises the steps of carrying out a first treatment on the surface of the Wherein the k target quantum states ρ _AB Target quantum state ρ in (a) _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 containing n quantum bits and a second quantum system B containing n quantum bits; k is a given positive integer; n is a positive integer greater than or equal to 1;

obtaining quantum-classical information obtained after total unidirectional local quantum operation and classical communication LOCC operation on k first quantum systems AWherein A' represents a new first quantum system obtained after the first quantum system A is subjected to the total unidirectional LOCC operation; m represents a classical system;

using the quantum-classical informationEstimating the target quantum state rho corresponding to the positive integer k _AB An estimate of unidirectional distillable entanglement of (c), said estimate being used to estimate said target quantum stateρ _AB Is a unidirectional distillable entanglement lower bound.

According to another aspect of the present disclosure, there is provided a distillable entanglement estimation device comprising:

an acquisition unit for obtaining k target quantum states ρ _AB The method comprises the steps of carrying out a first treatment on the surface of the Wherein the k target quantum states ρ _AB Target quantum state ρ in (a) _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 containing n quantum bits and a second quantum system B containing n quantum bits; k is a given positive integer; n is a positive integer greater than or equal to 1;

the processing unit is used for acquiring quantum-classical information obtained after the total unidirectional local quantum operation and classical communication LOCC operation are performed on the k first quantum systems AWherein A' represents a new first quantum system obtained after the first quantum system A is subjected to the total unidirectional LOCC operation; m represents a classical system; by means of the quantum-classical information->Estimating the target quantum state rho corresponding to the positive integer k _AB An estimate of unidirectional distillable entanglement of (c), said estimate being used to estimate said target quantum state ρ _AB Is a unidirectional distillable entanglement lower bound.

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.

Thus, the present disclosure provides a method for quantum-classical information through unidirectional LOCC operationThe method is simple, convenient and efficient, can be realized in classical equipment in a simulation mode, has practicability, and simultaneously has high efficiency.

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;

FIG. 2 is a schematic diagram of a structure of a parameterized quantum circuit in accordance with 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 diagram of a structure of an estimation device that can distill entanglement according to an embodiment of the disclosure;

FIG. 6 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.

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, the quantum operation is 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, e.g., AThe quantum system formed by part of the qubits owned by lice can be called a first quantum system (can be marked as A), and the quantum system formed by the rest of the qubits owned by Bob can be called a second quantum system (can be marked as B), and at this time, the physical operations allowed by Alice and Bob are as follows: 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 k target quantum states rho _AB 。

Here, the k target quantum states ρ _AB Target quantum state ρ in (a) _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 containing n quantum bits and a second quantum system B containing n quantum bits; the k is a given positive integer, for example, a positive integer with a value greater than or equal to 2 can be specifically adopted; n is a positive integer greater than or equal to 1.

Step S102: obtaining quantum-classical information obtained after total unidirectional local quantum operation and classical communication LOCC operation on k first quantum systems A

Here, a' represents a new first quantum system obtained after performing a total unidirectional LOCC operation on the first quantum system a; m represents the classical system.

Step S103: using the quantum-classical informationEstimating the target quantum state rho corresponding to the positive integer k _AB Is a one-way distillable entanglement estimate.

Here, the estimation value is used to estimate the target quantum state ρ _AB Is a unidirectional distillable entanglement lower bound. Further, in an example, the estimated value is the target quantum state ρ _AB Is a unidirectional distillable entanglement lower bound.

Thus, the present public scheme provides a method for utilizing quantum-classical information To estimate the target quantum state ρ _AB The method has the advantages of high accuracy, high efficiency, practicability, universality and expansibility.

In a specific example, the total unidirectional LOCC operation includes at least one unidirectional LOCC operation. "unidirectional" in the unidirectional LOCC operation means that classical communication in the LOCC operation is unidirectional; for example, all classical communications are directed by one node to another; for example, the unidirectional LOCC operation may specifically perform a local quantum operation on a qubit (such as a qubit in the first quantum system a) in a laboratory where the first node (e.g., alice) is located, and send a measurement result obtained by the local quantum operation to the second node (e.g., bob) through classical communication, so that the second node performs the local quantum operation on a qubit (such as a qubit in the second quantum system B) in the laboratory where the second node itself is located based on the measurement result sent by the first node.

In a specific example of the disclosed aspects, the following means can be employedTo the quantum-classical informationSpecifically, the above-described acquisition of quantum-classical information obtained after total unidirectional LOCC operation on k first quantum systems a ∈ - >The method specifically comprises the following steps:

carrying out total unidirectional LOCC operation on a total system corresponding to the k first quantum systems A, wherein the total unidirectional LOCC operation comprises a plurality of unidirectional LOCC operations, and the unidirectional LOCC operation in the plurality of unidirectional LOCC operations comprises local quantum operations, classical communication in a specified direction and a classical system M for compounding with the quantum systems;

obtaining quantum-classical information corresponding to the A' BM of the quantum-classical system

Here, the quantum-classical system a 'BM is obtained by combining the system information of the new first quantum system a' with the system information of the classical system M; said quantum-classical informationSystem information that characterizes the quantum-classical system a' BM.

In a specific example of the disclosed approach, the new first quantum system a' may be obtained in the following manner; specifically, the total unidirectional LOCC operation is performed on the total system corresponding to the k first quantum systems a, so as to obtain the quantum-classical system a' BM Quantum-classical informationThe method specifically comprises the following steps:

will parameterize quantum circuitActing on k first quantum systems A to obtain k new first quantum systems A'; wherein (1)>Representing parameterized quantum circuits->Is provided;

compounding the total system information of the k new first quantum systems A 'with the system information of the classical system M to obtain quantum-classical information corresponding to the quantum-classical system A' BMWherein the quantum-classical information

Thus, by parameterizing the quantum circuitThe method is simple and convenient, has strong operability, can be realized in a classical computer in a simulation mode, and can obtain the target quantum state rho for subsequent efficient estimation _AB Establishes a foundation for the estimation value of unidirectional distillable entanglement.

Further, in a specific example, the parameterized quantum circuitThe number of the comprised qubits is equal to the number of the comprised qubits of the first quantum system AThe amounts are related. For example, the parameterized quantum circuit +.>The number of comprised qubits is equal to the number of comprised qubits of the first quantum system a, i.e. the parameterized quantum circuit->The number of qubits contained is n, so that the use of parameterized quantum circuits is facilitated >To perform a total unidirectional LOCC operation on the first quantum system a.

Further, in a specific example, the parameterized quantum circuitComprising a parameterized single-bit quantum gate acting on the qubits, and a double-bit quantum gate that causes entanglement between the two qubits.

Here, in one example, the parameterized single-bit quantum gate is a single-quantum bit rotation gate, such as a u3 gate, which includes three independently adjustable rotation parameters. Alternatively, in another specific example, the two-bit quantum gate is a controlled not gate (CNOT gate), or a controlled unitary gate.

Thus, the scheme of the disclosure provides a specific structure of the parameterized quantum circuit, and the structure can effectively improve the expression capacity of the quantum circuit, is simple and convenient to realize, and lays a foundation for reducing required computing resources.

For example, parameterized quantum circuitsComprises a D-layer sub-circuit, in which case the +.>Can be specifically expressed asWherein said->Representing an s-th layer sub-circuit in the parameterized quantum circuit. Further, an adjustable parameter vector ++>Can be specifically expressed asSaid->Representing the s-th layer sub-circuit->Is provided.

Here, s 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 affects the expressive power and training efficiency of the parameterized quantum circuit, and thus may be selected based on actual requirements.

It should be noted that, for the parameterized quantum circuit, 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, in an example, the quantum circuit is parameterizedCircuit junction of each layer of sub-circuitThe structure is the same, and the adjustable parameters in each layer of sub-circuit are also the same; for example, in layer s->For example, at this time, as shown in FIG. 2, theComprising 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 parameterized quantum circuit comprises 3Dn adjustable rotation parameters.

Further, as shown in FIG. 2, the Also included are strong entanglement structures such as:

a CNOT gate controlled by the first quantum bit in the parameterized quantum circuit and acting on the first +1th quantum bit; here, l is 1 or more and n-1 or less;

is controlled by the nth qubit in the parameterized quantum circuit and acts as a CNOT gate for the 1 st qubit in the parameterized quantum circuit.

It should be noted that the circuit structure of the parameterized quantum circuit is merely exemplary, and other structures are also possible in practical application, which is not limited in this disclosure.

In a specific example of the present disclosure, fig. 3 is a second 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 k target quantum states rho _AB 。

Step S302: will parameterize quantum circuitActing on k first quantum systems A to obtain k new first quantum systems A'; wherein (1)>Representing parameterized quantum circuits->Is described.

Step S303: compounding the total system information of the k new first quantum systems A 'with the system information of the classical system M to obtain quantum-classical information corresponding to the quantum-classical system A' BM

Here, quantum-classical informationSystem information that characterizes the quantum-classical system a' BM.

Step S304: obtaining quantum-classical basedInformation processing systemConstructed objective loss function Is set, the objective function value of (a).

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

Here, the target quantum state ρ _AB Is used to estimate the target quantum state ρ _AB Is a unidirectional distillable entanglement lower bound.

In this way, the scheme of the disclosure utilizes the parameterized quantum circuit to estimate the lower bound of unidirectional distillable entanglement of a given target quantum state, and is applicable to any entangled state, thus having stronger universality; moreover, compared with the prior art, the scheme disclosed by the invention has higher precision, and simultaneously has high efficiency, practicability and expansibility.

In a specific example of the disclosed solution, the objective loss functionIs based on the quantum-classical information +.>Coherent information of->The obtained product.

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 distillable entanglement estimate.

For example, in one example, quantum-classical information may be directly combined Is of coherent information of (a)Is the negative of +.>At this time, the objective loss functionThe specific expression is:

wherein the k is a positive integer greater than or equal to 2. At this time, after the objective function value is obtained.The objective function value is the objective quantum state rho corresponding to the positive integer k _AB Is a one-way distillable entanglement estimate.

Further, in another example, quantum-classical information may be basedIs of coherent information of (a)Obtaining said target loss function->For example, objective loss function->The specific expression is:

wherein a is a constant greater than 0 and less than 1. At this time, after the objective function value is obtained, namely the target quantum state rho corresponding to the positive integer k _AB Is a one-way distillable entanglement estimate.

Further, in a specific example, the value at a isIn the case of (2) said target loss function +.>The expression of (2) is:

at this time, after the objective function value is obtained, the negative number of the objective function value is the target quantum state ρ corresponding to the positive integer k _AB Is a one-way distillable entanglement estimate.

Here, quantum-classical informationCoherent information of->The expression of (c) may be specifically:

here, tr represents a trace operator; Said->Representing taking the quantum-classical information->After k new first quantum systems (i.e. A' ^k ) Upper trace.

In a specific example of the disclosed approach, the objective loss function may be obtained in the following mannerIs set according to the objective function value of (1); specifically, the above results are based on quantum-classical information +.> Constructed target loss function->Specifically, the objective function value (i.e., step S304 described above) 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 function Is 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 value 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 present 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 information based on quantum-classical->Constructed objective loss functionFunction value of->The gradient descent optimization method is utilized to optimize the target loss functionIs +.>Making adjustments, e.g. from->Adjust to->Thus, the function value of the target loss function can be obtained>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 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 functionTarget function of (2)The numerical value concrete scheme has strong interpretability, can greatly reduce the calculation complexity and can quickly obtain the target quantum state rho _AB Is a distillable entanglement estimate.

The present disclosure is described in further detail below with reference to specific examples; the example provides a method for estimating unidirectional distillable entanglement of an entanglement, which obtains entanglement resources contained in the entanglement by estimating unidirectional distillable entanglement of the entanglement; in particular, the method estimates the lower bound of unidirectional distillable entanglement for a given entanglement state by optimizing adjustable parameters in a parameterized quantum circuit through machine learning, and particularly for any purifiable noisy entanglement state, the scheme disclosed by the invention can obtain the lower bound value of unidirectional distillable entanglement. Moreover, compared with the prior art, the scheme disclosed by the invention has higher precision, and also has high efficiency, practicability, universality and expansibility. Here, high efficiency means that the scheme of the present disclosure can efficiently calculate the lower bound of unidirectional distillable entanglement for a given entanglement state; utility means that the disclosed solution can be implemented in classical computers; versatility refers to the entangled state in which the present disclosure scheme is applicable to general situations; the expansibility refers to the lower bound of unidirectional distillable entanglement that the scheme of the present disclosure can employ flexible, diverse parameterized quantum circuits to estimate a given entanglement state.

In a specific example, a parameterized quantum circuit (e.g., an equivalently parameterized, quantum circuit of unitary transformation U) used in the present disclosure may be comprised 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 E _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, unidirectional distillable entanglement E _D，→ (ρ _AB ) There are the following equivalent expressions:

here the number of the elements is the number,representing the target quantum state ρ _AB Is a part of the information related to the data; wherein tr represents a trace operator; ρ _B ＝Tr _A (ρ _AB ) Representing the target quantum state ρ _AB A bias trace on the first quantum system a.

Here, note Namely the quantum-classical information of the quantum-classical system A' BM; then->Representation->Is expressed as:

here the number of the elements is the number,said->Representing taking the quantum-classical information->After k new first quantum systems (i.e. A' ^k ) Upper trace.

Here, T denotes all unidirectional LOCC operations, i.e. total unidirectional LOCC operations.

Here, t= { T _i }，T _i Representing a unidirectional LOCC operation; further, note unidirectional LOCC operation T _i The following mapping relationship can be expressed: t (T) _i ：A _i →A′ _i M _i I.e. representing the current first quantum system A _i Performing one-way LOCC operation T _i Obtaining a new first quantum system A' _i And will be a new first quantum system A' _i And classical system M _i Compounding to obtain a quantum-classical system A' _i M _i . Here, classical system M _i Representing unidirectional LOCC operation T _i Classical system M used. At this time, the unidirectional LOCC operation T _i The quantum-classical system A 'obtained later' _i M _i The quantum-classical information of (2) can be expressed as:

here the number of the elements is the number,representing the current first quantum system A _i Performing one-way LOCC operation T _i The new first quantum system A 'obtained after' _i System information of (2); i i><i| _M Representing unidirectional LOCC operation T _i Classical system M corresponding to _i Is set in the system information of (a).

Note that when i=1, a ₁ =a; i=1, it means that the current first quantum system does not perform unidirectional LOCC operation, in other words, the current first quantum system is the original first quantum system a.

Based on this, the quantum-classical information of the resulting quantum-classical system a' M after this total unidirectional LOCC operation T can be expressed as:

wherein a' represents a new first quantum system after the first quantum system a performs the overall unidirectional LOCC operation T. ρ _A Representing a system quantum state of the first quantum system a;representing a first quantum system A _i Is a system quantum state of (2); m represents the dimension of the classical system M.

Here, in a specific example, the classical system M may be embodied as a classical register.

Further, when n is any positive integer and k (k is not less than 2) is given, a target quantum state is obtainedρ _AB One achievable distillation ratio of (2), namely:

here, f (ρ _AB K) is the target quantum state ρ corresponding to the given positive integer k _AB Is a unidirectional distillable entangled lower bound.

Further, in this example, it is assumed that the local quantum operation in one simplified overall unidirectional LOCC operation T is configured in the following manner: alice performs a unitary transformation locally and makes a projective measurement, while classical communication is Alice directed to Bob. Meanwhile, assume that dimension m=2 of classical system M.

At this time, in this example, the locally performed unitary transformation may be implemented by an equivalent parameterized quantum circuit; the parameterized quantum circuit for realizing unitary transformation isIn an example, the parameterized quantum circuit +.>Can be composed of N quantum gates, in which case the parameterized quantum circuit>Can be specifically expressed as:

here, the describedThe parameterized quantum gate acting on the first quantum system A may be 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; />The quantum gate with a fixed parameter beta acting on the first quantum system a is shown. At this time, then->The 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 above parameterized quantum circuitThe 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 is directed to parameterized quantum circuitsIs 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 will be appreciated that ifQuantum gate with fixed parameter beta>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.

Based on this, the unidirectional local loc operation T on the first quantum system a may be specifically implemented by acting the above-described parameterized quantum circuit on the first quantum system aThen, compounding with a classical system M to obtain a quantum-classical system A' BM; at this time, quantum-classical information of the quantum-classical system A' BM, i.e. +.>The concrete steps are as follows:

further, based onIs coherent (i.e->) An objective loss function (which can be denoted as L _ρ,k (U)), namely:

here, the objective loss functionMiddle parameterized quantum circuit->Is>For the variables to be optimized, the optimization objective is to minimize the objective loss function +.>In (a) and (b); for example, the objective loss function may be made +.>To complete the optimization and obtain the objective function value, and the objective quantum state ρ can be obtained based on the objective function value _AB Is a one-way distillable entanglement lower bound estimate.

A specific scheme for obtaining an estimate of the unidirectional distillable entanglement lower bound for a given target quantum state using a parameterized 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 2n quantum bits _AB Giving a positive integer k; alice performs unitary transformation locally and performs projection measurement on total unidirectional LOCC operation T, namely parameterized quantum circuitThe dimension M of classical system M, such as m=2. The output result is: the target quantum state ρ corresponding to the given positive integer k _AB Is a one-way distillable entanglement lower bound.

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

step S401: input target quantum state ρ _AB Dimension M of classical system M, such as m=2, positive integer k, and parameterized quantum circuitAnd initializing an adjustable parameter vector +>Of (i.e. alpha ₁ ，α ₂ ，…，α _j ,…，α _N-1 )。

It should be noted that the value of k is related to the precision, and the greater the value of k, the greater the precision. Similarly, the value of N is related to the expression capability and training effect required by the parameterized quantum circuit, in other words, the value of N is also related to the accuracy, based on which k and N can be set based on the actual requirement, which is not limited by the scheme of the present disclosure.

Step S402: alice is local and will parameterize the quantum circuitActing on k first quantum systems A (i.e. parameterized quantum circuits +) >Acting on a total system which is a system formed by k first quantum systems A), obtaining k new first quantum systems A ', and compositing total system information of the k new first quantum systems A' with system information of a classical system M to obtain a quantum-classical system A 'BM, wherein at the moment, the quantum-classical information of the quantum-classical system A' BM is->The expression of (2) is:

step S403: based on quantum-menstruationClassical informationObtaining quantum-classical information->Is of coherent information of (a)Namely:

here the number of the elements is the number,said->Representing taking the quantum-classical information->After k new first quantum systems (i.e. A' ^k ) Offset on the upper part; the tr represents a trace operator.

Step S404: based on quantum-classical informationCoherent information of->The following objective loss function L is constructed _ρ,k (U)：

Step S405: using gradient descent or other optimization methods on adjustable parameter vectorsAdjustment is made to minimize the target loss function +.>In determining the target loss function->When the function value of (a) reaches the minimum value or the set iteration number, stopping optimization, and obtaining an adjustable parameter vector +.>Can be described as the optimum parameter vector +.>At the same time, the minimum function value is obtained>(i.e., the objective function values described above).

Step S406: output ofAt this time, the +.>Namely the target quantum state rho _AB Is a one-way distillable entanglement lower bound.

Application presentation

Here, an experimental result of 5-copy (i.e., k=5) isomorphous state (isomorphous state) is given for reference, and a specific form of the individual isomorphous state is:

ρ(p)＝pΦ ⁺ +(1-p)I/4；

wherein, p and other square performance parameters phi ⁺ One of four Bell states, the matrix form of which is

The unidirectional distillable entanglement lower bound estimation values of the above-mentioned isostatically behavior are obtained by using the existing scheme and the scheme of the present disclosure, respectively, and specific values thereof are shown in the following table:

by training the parameterized quantum circuit, we can get the purified fidelity.

By comparison, the estimated value of the unidirectional distillable entanglement lower bound obtained by the scheme of the present disclosure has smaller difference from the existing optimal upper bound, so that a more accurate estimated value of unidirectional distillable entanglement can be obtained (as shown in table 1). Here, the upper bound in the table above is the current optimal estimate of the unidirectional distillable entanglement upper bound.

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

firstly, the scheme disclosed by the invention can determine the adjustable parameters of the parameterized quantum gate by means of a parameterized quantum circuit and a machine learning method, namely can determine the specific form of local quantum operation which Alice needs to perform locally by means of the machine learning method, and further, gives an estimated value of the lower bound of unidirectional distillable entanglement of the target quantum state by utilizing unidirectional LOCC operation.

Second, the scheme of the present disclosure has versatility; the scheme disclosed by the disclosure is applicable to generalized distillable quantum states, is not limited to quantum states with specific structures, and is high in universality.

Thirdly, the scheme disclosed by the invention has high efficiency; the scheme disclosed by the disclosure can obtain the unidirectional distillable entangled lower bound through machine learning optimization, and is closer to the current optimal upper bound compared with the existing scheme, namely, the accuracy is higher compared with the existing scheme.

Fourth, the disclosed solution is expandable and practical; because the scheme adopts the parameterized quantum circuit, the flexible and diverse structure of the parameterized quantum circuit ensures that the scheme has strong expansibility and adaptability and can cope with different actual scenes.

The present disclosure also provides an estimation device for distillable entanglement, as shown in fig. 5, comprising:

an acquisition unit 501 for obtaining k target quantum states ρ _AB The method comprises the steps of carrying out a first treatment on the surface of the Wherein the k target quantum states ρ _AB Target quantum state ρ in (a) _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 containing n quantum bits and a second quantum system B containing n quantum bits; k is a given positive integer; n is a positive integer greater than or equal to 1;

A processing unit 502 for obtaining quantum-classical information obtained after performing total unidirectional local quantum operation and classical communication LOCC operation on k first quantum systems aWherein A' represents a new first quantum system obtained after the first quantum system A is subjected to the total unidirectional LOCC operation; m represents a classical system; by means of the quantum-classical information->Estimating the target quantum state rho corresponding to the positive integer k _AB An estimate of unidirectional distillable entanglement of (c), said estimate being used to estimate said target quantum state ρ _AB Is a unidirectional distillable entanglement lower bound.

In a specific example of the solution of the present disclosure, the processing unit 502 is specifically configured to:

carrying out total unidirectional LOCC operation on total systems corresponding to the k first quantum systems A; wherein the total unidirectional LOCC operation includes a plurality of unidirectional LOCC operations, one-way LOCC operations of the plurality of unidirectional LOCC operations including a local quantum operation, classical communication in a specified direction, and a classical system M for compounding with a quantum system;

obtaining quantum-classical information corresponding to the A' BM of the quantum-classical systemWherein the quantum-classical information +.>System information that characterizes the quantum-classical system a' BM.

In a specific example of the disclosed scheme, the parameterized quantum circuitThe number of qubits contained is related to the number of qubits contained in the first quantum system a.

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

obtaining quantum-classical informationConstructed target loss function->Is set according to the objective function value of (1);

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

In a specific example of the disclosed solution, the objective loss functionThe expression of (2) is:wherein a is a constant greater than 0 and less than 1.

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 a processor, implements the method described above as applied to a classical computing device;

alternatively, the computer program, when executed by at least one quantum processing unit QPU, implements the method described as applied to a quantum computing device.

The present disclosure also provides a quantum computing device comprising:

at least one 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 quantum processing units (quantum processing unit, QPU), also referred to as quantum processors or quantum chips, used in the description of the present disclosure may relate to physical chips comprising a plurality of quantum bits 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. 6 illustrates a schematic block diagram of an example computing device 600 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. 6, the apparatus 600 includes a computing unit 601 that can perform various appropriate actions and processes according to a computer program stored in a Read Only Memory (ROM) 602 or a computer program loaded from a storage unit 608 into a Random Access Memory (RAM) 603. In the RAM 603, various programs and data required for the operation of the device 600 may also be stored. The computing unit 601, ROM 602, and RAM 603 are connected to each other by a bus 604. An input/output (I/O) interface 605 is also connected to bus 604.

Various components in the device 600 are connected to the I/O interface 605, including: an input unit 606 such as a keyboard, mouse, etc.; an output unit 607 such as various types of displays, speakers, and the like; a storage unit 608, such as a magnetic disk, optical disk, or the like; and a communication unit 609 such as a network card, modem, wireless communication transceiver, etc. The communication unit 609 allows the device 600 to exchange information/data with other devices via a computer network, such as the internet, and/or various telecommunication networks.

The computing unit 601 may be a variety of general and/or special purpose processing components having processing and computing capabilities. Some examples of computing unit 601 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 601 performs the respective methods and processes described above, such as 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 608. In some embodiments, part or all of the computer program may be loaded and/or installed onto the device 600 via the ROM 602 and/or the communication unit 609. When the computer program is loaded into RAM 603 and executed by the computing unit 601, one or more steps of the distillable entanglement estimation method described above may be performed. Alternatively, in other embodiments, the computing unit 601 may be configured to perform the distillable entanglement estimation method in any other suitable way (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:

using the quantum-classical informationEstimating the target quantum state rho corresponding to the positive integer k _AB An estimate of unidirectional distillable entanglement of (c), said estimate being used to estimate said target quantum state ρ _AB Is a unidirectional distillable entanglement lower bound.

2. The method of claim 1, wherein the obtaining of quantum-classical information obtained after total unidirectional LOCC operation on k first quantum systems aComprising the following steps:

obtaining quantum-classical information corresponding to the A' BM of the quantum-classical systemWherein the quantum-classical informationSystem information that characterizes the quantum-classical system a' BM.

3. The method of claim 2, wherein the overall unidirectional LOCC operation is performed on the overall system corresponding to the k first quantum systems a to obtain quantum-classical information corresponding to the quantum-classical system a' BMComprising the following steps:

will k newThe total system information of the first quantum system A 'is compounded with the system information of the classical system M to obtain quantum-classical information corresponding to the quantum-classical system A' BMWherein the quantum-classical information

4. The method of claim 3, wherein the parameterized quantum circuitThe number of qubits contained is related to the number of qubits contained in the first quantum system a.

5. The method of claim 3 or 4, wherein the parameterized quantum circuitComprising a parameterized single-bit quantum gate acting on the qubits, and a double-bit quantum gate that causes entanglement between the two qubits.

6. The method of any of claims 3-5, wherein the utilizing the quantum-classical information Estimating the target quantum state rho corresponding to the positive integer k _AB An estimate of unidirectional distillable entanglement comprising:

7. The method of claim 6, wherein the objective loss functionIs based on the quantum-classical information +.>Coherent information of->The obtained product.

8. The method of claim 7, wherein the objective loss functionThe expression of (2) is:

wherein a is a constant greater than 0 and less than 1.

9. The method of any of claims 6-8, wherein the deriving is based on quantum-classical informationConstructed target loss function->Is set to the target function value of (2)Comprising:

10. A distillable entanglement estimation device comprising:

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

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

13. The apparatus of claim 12, wherein the parameterized quantum circuitThe number of qubits contained is related to the number of qubits contained in the first quantum system a.

14. The apparatus of claim 12 or 13, wherein the parameterized quantum circuitComprising a parameterized single-bit quantum gate acting on the qubits, and a double-bit quantum gate that causes entanglement between the two qubits.

15. The apparatus according to any of claims 12-14, wherein the processing unit is specifically configured to:

based on the instituteThe objective function value is used for obtaining the objective quantum state rho corresponding to the positive integer k _AB Is a one-way distillable entanglement estimate.

16. The apparatus of claim 15, wherein the objective loss functionIs based on the quantum-classical information +.>Coherent information of->The obtained product.

17. The apparatus of claim 16, wherein the objective loss functionThe expression of (2) is:

wherein a is a constant greater than 0 and less than 1.

18. The apparatus according to any of claims 15-17, wherein the processing unit is specifically configured to:

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.

21. A computer program product comprising a computer program which, when executed by at least one quantum processing unit, implements the method according to any one of claims 1-9;

or the computer program, when executed by a processor, implements the method according to any of claims 1-9.