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

Abstract

The present disclosure provides a method, apparatus, device and storage medium for estimating distillable entanglement, which relates to the field of computers, and in particular to the field of quantum computing. The specific implementation scheme is: obtain k target quantum states ρ AB ; Target quantum state ρ AB represents the entangled state of a 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 qubits and a second quantum system B containing n qubits; k is a given positive integer; the quantum-classical information obtained after performing a total unidirectional LOCC operation on the k first quantum systems A is obtained, and the target quantum state ρ is estimated using the quantum-classical information. AB The estimated value of the one-way distillable entanglement is used to estimate the target quantum state ρ AB A lower bound on the one-way distillable entanglement of .

Description

Technical Field

[0001] The present disclosure relates to the field of computer technology, and in particular to the field of quantum computing technology. Background Art

[0002] In practical applications, calculating the quantum entanglement resources inherent in any entangled state is one of the most central problems in quantum information. For example, calculating the lower bound of the one-way distillable entanglement of any entangled state is crucial, as it can be used to better estimate the distillable entanglement of that state. However, estimating the one-way distillable entanglement of a given entangled state remains a difficult task in the field. Summary of the Invention

[0003] The present disclosure provides a method, apparatus, device, and storage medium for estimating distillable entanglement.

[0004] According to one aspect of the present disclosure, a method for estimating distillable entanglement is provided, comprising:

[0005] Get k target quantum states ρ AB ; Wherein, the k target quantum states ρ AB The target quantum state ρ in AB represents the entangled state of a target quantum system AB comprising 2n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A comprising n qubits and a second quantum system B comprising n qubits; k is a given positive integer; and n is a positive integer greater than or equal to 1;

[0006] Obtain the quantum-classical information obtained after performing a total one-way local quantum operation and classical communication LOCC operation on k first quantum systems A Where A′ represents the new first quantum system obtained by performing a total unidirectional LOCC operation on the first quantum system A; M represents the classical system;

[0007] Using the quantum-classical information Estimate the target quantum state ρ corresponding to the positive integer k AB The estimated value of the one-way distillable entanglement is used to estimate the target quantum state ρ AB A lower bound on the one-way distillable entanglement of .

[0008] According to another aspect of the present disclosure, a device for estimating distillable entanglement is provided, comprising:

[0009] Acquisition unit, used to obtain k target quantum states ρ AB ; Wherein, the k target quantum states ρ ABThe target quantum state ρ in AB represents the entangled state of a target quantum system AB comprising 2n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A comprising n qubits and a second quantum system B comprising n qubits; k is a given positive integer; and n is a positive integer greater than or equal to 1;

[0010] A processing unit for obtaining quantum-classical information obtained after performing a total one-way local quantum operation and a classical communication LOCC operation on k first quantum systems A Wherein, A′ represents the new first quantum system obtained by performing a total one-way LOCC operation on the first quantum system A; M represents the classical system; using the quantum-classical information Estimate the target quantum state ρ corresponding to the positive integer k AB The estimated value of the one-way distillable entanglement is used to estimate the target quantum state ρ AB A lower bound on the one-way distillable entanglement of .

[0011] According to another aspect of the present disclosure, there is provided a computing device, comprising:

[0012] At least one quantum processing unit (QPU);

[0013] a memory coupled to the at least one QPU and configured to store executable instructions,

[0014] The instructions are executed by the at least one QPU, so that the at least one QPU can perform the above method;

[0015] Alternatively, include:

[0016] at least one processor; and

[0017] a memory communicatively connected to the at least one processor; wherein,

[0018] The memory stores instructions that can be executed by the at least one processor. The instructions are executed by the at least one processor to enable the at least one processor to perform the above-mentioned method.

[0019] According to another aspect of the present disclosure, a non-transitory computer-readable storage medium storing computer instructions is provided. When executed by at least one quantum processing unit, the computer instructions cause the at least one quantum processing unit to perform the method described above.

[0020] Alternatively, the computer instructions are used to enable the computer to execute the above method.

[0021] According to yet another aspect of the present disclosure, there is provided a computer program product, comprising a computer program, which implements the above method when executed by at least one quantum processing unit;

[0022] Or the computer program implements the above method when executed by a processor.

[0023] Thus, the disclosed solution provides a method for obtaining quantum-classical information by a one-way LOCC operation. Moreover, this method is simple and efficient, can be simulated and implemented in classic equipment, is practical, and is also efficient.

[0024] It should be understood that the contents described in this section are not intended to identify the key or important features of the embodiments of the present disclosure, nor are they intended to limit the scope of the present disclosure. Other features of the present disclosure will become readily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings are provided to facilitate a better understanding of the present invention and do not constitute a limitation of the present disclosure.

[0026] Figure 1 This is a schematic diagram of the implementation process of the method for estimating distillable entanglement according to the embodiment of the present disclosure. Figure 1 ;

[0027] Figure 2 is a schematic diagram of the structure of a parameterized quantum circuit according to an embodiment of the present disclosure;

[0028] Figure 3 This is a schematic diagram of the implementation process of the method for estimating distillable entanglement according to the embodiment of the present disclosure. Figure 2 ;

[0029] Figure 4 1 is a schematic diagram of an implementation flow of a method for estimating distillable entanglement according to an embodiment of the present disclosure in a specific embodiment;

[0030] Figure 5 is a schematic structural diagram of an estimation device capable of distilling entanglement according to an embodiment of the present disclosure;

[0031] Figure 6 4 is a block diagram of a computing device used to implement the method for estimating distillable entanglement according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0032] The following description of exemplary embodiments of the present disclosure is made in conjunction with the accompanying drawings, including various details of the embodiments of the present disclosure to facilitate understanding, which should be considered as merely exemplary. Therefore, it should be appreciated by those skilled in the art that various changes and modifications may be made to the embodiments described herein without departing from the scope of the present disclosure. Similarly, for the sake of clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0033] The term "and / or" in this article is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. The term "at least one" in this article means any combination of at least two of any one or more of a plurality of. For example, including at least one of A, B, and C, can mean including any one or more elements selected from the set consisting of A, B, and C. The terms "first" and "second" in this article refer to multiple similar technical terms and distinguish them, and do not mean to limit the order or to limit to only two. For example, the first feature and the second feature refer to two categories / two features. The first feature can be one or more, and the second feature can also be one or more.

[0034] In addition, numerous specific details are provided in the following detailed description to better illustrate the present disclosure. Those skilled in the art will appreciate that the present disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art are not described in detail in order to highlight the main points of the present disclosure.

[0035] Quantum computing and quantum information theory are currently developing rapidly. More and more quantum technologies are emerging, the technology of quantum hardware is improving year by year, and quantum communication and quantum Internet are also developing continuously.

[0036] One of the most important resources in quantum technology is quantum entanglement. Quantum entanglement is a fundamental component of quantum computing and quantum information processing, and a key resource for various quantum information technologies, including quantum secure communication, quantum computing, and quantum networking. The most important entangled resource in quantum entanglement is the maximally entangled state. For example, for a quantum system containing two qubits, the maximally entangled state is the Bell state. Typically, Bell states are distributed across different sites or laboratories as resources. Furthermore, Bell states are a crucial foundational resource for quantum information schemes such as quantum key distribution, quantum superdense coding, and quantum teleportation.

[0037] In practical applications, calculating the quantum entanglement resources inherent in any entangled state is one of the most central problems in quantum information. For example, calculating the lower bound of the one-way distillable entanglement of any entangled state is crucial, as it can be used to better estimate the distillable entanglement of that state. However, estimating the one-way distillable entanglement of a given entangled state remains a difficult task in the field.

[0038] Furthermore, the quantum operation is described in detail; specifically, the target quantum state ρ of the two quantum systems (which can be recorded as the target quantum system AB) is AB (Also called entangled state ρ AB ) as an example. In this case, Alice and Bob, in their respective laboratories, possess some of the qubits in the target quantum system AB. For example, the quantum system formed by the qubits owned by Alice can be called the first quantum system (denoted as A), and the quantum system formed by the remaining qubits owned by Bob can be called the second quantum system (denoted as B). At this point, the physical operations allowed for Alice and Bob are: Alice and Bob perform local quantum operations and classical communication (LOCC) in their respective laboratories, which can be called LOCC operations. Here, quantum operations generally refer to quantum gates and quantum measurements acting on qubits, while local quantum operations mean that Alice and Bob can only perform quantum operations on qubits in their respective laboratories. Classical communication can be used for Alice and Bob to communicate the measurement results obtained from their respective local quantum operations (such as quantum measurements).

[0039] Based on the above local quantum operations and classical communication (i.e., LOCC operations), one-way distillable entanglement describes the process from a given target quantum state ρ to a given target quantum state ρ. AB , through the one-way LOCC operation, entanglement distillation (Entanglement distillation), or also called entanglement purification (Entanglement purification), so that the target quantum state ρ is obtained by distillation in the limit case AB The number of entangled bits, that is, the target quantum state ρ is obtained by distillation AB For example, for the maximum entangled state in d dimensions, the corresponding maximum number of entangled bits is log2 d. For example, the Bell state of a two-quantum system has a maximum number of entangled bits of 1.

[0040] Here, it should be pointed out that the "one-way" in the one-way LOCC operation means that the classical communication is one-way, for example, all classical communications are from Alice to Bob; or, all classical communications are from Bob to Alice; for example, the one-way LOCC operation may specifically refer to Alice performing local quantum operations on the quantum bits in her own laboratory, and informing Bob through classical communication, so that Bob can perform local quantum operations on the quantum bits in his own laboratory based on the measurement results informed by Alice; or, the one-way LOCC operation may specifically refer to Bob performing local quantum operations on the quantum bits in his own laboratory, and informing Alice through classical communication, so that Alice can perform local quantum operations on the quantum bits in her own laboratory based on the measurement results informed by Bob.

[0041] Therefore, one-way distillable entanglement provides a method to measure the entanglement of an entangled state from the perspective of quantum operation protocols. However, how to calculate the one-way distillable entanglement of a given entangled state as accurately as possible, so as to understand the quantum entanglement resources it contains, is an urgent problem to be solved.

[0042] Based on this, the disclosed solution proposes a method for estimating the one-way distillable entanglement of an entangled state, thus laying the foundation for subsequent understanding of the quantum entanglement resources contained in the entangled state.

[0043] Specifically, Figure 1 This is a schematic diagram of the implementation process of the method for estimating distillable entanglement according to the embodiment of the present disclosure. Figure 1 ; This method can be optionally applied to a quantum computing device that has both classical computing capabilities, or can be applied to a classical computing device that has both quantum computing capabilities, or directly applied to a classical computing device, such as a personal computer, server, server cluster, or other electronic device with classical computing capabilities, or directly applied to a quantum computer. The present disclosure does not impose any restrictions on this.

[0044] Furthermore, the method includes at least part of the following contents. Figure 1 Shown, including:

[0045] Step S101: Get k target quantum states ρ AB .

[0046] Here, the k target quantum states ρ AB The target quantum state ρ in AB represents the entangled state of a target quantum system AB comprising 2n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A comprising n qubits and a second quantum system B comprising n qubits; k is a given positive integer, such as a positive integer greater than or equal to 2; and n is a positive integer greater than or equal to 1.

[0047] Step S102: Obtain the quantum-classical information obtained after performing a total one-way local quantum operation and a classical communication LOCC operation on the k first quantum systems A

[0048] Here, A′ represents the new first quantum system obtained after performing a total unidirectional LOCC operation on the first quantum system A; M represents the classical system.

[0049] Step S103: Using the quantum-classical information Estimate the target quantum state ρ corresponding to the positive integer k AB An estimate of the one-way distillable entanglement of .

[0050] Here, the estimated value is used to estimate the target quantum state ρ AB The lower bound of the one-way distillable entanglement. Further, in one example, the estimated value is the target quantum state ρ AB A lower bound on the one-way distillable entanglement of .

[0051] Thus, the present scheme provides a method for utilizing quantum-classical information To estimate the target quantum state ρ AB The specific scheme for estimating the value of the one-way distillable entanglement is provided. Moreover, the scheme disclosed in the present invention has higher accuracy, and is also efficient, practical, universal and extensible.

[0052] In a specific example, the total unidirectional LOCC operation includes at least one unidirectional LOCC operation. The "unidirectional" in the unidirectional LOCC operation refers to the fact that the classical communication in the LOCC operation is unidirectional; for example, all classical communication is from one node to another node. For example, the unidirectional LOCC operation can specifically perform a local quantum operation on a qubit in a laboratory of a first node (e.g., Alice) (e.g., a qubit in a first quantum system A), and transmit the measurement result obtained from the local quantum operation to a second node (e.g., Bob) via classical communication, so that the second node can perform a local quantum operation on a qubit in its own laboratory (e.g., a qubit in a second quantum system B) based on the measurement result transmitted by the first node.

[0053] In a specific example of the disclosed solution, the quantum-classical information can be obtained in the following manner: Specifically, the above-mentioned quantum-classical information obtained after performing a total one-way LOCC operation on k first quantum systems A is obtained. Specifically include:

[0054] performing a total one-way LOCC operation on a total system corresponding to the k first quantum systems A, wherein the total one-way LOCC operation includes multiple one-way LOCC operations, and the one-way LOCC operations in the multiple one-way LOCC operations include a local quantum operation, classical communication in a specified direction, and a classical system M for combining with the quantum system;

[0055] Get the quantum-classical information corresponding to the quantum-classical system A′BM

[0056] 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; the quantum-classical information It can characterize the system information of the quantum-classical system A′BM.

[0057] Thus, the disclosed solution provides a method for obtaining quantum-classical information by a one-way LOCC operation. Moreover, this method is simple and efficient, can be simulated and implemented in classic equipment, is practical, and is also efficient.

[0058] In a specific example of the disclosed solution, the following method can be used to obtain a new first quantum system A′; specifically, the above-mentioned total unidirectional LOCC operation is performed on the total system corresponding to the k first quantum systems A to obtain the quantum-classical information corresponding to the quantum-classical system A′BM. Specifically include:

[0059] Parameterized quantum circuits Acting on k first quantum systems A, we get k new first quantum systems A′; where, Representing parameterized quantum circuits The adjustable parameter vector of ;

[0060] Combine the total system information of k new first quantum systems A′ with the system information of the classical system M to obtain the quantum-classical information corresponding to the quantum-classical system A′BM Wherein, the quantum-classical information

[0061] Thus, by parameterizing the quantum circuit To realize the local quantum operation in the total one-way LOCC operation, this method is simple, highly operable, and can be simulated in a classical computer, so that the target quantum state ρ can be obtained efficiently in the subsequent estimation. AB This lays the foundation for estimating the value of one-way distillable entanglement.

[0062] Furthermore, in a specific example, the parameterized quantum circuit The number of quantum bits included is related to the number of quantum bits included in the first quantum system A. For example, the parameterized quantum circuit The number of quantum bits contained is equal to the number of quantum bits contained in the first quantum system A, that is, the parameterized quantum circuit The number of quantum bits involved is n, so it is easy to use parameterized quantum circuits To perform a total unidirectional LOCC operation on the first quantum system A.

[0063] Furthermore, in a specific example, the parameterized quantum circuit It includes parameterized single-bit quantum gates that act on quantum bits, and two-bit quantum gates that create entanglement between two quantum bits.

[0064] Here, in one example, the parameterized single-bit quantum gate is a single-qubit 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.

[0065] In this way, the disclosed solution provides a specific structure of a parameterized quantum circuit, which can effectively improve the expressive power of the quantum circuit and is simple and easy to implement, laying the foundation for reducing the required computing resources.

[0066] For example, parameterized quantum circuits Contains D-layer sub-circuit, at this time, the It can be specifically expressed as Among them, the represents the s-th layer subcircuit in the parameterized quantum circuit. It can be specifically expressed as described Represents the s-th layer subcircuit The adjustable parameters in .

[0067] Here, s is a positive integer greater than or equal to 1 and less than or equal to D. D is a positive integer greater than or equal to 1. It should be noted that the value of D affects the expressiveness and training efficiency of the parameterized quantum circuit, and therefore, it can be selected based on actual needs.

[0068] It should be pointed out that for parameterized quantum circuits, the circuit structures of sub-circuits in different layers can be the same or different, and the present disclosure does not impose any restrictions on this. For example, a circuit template can be set, and different sub-circuits contain at least part of the structure in the circuit template. In this case, the circuit structures of different sub-circuits may be different, but they are all structures in the circuit template. In other words, the circuit structures of different sub-circuits are similar; moreover, the adjustable parameters in sub-circuits in different layers can be the same or different, and the present disclosure does not impose any restrictions on this.

[0069] Furthermore, in one example, the parameterized quantum circuit The circuit structure of each layer of sub-circuits is the same, and the adjustable parameters of each layer of sub-circuits are also the same; for example, in the sth layer For example, at this time, if Figure 2 As shown, the This includes a single-qubit rotation gate acting on each qubit, such as a u3 gate, which includes three independently adjustable rotation parameters, such as rotation angle X, rotation angle Y, and rotation angle Z. Based on this, the parameterized quantum circuit includes 3Dn adjustable rotation parameters.

[0070] Further, if Figure 2 As shown, the It also includes strongly entangled structures, such as:

[0071] A CNOT gate controlled by the lth qubit in the parameterized quantum circuit and acting on the l+1th qubit; where l is greater than or equal to 1 and less than or equal to n-1;

[0072] A CNOT gate controlled by the nth qubit in the parameterized quantum circuit and acting on the first qubit in the parameterized quantum circuit.

[0073] It should be noted that the circuit structure of the parameterized quantum circuit described above is only an example. In actual applications, other structures may be used, and the present disclosure does not limit this.

[0074] In a specific example of the present disclosure, Figure 3 This is a schematic diagram of the implementation process of the method for estimating distillable entanglement according to the embodiment of the present disclosure. Figure 2 The method can be optionally applied to a quantum computing device with classical computing capabilities, or to a classical computing device with quantum computing capabilities, or directly applied to a classical computing device, such as a personal computer, server, server cluster, or other electronic device with classical computing capabilities, or directly applied to a quantum computer, and the present disclosure does not impose any restrictions on this. It is understood that the above Figure 1 The relevant contents of the method shown can also be applied to this example, and this example will not elaborate on the relevant contents.

[0075] Furthermore, the method includes at least part of the following contents. Figure 3 Shown, including:

[0076] Step S301: Get k target quantum states ρ AB .

[0077] Here, the k target quantum states ρ AB The target quantum state ρ in AB represents the entangled state of a target quantum system AB comprising 2n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A comprising n qubits and a second quantum system B comprising n qubits; k is a given positive integer, such as a positive integer greater than or equal to 2; and n is a positive integer greater than or equal to 1.

[0078] Step S302: parameterize the quantum circuit Acting on k first quantum systems A, we get k new first quantum systems A′; where, Representing parameterized quantum circuits A vector of adjustable parameters.

[0079] Step S303: Combine the total system information of the k new first quantum systems A′ with the system information of the classical system M to obtain the quantum-classical information corresponding to the quantum-classical system A′BM

[0080] Here, quantum-classical information It can characterize the system information of the quantum-classical system A′BM.

[0081] Step S304: Obtaining quantum-classical information The constructed objective loss function The objective function value of .

[0082] Step S305: Based on the objective function value, obtain the target quantum state ρ corresponding to the positive integer k AB An estimate of the one-way distillable entanglement of .

[0083] Here, the target quantum state ρ AB The estimated value of the one-way distillable entanglement is used to estimate the target quantum state ρ AB A lower bound on the one-way distillable entanglement of .

[0084] In this way, the disclosed scheme uses parameterized quantum circuits to estimate the lower bound of the one-way distillable entanglement of a given target quantum state. This scheme is applicable to any entangled state and is therefore highly universal. Moreover, compared with existing schemes, the disclosed scheme has higher accuracy and is also efficient, practical, and scalable.

[0085] In a specific example of the disclosed solution, the objective loss function It is based on the quantum-classical information Related information Income.

[0086] Thus, the disclosed solution provides a specific solution for constructing the target loss function, which has strong interpretability and can greatly reduce the computational complexity and quickly obtain the target quantum state ρ AB An estimate of the distillable entanglement.

[0087] For example, in one example, quantum-classical information can be directly converted to Related information The negative number is used as the target loss function At this time, the objective loss function The specific expression is:

[0088]

[0089] Wherein, the value of k is a positive integer greater than or equal to 2. At this time, after obtaining the objective function value. The objective function value is the target quantum state ρ corresponding to the positive integer k AB An estimate of the one-way distillable entanglement of .

[0090] Furthermore, in another example, based on quantum-classical information Related information Get the target loss function For example, the target loss function The specific expression is:

[0091]

[0092] Wherein, a is a constant greater than 0 and less than 1. At this time, after obtaining the objective function value, That is, the target quantum state ρ corresponding to the positive integer k AB An estimate of the one-way distillable entanglement of .

[0093] Furthermore, in a specific example, when a is In the case of The expression is:

[0094]

[0095] At this time, after obtaining the objective function value, the negative of the objective function value is the target quantum state ρ corresponding to the positive integer k. AB An estimate of the one-way distillable entanglement of .

[0096] Here, quantum-classical information Related information The expression can be specifically as follows:

[0097]

[0098] Here, tr represents the trace operator; described Representation of quantum-classical information In k new first quantum systems (i.e. A′ k ) on the deviation track.

[0099] Thus, the disclosed solution provides a specific solution for constructing the target loss function, which has strong interpretability and can greatly reduce the computational complexity and quickly obtain the target quantum state ρ AB An estimate of the distillable entanglement.

[0100] In a specific example of the disclosed solution, the target loss function can be obtained in the following way: The objective function value of ; Specifically, the above is based on quantum-classical information The constructed objective loss function The objective function value (i.e., step S304 described above) specifically includes:

[0101] To minimize the objective loss function For the preset optimization target, the target loss function The adjustable parameter vector in Make adjustments;

[0102] When the preset optimization conditions are met, the target loss function is obtained. The objective function value of .

[0103] It should be noted that a gradient descent optimization method or other optimization method can be used to achieve the preset optimization goal; 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 by the current optimization process and the objective function value obtained by the previous optimization process is less than or equal to a preset threshold value. Here, the preset threshold value is an empirical value that can be set according to actual needs, and the present disclosure does not limit this. Alternatively, the preset optimization condition can also be specifically achieved by reaching a preset number of optimization iterations, that is, when the current number of iterations reaches the preset number of optimization iterations, it can be determined that the preset optimization condition is met.

[0104] For example, for the target loss function The adjustable parameter vector in Assign values, such as the initial assignment is Then we get the quantum-classical information The constructed objective loss function The function value of The objective loss function is optimized using the gradient descent optimization method The adjustable parameter vector in Make adjustments, such as Adjust to In this way, the function value of the target loss function can be obtained Repeat the above optimization process until the objective function value of the objective loss function converges to the minimum value or the actual optimization number reaches the preset optimization iteration number. At this time, the adjustable parameter vector is obtained. The target parameter value And the target parameter value The corresponding objective function value

[0105] Thus, the disclosed solution provides a method for obtaining a target loss function. The specific scheme of the objective function value is highly interpretable and can greatly reduce the computational complexity and quickly obtain the target quantum state ρ AB An estimate of the distillable entanglement.

[0106] The following is a detailed explanation of the disclosed solution with reference to specific examples. This example proposes a method for estimating the one-way distillable entanglement of an entangled state. This method estimates the entanglement resources contained in the entangled state by estimating the one-way distillable entanglement of the entangled state. Specifically, this method estimates the lower bound of the one-way distillable entanglement of a given entangled state by optimizing the adjustable parameters in a parameterized quantum circuit through machine learning. In particular, for any purifiable noisy entangled state, the disclosed solution can obtain a lower bound of its one-way distillable entanglement. Moreover, compared with existing solutions, the disclosed solution has higher accuracy and is also efficient, practical, universal, and extensible. Here, efficiency means that the disclosed scheme can efficiently calculate the lower bound of the one-way distillable entanglement of a given entangled state; practicality means that the disclosed scheme can be implemented in a classical computer; universality means that the disclosed scheme is applicable to entangled states in general situations; and extensibility means that the disclosed scheme can use flexible and diverse parameterized quantum circuits to estimate the lower bound of the one-way distillable entanglement of a given entangled state.

[0107] In a specific example, the parameterized quantum circuit used in the disclosed solution (e.g., the equivalent parameterized quantum circuit of the unitary transformation U) can be composed of several single-qubit rotation gates and controlled null-return gates (CNOT gates), where the rotation angles of the several single-qubit rotation gates constitute the adjustable parameter vector of the parameterized quantum circuit. Furthermore, the optimization described in the disclosed solution is to optimize the parameter value of the adjustable parameter vector in the parameterized quantum circuit, thereby achieving the optimization goal.

[0108] Specifically, this example gives a target quantum system AB containing 2n qubits (formed by a first quantum system A containing n qubits and a second quantum system B containing n qubits) with a target quantum state ρ AB , the target quantum state ρ AB is an entangled state; further, measure the target quantum state ρ AB An important physical quantity of the entanglement resource is the one-way distillable entanglement, which is defined as: from a given target quantum state ρ through one-way local quantum operation and classical communication (that is, the one-way LOCC operation mentioned above), AB The highest distillation ratio of the maximum entangled state is obtained from the given target quantum state ρ AB The number of entangled bits in the extreme case (that is, the maximum number of entangled bits) is obtained.

[0109] Based on this, one-way distillable entanglement can be recorded as E D，→ (ρ AB ), which is expressed as:

[0110]

[0111] Here, r is the variable to be solved; Λ represents all LOCC operations performed on the first quantum system A and the second quantum system B; is a standard d-dimensional maximally entangled state, where d is related to the number of quantum bits contained in the first quantum system A or the second quantum system B, for example, d = 2 n .

[0112] Furthermore, the one-way distillable entanglement E D，→ (ρ AB ) has the following equivalent expressions:

[0113]

[0114] here, represents the target quantum state ρ AB coherent information; wherein, tr represents the trace operator; ρ B =Tr A (ρ AB ), indicating the target quantum state ρ AB Deviation trace on the first quantum system A.

[0115] Here, remember That is the quantum-classical information of the quantum-classical system A′BM; then express The relevant information of is expressed as:

[0116]

[0117] here, described Representation of quantum-classical information In k new first quantum systems (i.e. A′ k ) on the deviation track.

[0118] Here, T represents all unidirectional LOCC operations, that is, total unidirectional LOCC operations.

[0119] Here, let T = {T i}, T i Indicates a one-way LOCC operation; further, the one-way LOCC operation T i The following mapping relationship can be expressed: T i :A i →A′ i M i , which means that the current first quantum system A i Perform one-way LOCC operation T i , and obtain the new first quantum system A′ i , and the new first quantum system A′i With the classic system M i Perform the compounding to obtain the quantum-classical system A′ i M i Here, the classical system M i Indicates one-way LOCC operation T i The classical system M is used. At this time, the one-way LOCC operation T i The resulting quantum-classical system A′ i M i The quantum-classical information can be expressed as:

[0120]

[0121] here, Represents the current first quantum system A i Perform one-way LOCC operation T i The new first quantum system A′ obtained i System information;|i> <i| M Indicates one-way LOCC operation T i The corresponding classical system M i System information.

[0122] It should be noted that when i=1, A1=A; that is, when i=1, it indicates that the current first quantum system does not perform a one-way LOCC operation. In other words, the current first quantum system is the original first quantum system A.

[0123] Based on this, the quantum-classical information of the quantum-classical system A′M obtained after the total one-way LOCC operation T can be expressed as:

[0124]

[0125] Where A′ represents the new first quantum system after the first quantum system A undergoes a total unidirectional LOCC operation T. A represents the system quantum state of the first quantum system A; Denotes the first quantum system A i The system quantum state; m represents the dimension of the classical system M.

[0126] Here, in a specific example, the classical system M may be specifically a classical register.

[0127] Furthermore, when n is any positive integer and k is given (k ≥ 2), the target quantum state ρ is obtained. AB An achievable distillation ratio is:

[0128]

[0129] Here, f(ρ AB ,k) is the target quantum state ρ corresponding to the given positive integer k AB A lower bound on one-way distillable entanglement.

[0130] Furthermore, in this example, we assume that the local quantum operations in a simplified total one-way LOCC operation T are constructed as follows: Alice performs a unitary transformation and a projection measurement locally, while the classical communication is from Alice to Bob. Furthermore, we assume that the dimension of the classical system M is m = 2.

[0131] At this point, in this example, the local unitary transformation can be realized by an equivalent parameterized quantum circuit; the parameterized quantum circuit that realizes the unitary transformation is denoted as In one example, the parameterized quantum circuit It can be composed of N quantum gates. In this case, the parameterized quantum circuit It can be specifically expressed as:

[0132]

[0133] Here, the represents the parameterized quantum gate acting on the first quantum system A, which can be called the jth 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 jth quantum gate Adjustable parameters; represents a quantum gate with fixed parameter β acting on the first quantum system A. In this case, The parameter vector consisting of the adjustable parameters of all parameterized quantum gates can be called the adjustable parameter vector.

[0134] It is understandable that the above parameterized quantum circuit The expression is only a specific example. In practical applications, the quantum gate with fixed parameter β The position of action can be changed. For example, the above expression can also be specifically expressed as:

[0135] or,

[0136]

[0137] In other words, the disclosed solution is effective for parameterized quantum circuits. There is no restriction on the form of expression.

[0138] In addition, it should be noted that the quantum gate with fixed parameter β It can specifically refer to a quantum gate, or multiple quantum gates with fixed parameters, etc., and the present disclosure does not limit this. It is understandable that if the quantum gate with fixed parameter β Refers to multiple quantum gates with fixed parameters. In this case, the parameter β can be specifically expressed by a parameter vector. Similarly, a parameterized quantum gate can also specifically refer to one parameterized quantum gate or multiple parameterized quantum gates. The present disclosure does not impose any restrictions on this. Accordingly, if a parameterized quantum gate, such as Represents multiple parameterized quantum gates, in which case the adjustable parameter α j It can also be specifically expressed through a parameter vector.

[0139] Based on this, the one-way local LOCC operation T is performed on the first quantum system A. Specifically, the parameterized quantum circuit described above is applied to the first quantum system A. After that, it is combined with the classical system M to obtain the quantum-classical system A′BM. At this time, the quantum-classical information of the quantum-classical system A′BM is Specifically expressed as:

[0140]

[0141] Further, based on The relevant information (i.e. ), construct the target loss function (which can be recorded as L ρ,k (U)), that is:

[0142]

[0143] Here, the objective loss function Parameterized quantum circuits The adjustable parameter vector is the variable to be optimized, and the optimization goal is to minimize the target loss function For example, gradient descent or other optimization methods can be used to make the objective loss function To complete the optimization, and obtain the objective function value, based on which the target quantum state ρ can be obtained AB An estimate of the lower bound on the one-way distillable entanglement.

[0144] The following is a specific scheme for using parameterized quantum circuits to obtain an estimated value of the lower bound of the one-way distillable entanglement of a given target quantum state, combined with specific figures.

[0145] Here, the input of this example is: a target quantum state ρ of a target quantum system AB containing 2n qubits AB , given a positive integer k; Alice performs a total one-way LOCC operation T locally by performing a unitary transformation and a projection measurement, i.e., a parameterized quantum circuit The dimension m of the classical system M is, for example, m = 2. The output result is: the target quantum state ρ corresponding to the given positive integer kAB An estimate of the lower bound of the one-way distillable entanglement.

[0146] like Figure 4 As shown, the specific steps include:

[0147] Step S401: Input target quantum state ρ AB , the dimension m of the classical system M, such as m = 2, the positive integer k, and the parameterized quantum circuit And initialize the adjustable parameter vector The adjustable parameters in (i.e. α1, α2, ..., α j ,…,α N-1 ).

[0148] It should be noted that the value of k is related to precision: a larger value of k results in greater precision. Similarly, the value of N is related to the expressive power and training effectiveness required for parameterizing quantum circuits. In other words, the value of N is also related to precision. Therefore, k and N can be set based on actual needs, and this disclosure does not impose any restrictions on this.

[0149] Step S402: Alice locally parameters the quantum circuit Act on k first quantum systems A (that is, parameterized quantum circuits Acting on a total system, which is a system formed by k first quantum systems A), k new first quantum systems A′ are obtained, and the total system information of the k new first quantum systems A′ is combined with the system information of the classical system M to obtain a quantum-classical system A′BM. At this time, the quantum-classical information of the quantum-classical system A′BM is The expression is:

[0150]

[0151] Step S403: Based on quantum-classical information Obtaining quantum-classical information Related information Right now:

[0152]

[0153] here, described Representation of quantum-classical information In k new first quantum systems (i.e. A′ k ) on the partial trace; the tr represents the trace operator.

[0154] Step S404: Based on quantum-classical information Related information Construct the following target loss function L ρ,k (U):

[0155]

[0156] Step S405: Use gradient descent or other optimization methods to optimize the adjustable parameter vector Adjust to minimize the objective loss function In determining the target loss function When the function value reaches the minimum or the set number of iterations, the optimization is stopped and the adjustable parameter vector is obtained. The optimal parameter value can be recorded as the optimal parameter vector At the same time, the minimum function value is obtained (That is, the objective function value mentioned above).

[0157] Step S406: Output At this time, the That is the target quantum state ρ AB An estimate of the lower bound of the one-way distillable entanglement.

[0158] Application Display

[0159] Here is a numerical experimental result of a 5-copy (i.e., k = 5) isotropic state for reference. The specific form of a single isotropic state is:

[0160] ρ(p)=pΦ + +(1-p)I / 4;

[0161] Among them, p isotropic parameters, Φ + is one of the four Bell states, and its matrix form is

[0162]

[0163] The estimated lower bounds of the one-way distillable entanglement of the above-mentioned isotropic state are obtained using the existing scheme and the disclosed scheme respectively. The specific values ​​are shown in the following table:

[0164] By training parameterized quantum circuits, we can obtain refined fidelity.

[0165]

[0166] By comparison, the difference between the estimated lower bound of one-way distillable entanglement obtained by the disclosed solution and the existing optimal upper bound is smaller, that is, a more accurate estimate of one-way distillable entanglement can be obtained (as shown in Table 1). Here, the upper bound in the above table is the current optimal estimate of the upper bound of one-way distillable entanglement.

[0167] In summary, the disclosed solution has the following advantages:

[0168] First, the disclosed solution can use parameterized quantum circuits and machine learning methods to determine the adjustable parameters of parameterized quantum gates. That is, it can determine the specific form of the local quantum operation that Alice needs to perform locally through machine learning methods. Then, using the one-way LOCC operation, it gives an estimated lower bound on the one-way distillable entanglement of the target quantum state. This solution is simple, can be implemented in classical devices, and has strong practicality.

[0169] Second, the disclosed solution is universal; the disclosed solution is applicable to generalized distillable quantum states and is not limited to quantum states of specific structures. Therefore, it has strong universality.

[0170] Third, the disclosed scheme is highly efficient; the lower bound of one-way distillable entanglement that can be obtained through machine learning optimization by the disclosed scheme is closer to the current optimal upper bound compared to existing schemes, that is, it is more accurate than existing schemes.

[0171] Fourth, the disclosed solution is scalable and practical; since the disclosed solution adopts parameterized quantum circuits, its flexible and diverse structure makes the disclosed solution highly scalable and adaptable, and can cope with different practical scenarios.

[0172] The disclosed solution also provides an estimation device capable of distilling entanglement, such as Figure 5 As shown, including:

[0173] Acquisition unit 501, used to obtain k target quantum states ρ AB ; Wherein, the k target quantum states ρ AB The target quantum state ρ in AB represents the entangled state of a target quantum system AB comprising 2n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A comprising n qubits and a second quantum system B comprising n qubits; k is a given positive integer; and n is a positive integer greater than or equal to 1;

[0174] Processing unit 502 is used to obtain quantum-classical information obtained after performing a total one-way local quantum operation and a classical communication LOCC operation on k first quantum systems A. Wherein, A′ represents the new first quantum system obtained by performing a total one-way LOCC operation on the first quantum system A; M represents the classical system; using the quantum-classical information Estimate the target quantum state ρ corresponding to the positive integer k AB The estimated value of the one-way distillable entanglement is used to estimate the target quantum state ρAB A lower bound on the one-way distillable entanglement of .

[0175] In a specific example of the disclosed solution, the processing unit 502 is specifically configured to:

[0176] Performing a total one-way LOCC operation on a total system corresponding to the k first quantum systems A; wherein the total one-way LOCC operation includes multiple one-way LOCC operations, and the one-way LOCC operations in the multiple one-way LOCC operations include a local quantum operation, classical communication in a specified direction, and a classical system M for combining with the quantum system;

[0177] Get the quantum-classical information corresponding to the quantum-classical system A′BM Wherein, the quantum-classical information It can characterize the system information of the quantum-classical system A′BM.

[0178] In a specific example of the disclosed solution, the processing unit 502 is specifically configured to:

[0179] Parameterized quantum circuits Acting on k first quantum systems A, we get k new first quantum systems A′; where, Representing parameterized quantum circuits The adjustable parameter vector of ;

[0180] Combine the total system information of k new first quantum systems A′ with the system information of the classical system M to obtain the quantum-classical information corresponding to the quantum-classical system A′BM Wherein, the quantum-classical information

[0181] In a specific example of the disclosed solution, the parameterized quantum circuit The number of quantum bits included is related to the number of quantum bits included in the first quantum system A.

[0182] In a specific example of the disclosed solution, the parameterized quantum circuit It includes parameterized single-bit quantum gates that act on quantum bits, and two-bit quantum gates that create entanglement between two quantum bits.

[0183] In a specific example of the disclosed solution, the processing unit 502 is specifically configured to:

[0184] Get based on quantum-classical information The constructed objective loss function The objective function value of

[0185] Based on the objective function value, the target quantum state ρ corresponding to the positive integer k is obtained. AB An estimate of the one-way distillable entanglement of .

[0186] In a specific example of the disclosed solution, the objective loss function It is based on the quantum-classical information Related information Income.

[0187] In a specific example of the disclosed solution, the objective loss function The expression is: Here, a is a constant greater than 0 and less than 1.

[0188] In a specific example of the disclosed solution, the processing unit 502 is specifically configured to:

[0189] To minimize the objective loss function For the preset optimization target, the target loss function The adjustable parameter vector in Make adjustments;

[0190] When the preset optimization conditions are met, the target loss function is obtained. The objective function value of .

[0191] For the description of specific functions and examples of each unit of the device in the embodiment of the present disclosure, please refer to the relevant description of the corresponding steps in the above method embodiment, which will not be repeated here.

[0192] The disclosed solution also provides a non-transitory computer-readable storage medium storing computer instructions. When executed by at least one quantum processing unit, the computer instructions cause the at least one quantum processing unit to perform the above method of applying a quantum computing device.

[0193] The present disclosure also provides a computer program product, including a computer program, which, when executed by a processor, implements the method described above as applied to a classical computing device;

[0194] Alternatively, the computer program, when executed by at least one quantum processing unit (QPU), implements the method described for use in a quantum computing device.

[0195] The present disclosure also provides a quantum computing device, comprising:

[0196] At least one quantum processing unit (QPU);

[0197] a memory coupled to the at least one QPU and configured to store executable instructions,

[0198] The instructions are executed by the at least one QPU to enable the at least one QPU to perform the method described for use in a quantum computing device.

[0199] It will be appreciated that the quantum processing unit (QPU) used in the present disclosure, which may also be referred to as a quantum processor or quantum chip, may involve a physical chip comprising a plurality of quantum bits interconnected in a specific manner.

[0200] Furthermore, it is understood that the qubit described in the present disclosure may refer to the basic information unit of a quantum computing device. A qubit is contained in a QPU and generalizes the concept of a classical digital bit.

[0201] Furthermore, according to an embodiment of the present disclosure, the present disclosure also provides a computing device, a readable storage medium, and a computer program product.

[0202] Figure 6 A schematic block diagram of an example computing device 600 that can be used to implement embodiments of the present disclosure is shown. Computing device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Computing device can also represent various forms of mobile devices, such as personal digital assistants, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are provided as examples only and are not intended to limit the implementation of the present disclosure described and / or claimed herein.

[0203] like Figure 6 As shown, the device 600 includes a computing unit 601, which 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. Various programs and data required for the operation of the device 600 can also be stored in the RAM 603. The computing unit 601, the ROM 602, and the RAM 603 are connected to each other via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0204] Various components in device 600 are connected to 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, etc.; a storage unit 608, such as a magnetic disk, optical disk, etc.; and a communication unit 609, such as a network card, modem, wireless communication transceiver, etc. The communication unit 609 allows device 600 to exchange information / data with other devices via a computer network such as the Internet and / or various telecommunication networks.

[0205] The computing unit 601 can be any general-purpose and / or specialized processing component with processing and computing capabilities. Some examples of the 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 appropriate processor, controller, microcontroller, etc. The computing unit 601 performs the various methods and processes described above, such as the method for estimating distillable entanglement. For example, in some embodiments, the method for estimating distillable entanglement can be implemented as a computer software program tangibly embodied in a machine-readable medium, such as the storage unit 608. In some embodiments, part or all of the computer program can be loaded and / or installed on the device 600 via the ROM 602 and / or the communication unit 609. When the computer program is loaded into the RAM 603 and executed by the computing unit 601, one or more steps of the method for estimating distillable entanglement described above can be performed. Alternatively, in other embodiments, the computing unit 601 may be configured to perform the distillable entanglement estimation method in any other appropriate manner (for example, by means of firmware).

[0206] Various embodiments of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), system-on-chip systems (SOCs), programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments can include being implemented in one or more computer programs that are executable and / or interpreted on a programmable system comprising at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0207] The program code for implementing the method of the present disclosure can be written in any combination of one or more programming languages. These program codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device so that when the program code is executed by the processor or controller, the functions / operations specified in the flow chart and / or block diagram are implemented. The program code can be executed entirely on the machine, partially on the machine, as a stand-alone software package, partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0208] In the context of the present disclosure, a machine-readable medium can be a tangible medium that can contain or store a program for use by or in conjunction with an instruction execution system, device or equipment. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium can include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium can include an electrical connection based on one or more lines, a portable computer disk, 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 disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0209] To provide interaction with a user, the systems and techniques described herein 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 the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0210] The systems and techniques described herein can be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, 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 a local area network (LAN), a wide area network (WAN), and the Internet.

[0211] A computer system may include a client and a server. The client and server are generally remote from each other and typically interact through a communication network. The client-server relationship arises through computer programs running on the respective computers and having a client-server relationship with each other. The server may be a cloud server, a server in a distributed system, or a server integrated with a blockchain.

[0212] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this disclosure can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in this disclosure can be achieved. This is not limited herein.

[0213] The above specific embodiments do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the principles of this disclosure shall be included within the scope of protection of this disclosure.

Claims

1. A method for estimating distillable entanglement, comprising: Get k target quantum states ρ AB ; Wherein, the k target quantum states ρ AB The target quantum state ρ in AB represents the entangled state of a target quantum system AB comprising 2n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A comprising n qubits and a second quantum system B comprising n qubits; k is a given positive integer; and n is a positive integer greater than or equal to 1; Obtain the quantum-classical information obtained after performing a total one-way local quantum operation and classical communication LOCC operation on k first quantum systems A Where A′ represents the new first quantum system obtained by performing a total unidirectional LOCC operation on the first quantum system A; M represents the classical system; Using the quantum-classical information Estimate the target quantum state ρ corresponding to the positive integer k AB The estimated value of the one-way distillable entanglement is used to estimate the target quantum state ρ AB The lower bound of the one-way distillable entanglement; Wherein, the use of the quantum-classical information Estimate the target quantum state ρ corresponding to the positive integer k AB The estimated value of the one-way distillable entanglement includes: Get based on quantum-classical information The constructed objective loss function in, Representation is used to construct quantum-classical information The parameterized quantum circuit of Representing parameterized quantum circuits The adjustable parameter vector of ; To minimize the objective loss function For the preset optimization target, the target loss function The adjustable parameter vector in Make adjustments; When the preset optimization conditions are met, the target loss function is obtained The objective function value of Based on the objective function value, the target quantum state ρ corresponding to the positive integer k is obtained. AB An estimate of the one-way distillable entanglement of .

2. The method according to claim 1, wherein The quantum-classical information obtained by performing a total one-way LOCC operation on k first quantum systems A is obtained include: Performing a total one-way LOCC operation on a total system corresponding to the k first quantum systems A; wherein the total one-way LOCC operation includes multiple one-way LOCC operations, and the one-way LOCC operations in the multiple one-way LOCC operations include a local quantum operation, classical communication in a specified direction, and a classical system M for combining with the quantum system; Get the quantum-classical information corresponding to the quantum-classical system A′BM Wherein, the quantum-classical information It can characterize the system information of the quantum-classical system A′BM.

3. The method according to claim 2, wherein: The total system corresponding to the k first quantum systems A is subjected to a total one-way LOCC operation to obtain the quantum-classical information corresponding to the quantum-classical system A′BM. include: Parameterized quantum circuits Acting on k first quantum systems A, we get k new first quantum systems A′; where, Representing parameterized quantum circuits The adjustable parameter vector of ; The total system information of k new first quantum systems A′ is combined with the system information of the classical system M to obtain the quantum-classical information corresponding to the quantum-classical system A′BM Wherein, the quantum-classical information 4. The method according to claim 3, wherein: The parameterized quantum circuit The number of quantum bits included is related to the number of quantum bits included in the first quantum system A.

5. The method according to claim 4, wherein The parameterized quantum circuit It includes parameterized single-bit quantum gates that act on quantum bits, and two-bit quantum gates that create entanglement between two quantum bits.

6. The method according to any one of claims 1 to 5, wherein: The objective loss function It is based on the quantum-classical information Related information Income.

7. The method according to claim 6, wherein: The objective loss function The expression is: Here, a is a constant greater than 0 and less than 1.

8. A device for estimating distillable entanglement, comprising: Acquisition unit, used to obtain k target quantum states ρ AB ; Wherein, the k target quantum states ρ AB The target quantum state ρ in AB represents the entangled state of a target quantum system AB comprising 2n qubits; the target quantum system AB is a double quantum system consisting of a first quantum system A comprising n qubits and a second quantum system B comprising n qubits; k is a given positive integer; and n is a positive integer greater than or equal to 1; A processing unit for obtaining quantum-classical information obtained after performing a total one-way local quantum operation and a classical communication LOCC operation on k first quantum systems A Wherein, A′ represents the new first quantum system obtained by performing a total one-way LOCC operation on the first quantum system A; M represents the classical system; using the quantum-classical information Estimate the target quantum state ρ corresponding to the positive integer k AB The estimated value of the one-way distillable entanglement is used to estimate the target quantum state ρ AB The lower bound of the one-way distillable entanglement; The processing unit is specifically configured to: Get based on quantum-classical information The constructed objective loss function in, Representation is used to construct quantum-classical information The parameterized quantum circuit of Representing parameterized quantum circuits The adjustable parameter vector of ; To minimize the objective loss function For the preset optimization target, the target loss function The adjustable parameter vector in Make adjustments; When the preset optimization conditions are met, the target loss function is obtained The objective function value of Based on the objective function value, the target quantum state ρ corresponding to the positive integer k is obtained. AB An estimate of the one-way distillable entanglement of .

9. The device according to claim 8, wherein The processing unit is specifically configured to: Performing a total one-way LOCC operation on a total system corresponding to the k first quantum systems A; wherein the total one-way LOCC operation includes multiple one-way LOCC operations, and the one-way LOCC operations in the multiple one-way LOCC operations include a local quantum operation, classical communication in a specified direction, and a classical system M for combining with the quantum system; Get the quantum-classical information corresponding to the quantum-classical system A′BM Wherein, the quantum-classical information It can characterize the system information of the quantum-classical system A′BM.

10. The device according to claim 9, wherein The processing unit is specifically configured to: Parameterized quantum circuits Acting on k first quantum systems A, we get k new first quantum systems A′; where, Representing parameterized quantum circuits The adjustable parameter vector of ; The total system information of k new first quantum systems A′ is combined with the system information of the classical system M to obtain the quantum-classical information corresponding to the quantum-classical system A′BM Wherein, the quantum-classical information 11. The device according to claim 10, wherein The parameterized quantum circuit The number of quantum bits included is related to the number of quantum bits included in the first quantum system A.

12. The device according to claim 11, wherein The parameterized quantum circuit It includes parameterized single-bit quantum gates that act on quantum bits, and two-bit quantum gates that create entanglement between two quantum bits.

13. The device according to any one of claims 8 to 12, wherein: The objective loss function It is based on the quantum-classical information Related information Income.

14. The device according to claim 13, wherein The objective loss function The expression is: Here, a is a constant greater than 0 and less than 1.

15. 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 of any one of claims 1 to 7; Alternatively, include: at least one processor; and a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method according to any one of claims 1 to 7.

16. A non-transitory computer-readable storage medium storing computer instructions, characterized in that: When executed by at least one quantum processing unit, the computer instructions cause the at least one quantum processing unit to perform the method according to any one of claims 1 to 7; Alternatively, the computer instructions are used to cause the computer to execute the method according to any one of claims 1 to 7.

17. 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 to 7; Or the computer program implements the method according to any one of claims 1 to 7 when executed by a processor.

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