Method, device, equipment and storage medium for determining quantum state components

Abstract

The present disclosure provides a method, apparatus, device, and storage medium for determining quantum state components, relating to the field of computer technology, particularly to the field of quantum computing technology. A specific implementation scheme is as follows: a component analysis step, including: in a current sub-process, when the total initial quantum state is used as the total input quantum state of a block-coded quantum circuit corresponding to a simulated block-coded unitary operator #imgabs0#, obtaining a first characteristic phase λ corresponding to the block-coded unitary operator #imgabs1#, and a first characteristic state corresponding to the first characteristic phase λ; when it is determined that the measurement result corresponding to the target auxiliary register in the block-coded quantum circuit meets a preset requirement, obtaining first component information of the target quantum state ρ based on the first characteristic phase λ and the first characteristic state corresponding to the first characteristic phase λ; the first component information includes at least one of the following: a target eigenvalue of the target quantum state ρ, and a target eigenstate corresponding to the target eigenvalue.

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] Extracting the components of a quantum state is generally very difficult. Classical computing often requires operations like tomography on the quantum state, which consumes resources exponentially with the size of the quantum system. Furthermore, computations on large-scale quantum systems are difficult. Furthermore, current approaches capable of performing quantum principal component analysis (QPCA) have high requirements for quantum circuit width. Therefore, based on recent quantum devices, more efficient and practical QPCA approaches are urgently needed. Summary of the Invention

[0003] The present disclosure provides a method, apparatus, device, and storage medium for determining quantum state components.

[0004] According to one aspect of the present disclosure, a method for determining a quantum state component is provided, comprising:

[0005] Component analysis step; wherein the component analysis step includes:

[0006] In the current sub-process, the total initial quantum state is used as the simulated block coded unitary operator Given the total input quantum state of the corresponding block-coded quantum circuit, the block-coded unitary operator is obtained The first characteristic phase λ corresponding to the first characteristic phase λ, and the first characteristic state corresponding to the first characteristic phase λ; wherein the first characteristic state corresponding to the first characteristic phase λ is the block coding unitary operator The system quantum state of the corresponding block-coded quantum system; the block-coded quantum system includes a first quantum system and a total auxiliary quantum system; the block-coded quantum circuit includes a target auxiliary register corresponding to the total auxiliary quantum system, and a target main register corresponding to the first quantum system; the total initial quantum state is obtained based on the target quantum state ρ of the first quantum system, and is a preset total initial quantum state, or the first characteristic state obtained in the previous process;

[0007] When it is determined that the measurement result corresponding to the target auxiliary register in the block coded quantum circuit meets preset requirements, first component information of the target quantum state ρ is obtained based on the first characteristic phase λ and the first characteristic state corresponding to the first characteristic phase λ; wherein the first component information includes at least one of the following: a target eigenvalue of the target quantum state ρ, and a target eigenstate corresponding to the target eigenvalue.

[0008] According to another aspect of the present disclosure, there is provided a device for determining a quantum state component, comprising:

[0009] A component processing unit is used to perform a component analysis step; wherein the component analysis step includes: in the current sub-process, the total initial quantum state is used as a simulated block coding unitary operator Given the total input quantum state of the corresponding block-coded quantum circuit, the block-coded unitary operator is obtained The first characteristic phase λ corresponding to the first characteristic phase λ, and the first characteristic state corresponding to the first characteristic phase λ; wherein the first characteristic state corresponding to the first characteristic phase λ is the block coding unitary operator The block coded quantum system includes a first quantum system and a total auxiliary quantum system; the block coded quantum circuit includes a target auxiliary register corresponding to the total auxiliary quantum system, and a target main register corresponding to the first quantum system; the total initial quantum state is obtained based on the target quantum state ρ of the first quantum system, which is a preset total initial quantum state or a first eigenstate obtained in a previous process; when it is determined that the measurement result corresponding to the target auxiliary register in the block coded quantum circuit meets a preset requirement, first component information of the target quantum state ρ is obtained based on the first eigenphase λ and the first eigenstate corresponding to the first eigenphase λ;

[0010] An output unit is used to output the first component information of the target quantum state ρ; wherein the first component information includes at least one of the following: a target eigenvalue of the target quantum state ρ, and a target eigenstate corresponding to the target eigenvalue.

[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] In this way, by using the block-coded quantum circuit corresponding to the target quantum state, the component information of the target quantum state is obtained. The circuit structure is simple, the required resources are low, and it is easier to implement on the recent quantum computer, which is highly practical. At the same time, the disclosed scheme does not need to block-code the unitary operator. Therefore, it has a wide range of application scenarios.

[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 determining the quantum state component according to the embodiment of the present disclosure. Figure 1 ;

[0027] Figure 2 This is a schematic diagram of the implementation process of the method for determining the quantum state component according to the embodiment of the present disclosure. Figure 2 ;

[0028] Figure 3 is a schematic diagram of the structure of a block-coded quantum circuit according to an embodiment of the present disclosure;

[0029] Figure 4(a) to Figure 4(c) is a schematic diagram of the structure of a preset parameterized quantum circuit according to an embodiment of the present disclosure;

[0030] FIG5( a ) and FIG5 ( b ) are schematic diagrams of the structure of a target quantum circuit according to an embodiment of the present disclosure;

[0031] Figure 6This is a schematic diagram of an implementation flow of a method for determining quantum state components according to an embodiment of the present disclosure in a specific embodiment;

[0032] Figure 7 This is a statistical diagram of characteristic values ​​in an example according to an embodiment of the present disclosure;

[0033] Figure 8 is a schematic structural diagram of a device for determining quantum state components according to an embodiment of the present disclosure;

[0034] Figure 9 4 is a block diagram of a computing device used to implement the method for determining quantum state components according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0035] 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.

[0036] 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.

[0037] 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.

[0038] The field of quantum computing has recently developed rapidly, progressing steadily towards scale and practical application, from quantum algorithms and quantum hardware devices to integrated quantum hardware and software platforms. Solving practical problems through quantum computing and achieving quantum advantage has attracted considerable attention. Within this area, analyzing the principal components of a system's quantum state, also known as quantum principal component analysis (QPCA), is a crucial issue. Quantum states represent the characteristics of a physical process, and determining their principal eigenvalues ​​and eigenvectors can be used to study quantum systems, which is of great significance for scientific research and industrial development. For example, QPCA can estimate the energies of different energy levels in a quantum system, which can then be applied to quantum chemistry analysis, such as obtaining detailed information about chemical reactions. Furthermore, multi-particle entangled states, which arise in condensed matter and quantum information, are extremely important. Extracting information about these quantum states has become a crucial task in experimental physics, for example, in confirming the preparation of three-photon and eight-ion entangled states, testing controlled NOT gates, and characterizing optical devices. Furthermore, determining the principal components of quantum systems is a core step in many quantum applications, such as quantum recommendation systems and quantum state resolution.

[0039] Generally speaking, extracting the principal components of a quantum state is extremely difficult. Classical computing, in order to accomplish this task, requires operations such as tomography of the quantum state. This resource consumption increases exponentially with the size of the quantum system, and computations on larger quantum systems are difficult. Furthermore, current solutions capable of performing quantum principal component analysis (QPCA) place high demands on the quantum circuit width, among other factors. Therefore, based on recent quantum devices, there is an urgent need for more efficient and practical QPCA solutions. These solutions could address the issue of the intrinsic energy of quantum systems while also facilitating more practical applications in quantum computing for solving chemistry and machine learning problems.

[0040] The following describes the core problem that quantum principal component analysis needs to solve: Mathematically, a quantum state can be represented as a positive semi-definite matrix with a trace of 1. For example, if a quantum system is composed of n qubits, then the quantum state ρ of the quantum system is a 2 n ×2 n The Hermitian matrix of , that is, a conjugate symmetric complex matrix, has non-negative eigenvalues ​​and tr(ρ)=1, where tr represents the trace.

[0041] In quantum computing, quantum states are typically prepared using a quantum circuit. Specifically, assuming that the quantum state ρ is a preparable quantum mixed state, there exists a unitary operator U or a quantum circuit corresponding to the unitary operator U (also known as an equivalent circuit of the unitary operator U). In this case, the unitary operator U or the quantum circuit corresponding to the unitary operator U can act on a dual quantum system (for example, comprising quantum system A and quantum system B), causing the state of one of the quantum systems to be ρ. This can be expressed mathematically as: U|0> BA =|Ψ> BA and tr B (|Ψ><Ψ|)=ρ, where tr B It means taking the deviation trace on quantum system B, and the state of quantum system A is ρ.

[0042] It should be noted that if the quantum state ρ represents the state corresponding to a quantum system composed of n qubits, then the quantum system A is also a quantum system composed of n qubits. The number of qubits contained in the quantum system B (which can be recorded as n) B ) must meet the following requirements:

[0043]

[0044] Based on this, the quantum principal component analysis problem of the disclosed solution can be described as follows: given a quantum circuit used to prepare a quantum state ρ, output an eigenvalue of the quantum state ρ and its corresponding eigenstate. Furthermore, output a larger eigenvalue of the quantum state ρ and the eigenstate corresponding to the larger eigenvalue.

[0045] Based on this, the disclosed solution provides a quantum state principal component analysis method to determine the eigenvalue of the target quantum state ρ and its corresponding eigenstate.

[0046] Specifically, Figure 1 This is a schematic diagram of the implementation process of the method for determining the quantum state component 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.

[0047] Furthermore, the method includes at least part of the following contents. Figure 1 As shown, the method for determining the quantum state components includes: a component analysis step; further, the component analysis step includes:

[0048] Step S101: In the current process, the total initial quantum state is used as the simulated block coded unitary operator Given the total input quantum state of the corresponding block-coded quantum circuit, the block-coded unitary operator is obtained The corresponding first characteristic phase λ, and the first characteristic state corresponding to the first characteristic phase λ.

[0049] Here, the first eigenstate corresponding to the first eigenphase λ is the block coding unitary operator The block-coded quantum system includes a first quantum system and a total auxiliary quantum system; the block-coded quantum circuit includes a target auxiliary register corresponding to the total auxiliary quantum system and a target main register corresponding to the first quantum system; the total initial quantum state is obtained based on the target quantum state ρ of the first quantum system, and is a preset total initial quantum state or a first eigenstate obtained in the previous process.

[0050] That is, the block coded quantum circuit is the quantum circuit corresponding to the block coded quantum system; accordingly, the target main register in the block coded quantum circuit corresponds to the first quantum system in the block coded quantum system, and the target auxiliary register in the block coded quantum circuit corresponds to the total auxiliary quantum system in the block coded quantum system.

[0051] Step S102: When it is determined that the measurement result corresponding to the target auxiliary register in the block coded quantum circuit meets a preset requirement, first component information of the target quantum state ρ is obtained based on the first characteristic phase λ and a first characteristic state corresponding to the first characteristic phase λ.

[0052] Here, the first component information includes at least one of the following: a target eigenvalue of the target quantum state ρ, and a target eigenstate corresponding to the target eigenvalue of the target quantum state ρ. For example, in one example, the first component information includes the target eigenvalue of the target quantum state ρ and the target eigenstate corresponding to the target eigenvalue of the target quantum state ρ; or, in another example, the first component information includes the target eigenvalue of the target quantum state ρ; or, in yet another example, the first component information includes the target eigenstate corresponding to the target eigenvalue of the target quantum state ρ.

[0053] In this way, the disclosed solution can use the block coding quantum circuit corresponding to the target quantum state to obtain the component information of the target quantum state. Moreover, the block coding quantum circuit used in the disclosed solution has a simple circuit structure and requires low resources. Therefore, it is easier to implement on the recent quantum computer and has strong practicality. At the same time, the disclosed solution does not need to block code the unitary operator. Therefore, it has a wide range of application scenarios.

[0054] It should be noted that a quantum state can be represented by its density matrix. For example, the target quantum state can be represented by the density matrix ρ of the target quantum state. In this case, it can be recorded as the target quantum state ρ.

[0055] In a specific example, the target quantum state ρ is obtained by using the target unitary operator U ρ Prepared; Accordingly, the block coding unitary operator is based on the target unitary operator U ρ Income.

[0056] For example, the block coded unitary operator It can be expressed as follows: the upper left corner is the unitary matrix of the density matrix ρ of the target quantum state, that is

[0057]

[0058] Figure 2 This is a schematic diagram of the implementation process of the method for determining the quantum state component 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.

[0059] Furthermore, the method includes at least part of the following contents. Figure 2 As shown, the method for determining the quantum state components includes: a component analysis step; further, the component analysis step includes:

[0060] Step S201: In the current process, the total initial quantum state is used as the simulated block coded unitary operator Given the total input quantum state of the corresponding block-coded quantum circuit, the block-coded unitary operator is obtained The corresponding first characteristic phase λ, and the first characteristic state corresponding to the first characteristic phase λ.

[0061] Here, the first eigenstate corresponding to the first eigenphase λ is the block coding unitary operator The block-coded quantum system includes a first quantum system and a total auxiliary quantum system; the block-coded quantum circuit includes a target auxiliary register corresponding to the total auxiliary quantum system and a target main register corresponding to the first quantum system.

[0062] Furthermore, in the disclosed solution, the total initial quantum state is obtained based on the target quantum state ρ of the first quantum system, which is a preset total initial quantum state. For example, in the first process, the total initial quantum state is a preset total initial quantum state, such as Here, BA refers to the total auxiliary quantum system. In other words, in the first pass, the input quantum state of the total auxiliary quantum system is the zero state, while the input quantum state of the first quantum system is the target quantum state ρ. Alternatively, in a non-first pass, the total initial quantum state, also known as the total input quantum state of the block-coded quantum circuit, or the total input quantum state of the block-coded quantum system, is the first eigenstate obtained in the previous pass, that is, the output quantum state of the block-coded quantum system in the previous pass.

[0063] Step S202: Determine whether the measurement result corresponding to the target auxiliary register in the block coded quantum circuit meets the preset requirements. If so, execute step S203; otherwise, execute step S204.

[0064] Step S203: obtaining first component information of the target quantum state ρ based on the first characteristic phase λ and the first characteristic state corresponding to the first characteristic phase λ.

[0065] Here, the first component information includes at least one of the following: a target eigenvalue of the target quantum state ρ, and a target eigenstate corresponding to the target eigenvalue of the target quantum state ρ.

[0066] Step S204: Update the total initial quantum state to the first characteristic state obtained by the current process, and return to step S201 to enter the next process to obtain the block coding unitary operator The corresponding new first characteristic phase λ and the first characteristic state corresponding to the new first characteristic phase λ are cycled in this way until the measurement result corresponding to the target auxiliary register meets the preset requirements.

[0067] In a specific example, if the measurement result corresponding to the target auxiliary register is a preset state, for example, a zero state, the preset requirement is met and step S203 is executed; otherwise, step S204 is executed. That is, when the measurement result indicates that the system quantum state of the total auxiliary quantum system is a zero state, the preset requirement is met. At this time, the block coded unitary operator can be obtained. The first component information of the target quantum state ρ is calculated based on the first characteristic phase λ and the first characteristic state corresponding to the first characteristic phase λ. Otherwise, the total initial quantum state is updated based on the first characteristic state obtained in the current process, and the next process is entered. This cycle continues until the measurement result corresponding to the target auxiliary register meets the preset requirements. At this time, the first component information of the target quantum state ρ can be obtained based on the most recently obtained first characteristic phase λ and the first characteristic state corresponding to the first characteristic phase λ.

[0068] It should be pointed out that the measurement results that meet the preset requirements, that is, the system quantum state of the total auxiliary quantum system, are related to the preset total initial quantum state in the first process, and further, are related to the input quantum state of the total auxiliary quantum system in the preset total initial quantum state of the first process. The present disclosure does not impose specific restrictions on this.

[0069] In a specific example, the input quantum state of the total auxiliary quantum system in the preset total initial quantum state of the first process is zero state. At this time, the measurement result that meets the preset requirements is also zero state. However, in actual applications, the input quantum state of the total auxiliary quantum system in the preset total initial quantum state of the first process can be based on a given target unitary operator U ρ And adjust.

[0070] For example, in a specific example, Figure 3 As shown, the block coding quantum circuit includes a target main register and a target auxiliary register; wherein the target main register corresponds to the first quantum system, and the target auxiliary register corresponds to the total auxiliary quantum system.

[0071] Furthermore, the total auxiliary quantum system includes a first subsystem (also referred to as subsystem A) and a second subsystem (also referred to as subsystem B). Accordingly, the first sub-auxiliary register in the block coded quantum circuit corresponds to the first subsystem, and the second sub-auxiliary register in the block coded quantum circuit corresponds to the second subsystem.

[0072] Furthermore, when the first quantum system contains n (a positive integer greater than or equal to 1) quantum bits, as Figure 3 As shown, the target main register contains n qubits; further, the first subsystem also contains n qubits, that is, the first sub-auxiliary register contains n qubits; the second subsystem contains n' qubits, that is, the second sub-auxiliary register contains n' qubits. At this time, the number of qubits contained in the block coded quantum circuit is: 2n+n'. Here, n is a positive integer greater than or equal to 1, and n' is a positive integer that satisfies 2 n′ ≤ rank(ρ) requires a positive integer.

[0073] Furthermore, the block-coded quantum circuit (according to the order of action of quantum gates) includes:

[0074] The target unitary operator U acting on the first sub-auxiliary register and the second sub-auxiliary register (that is, acting on the target auxiliary register) ρ ;

[0075] A SWAP gate acting on the target primary register and the first sub-auxiliary register;

[0076] The target unitary operator U acting on the first sub-auxiliary register and the second sub-auxiliary register (that is, acting on the target auxiliary register) ρ The conjugate transpose of

[0077] A reflection operator R is applied to the first sub-auxiliary register and the second sub-auxiliary register (ie, to the target auxiliary register).

[0078] Here, the target unitary operator U ρ is the unitary operator for preparing the target quantum state ρ, and is a known term. The SWAP gate is a quantum gate that can exchange two quantum systems (such as the first quantum system and the first subsystem); further, the reflection operator R (Reflector) is of the following form:

[0079]

[0080] Here, the is the initial quantum state of the first subsystem (ie, subsystem A) corresponding to the first sub-auxiliary register, is the initial quantum state of the second subsystem (ie, subsystem B) corresponding to the second sub-auxiliary register, Represents a tensor product operation, the I BA is the identity matrix.

[0081] Here, when the target unitary operator U ρ , SWAP gate, conjugate transpose And the reflection operator R is as follows Figure 3 After the construction shown, the block encoding unitary operator It can be expressed as: the upper left corner is the unitary matrix of the density matrix ρ of the target quantum state, that is

[0082]

[0083] In other words, at this time, the block coding unitary operator That is the block coding matrix of the target quantum state ρ. At this time, the block coding unitary operator can be used The corresponding eigenstate and eigenphase are used to obtain the target quantum state ρ, which is also the eigenstate and eigenphase of the first quantum system.

[0084] It should be noted that in the first process, Figure 3 The input quantum states of the two subsystems (i.e., subsystem A and subsystem B) shown in the figure can be fixed to zero state. At this time, the unitary operator acting on the two sub-quanta, i.e., the target unitary operator U ρ This satisfies:

[0085]

[0086] It should be noted that in actual application, the first process Figure 3 The input quantum states of the two subsystems (i.e., subsystem A and subsystem B) can be calculated based on the given target unitary operator U ρ The present disclosure does not impose any restrictions on adjustments, as long as the following requirements are met:

[0087]

[0088] Here, ρ B represents the input quantum state of subsystem B in the first process, ρ A represents the input quantum state of subsystem B in the first process. More generally, as long as the following requirements are met:

[0089]

[0090] In this way, the disclosed solution can utilize the block-coded quantum circuit corresponding to the target quantum state and determine the component information of the target quantum state based on the cyclic processing process; moreover, the block-coded quantum circuit used in the disclosed solution has a simple circuit structure and requires low resources, so it is easier to implement on recent quantum computers and has strong practicality. At the same time, the disclosed solution does not require the block-coded unitary operator. Therefore, it has a wide range of application scenarios.

[0091] In a specific example of the disclosed solution, the principal component information of the target quantum state ρ may also be obtained; specifically, the determination method further includes:

[0092] Performing the component analysis step multiple times to obtain multiple pieces of first component information of the target quantum state ρ;

[0093] Based on the multiple first component information of the target quantum state ρ, the principal component information of the target quantum state ρ is obtained; wherein the target eigenvalue corresponding to the principal component information of the target quantum state ρ is greater than the target eigenvalue corresponding to other first component information.

[0094] In a specific example, after performing multiple component analysis steps, multiple target eigenvalues ​​can be obtained. At this time, the largest target eigenvalue can be selected from the multiple target eigenvalues. The largest target eigenvalue and the target eigenstate corresponding to the largest target eigenvalue are the principal component information of the target quantum state ρ.

[0095] Thus, the disclosed solution provides a novel and efficient method for implementing quantum principal component analysis using block-coded quantum circuits. This solution is also more easily implemented on near-term quantum computers and has strong practicality. Furthermore, there is no need to specify the target quantum state ρ. In other words, the disclosed solution can extract the principal components of any quantum state, thus having a wide range of application scenarios.

[0096] In a specific example of the disclosed solution, the entanglement degree (such as entanglement spectrum) of the total auxiliary quantum system can also be obtained; specifically, the determination method further includes:

[0097] Entanglement spectrum determination step;

[0098] Furthermore, the entanglement spectrum determination step includes:

[0099] When multiple target eigenvalues ​​are obtained, at least two target eigenvalues ​​that meet the numerical requirements are selected from the multiple target eigenvalues, and based on the at least two selected target eigenvalues, the entangled spectrum of the two-component quantum state corresponding to the target quantum state ρ is obtained.

[0100] That is to say, when the target quantum state ρ is the quantum state corresponding to a quantum system in a two-component quantum system, the disclosed solution can also obtain the entanglement spectrum of the two-component quantum state corresponding to the two-component quantum system.

[0101] Here, the bipartite quantum state refers to the system quantum state of a bipartite quantum system consisting of the quantum system corresponding to the target quantum state ρ (i.e., the first quantum system described above) and another quantum system (which can be referred to as the second quantum system). For example, assuming the bipartite quantum state of the two quantum systems (i.e., the first quantum system and the second quantum system) is denoted by |ψ>, then the target quantum state ρ = Tr2(|ψ><ψ|), that is, the target quantum state ρ is equal to the partial trace of the bipartite quantum state |ψ> in the second quantum system.

[0102] For example, after obtaining multiple target eigenvalues, the multiple target eigenvalues ​​are arranged in descending order, and the top k target eigenvalues ​​are selected. The top k selected target eigenvalues ​​can then be used as an estimate of the degree of entanglement of the binary quantum state corresponding to the target quantum state ρ, such as an estimate of the entanglement spectrum.

[0103] In this way, the disclosed solution provides a novel and efficient solution for estimating the degree of entanglement using block-coded quantum circuits. This solution is easier to implement on recent quantum computers, has strong practicality, and has a wide range of application scenarios.

[0104] In a specific example of the presently disclosed scheme, the first component information of the target quantum state ρ can be obtained in the following manner; specifically, the above-described first component information of the target quantum state ρ based on the first characteristic phase λ and the first characteristic state corresponding to the first characteristic phase λ is obtained, specifically including: obtaining the target characteristic value of the target quantum state ρ based on the first characteristic phase λ; obtaining the target characteristic state corresponding to the target characteristic value of the target quantum state ρ based on the first characteristic state corresponding to the first characteristic phase λ.

[0105] In this way, the disclosed solution can use the block coded quantum circuit corresponding to the target quantum state to determine the target eigenvalue and target eigenstate of the target quantum state; moreover, the block coded quantum circuit used in the disclosed solution has a simple circuit structure and requires low resources, so it is easier to implement on a recent quantum computer and has strong practicality. At the same time, the disclosed solution does not need to block coded unitary operators. Therefore, it has a wide range of application scenarios.

[0106] Furthermore, in a specific example, the target eigenvalue of the target quantum state ρ can be obtained in the following manner. Specifically, the above-described method of obtaining the target eigenvalue of the target quantum state ρ based on the first characteristic phase λ specifically includes: obtaining the eigenvalue cos(λ) based on the first characteristic phase λ; wherein the eigenvalue cos(λ) is the target eigenvalue of the target quantum state ρ.

[0107] Furthermore, in a specific example, the target eigenstate corresponding to the target eigenvalue of the target quantum state ρ can be obtained in the following manner. Specifically, the above-described method of obtaining the target eigenstate corresponding to the target eigenvalue of the target quantum state ρ based on the first eigenstate corresponding to the first eigenphase λ specifically includes: obtaining the deviation trace of the first eigenstate on the total auxiliary quantum system based on the first eigenstate corresponding to the first eigenphase λ; wherein the deviation trace is the target eigenstate corresponding to the target eigenvalue of the target quantum state ρ.

[0108] For example, |target feature state>=tr BA (|first characteristic state>), where BA refers to the total auxiliary quantum system.

[0109] In this way, the disclosed solution can utilize the block-coded quantum circuit corresponding to the target quantum state to determine the target eigenvalue of the target quantum state and the target eigenstate corresponding to the target eigenvalue of the target quantum state. The process is simple, highly interpretable, and requires low resources. Therefore, it is easier to implement on recent quantum computers, has strong practicality, and also has a wide range of application scenarios.

[0110] In a specific example of the disclosed solution, the disclosed solution adopts a quantum phase search scheme to obtain a block coded unitary operator The corresponding first characteristic phase λ; the phase search scheme adopted by the disclosed solution is described in detail below. Specifically, the determination method further includes:

[0111] Quantum phase search step;

[0112] Furthermore, the quantum phase search step specifically includes:

[0113] Obtaining the block-coded unitary operator of a block-coded quantum system T phase estimation values; the T phase estimation values ​​meet the phase estimation accuracy requirement, and the value of T is at least related to the phase estimation accuracy requirement;

[0114] Based on this, the block coding unitary operator described above is obtained The corresponding first characteristic phase λ may specifically include: obtaining the block coding unitary operator based on the T phase estimation values The corresponding first characteristic phase λ. Here, the first characteristic phase λ is the block coding unitary operator The estimated value of the corresponding characteristic phase.

[0115] Here, the T phase estimation values ​​meet the phase estimation accuracy requirement, for example, each phase estimation value in the T phase estimation values ​​meets the phase estimation accuracy δ. Further, in one example, T is a positive integer greater than or equal to 1, and its value is at least related to the phase estimation accuracy requirement.

[0116] Thus, the disclosed solution obtains the block coded unitary operator by a quantum phase search scheme. T phase estimation values ​​are obtained, and then the block coding unitary operator is estimated The first eigenphase λ of the scheme is corresponding to the block coding unitary operator Without any restrictions, in other words, any block coding unitary operator can be implemented The corresponding characteristic phase estimation has strong versatility. Furthermore, the disclosed solution can also be applied to large-scale block coding unitary operators. Therefore, it is also scalable.

[0117] In addition, it should be noted that the disclosed solution does not require the preparation of block coding unitary operators. The characteristic state of , the block coding unitary operator can be searched The corresponding characteristic phase, therefore, has low resource consumption and a wider range of usage scenarios.

[0118] In a specific example of the disclosed solution, the t-th phase estimation value among the T phase estimation values ​​may be obtained in the following manner; specifically, the quantum phase search step further includes:

[0119] Based on the t-th phase search process, the t-th phase estimation value among the T phase estimation values ​​is obtained, where t is a positive integer greater than or equal to 1 and less than or equal to T. This process is repeated T times to obtain T phase estimation values.

[0120] Furthermore, the t-th phase search process includes:

[0121] Step 1: Determine the t-1th quantum related information required for the tth phase search process.

[0122] Here, the t-1th quantum-related information is obtained based on the t-1th phase search process. Further, in a specific example, the t-1th quantum-related information includes the output result of the t-1th phase search process, and the output result of the t-1th phase search process includes:

[0123] The t-1th phase estimate λ t-1 , the first unitary operator U t-1 , t-1th target interval, t-1th target output quantum state.

[0124] Here, the first unitary operator U t-1 is based on the t-1th phase estimate and the block coding unitary operator Determined; When t is equal to 1, the first unitary operator U0 is the block coding unitary operator When the value of t is 1, the 0th target output quantum state is the preset total initial quantum state, or the first characteristic state obtained in the previous process.

[0125] Step 2: Perform Q interval compression on the t-1th target interval in the t-1th quantum related information to obtain the first interval (t-1) Q .

[0126] Here, Q is a positive integer greater than or equal to 1. Furthermore, in practical applications, the value of Q is related to the accuracy of the output result, i.e., the first characteristic phase λ. For example, within a certain range, a larger value of Q results in a more accurate output result. Similarly, the value of T is also related to the accuracy of the output result, i.e., the first characteristic phase λ. For example, within a certain range, a larger value of T results in a more accurate output result.

[0127] Step 3: Based on the first interval (t-1) Q Get the t-th phase estimate, for example, denoted as λ t .

[0128] Furthermore, the output result of the t-th phase search process serves as the t-th quantum-related information; in this example, the t-th quantum-related information, that is, the output result of the t-th phase search process includes the t-th phase estimation value, thereby laying a data foundation for the subsequent t+1-th phase search process.

[0129] In this way, when t takes values ​​from 1 to T in sequence, the first phase estimate to the Tth phase estimate can be obtained in sequence, for a total of T phase estimates. In other words, steps 1 to 3 above provide the specific steps of the tth phase search process, and each phase search process can adopt the above steps. Furthermore, based on the above steps, it can be seen that the current phase search process depends on the processing results of the previous phase search process. For example, the tth phase search process depends on the output result of the t-1th phase search process, that is, the t-1th quantum related information. In this way, the cyclic processing can obtain T phase estimates.

[0130] Furthermore, in a specific example, the first characteristic phase here, The Δ is a preset constant.

[0131] In this way, the disclosed solution provides a method for estimating the tth phase estimation value through a phase search process, and then obtaining T phase estimation values. This solution requires low quantum resources, thereby increasing the feasibility of solving quantum characteristics with medium-scale quantum computing devices.

[0132] In a specific example of the disclosed solution, the t-th phase search process also requires the first interval (t-1) Q Perform the update process, and thus obtain another output result of the t-th phase search process, namely the t-th target interval, which provides data support for the smooth execution of the subsequent t+1-th phase search process. Specifically, after obtaining the t-th phase estimation value λ t Afterwards, the quantum phase search step further includes:

[0133] Based on the t-th phase estimation value λt , for the first interval (t-1) Q Update to obtain the t-th target interval; wherein the t-th target interval is the interval obtained after the t-th phase search process, which is used as the t-th quantum related information required for the t+1-th phase search process.

[0134] That is to say, in one example, the output result of the tth phase search process includes the tth phase estimation value and the tth target interval, and then the tth phase estimation value and the tth target interval are used together as the tth quantum related information to provide data support for the smooth execution of the t+1th phase search process.

[0135] In a specific example, the first interval (t-1) Q , recorded as At this time, the tth phase estimate λ t It can be obtained using the following formula:

[0136]

[0137] Furthermore, the first interval (t-1) is analyzed in the following manner: Q Update and get the tth target interval (ζ lt ,ζ ut ),Right now

[0138]

[0139]

[0140] Here, Δ is a preset constant, In this way, the foundation is laid for obtaining the t+1th phase estimation value.

[0141] It should be noted that, when the value of t is 1, that is, in the first phase search process, the first interval 0 (ζ l0 ,ζ u0 ) is the preset initial interval, for example, ζ l0 =-π,ζ u0 =π.

[0142] Furthermore, in a specific example of the disclosed solution, the t-th phase search process also needs to use the first unitary operator U used in the process t-1 Perform the update process, and thus obtain another output result of the t-th phase search process, namely the first unitary operator U t , providing data support for the smooth execution of the subsequent t+1th phase search process.

[0143] Specifically, after obtaining the tth phase estimation value λ tAfterwards, the quantum phase search step further includes:

[0144] Based on the t-th phase estimation value, the first unitary operator U in the t-1-th quantum related information is t-1 Update and get the first unitary operator U t ; The first unitary operator U t is the unitary operator obtained after the t-th phase search process, and is used as the t-th quantum related information required for the t+1-th phase search process.

[0145] Here, the first unitary operator U t-1 is the output of the t-1th phase search process, which is based on the t-1th phase estimate λ t-1 With the block coded unitary operator Determined; When t is equal to 1, the first unitary operator U0 is the block coding unitary operator

[0146] That is, in another example, the output result of the t-th phase search process includes the t-th phase estimation value, the t-th target interval, and the first unitary operator U t , and then the t-th phase estimate λ t , the tth target interval and the first unitary operator U t Together they serve as the t-th quantum-related information, providing data support for the smooth execution of the t+1-th phase search process.

[0147] In a specific example, the first unitary operator U can be calculated as follows: t-1 Update and get the first unitary operator U t ,Right now

[0148] (Here, i is an imaginary number)

[0149] Here, the The Δ is a preset constant, which lays the foundation for obtaining the t+1th phase estimation value.

[0150] The following two methods of interval compression are given for different values ​​of Q. Specifically,

[0151] Compression method 1: For the t-th phase search process, the value of Q is 1. That is, in this method 1, in the t-th phase search process, the interval compression process is performed once without the need for multiple cycles.

[0152] Specifically, the above-mentioned t-1th target interval in the t-1th quantum related information is compressed Q times to obtain the first interval (t-1) Q , specifically including:

[0153] Step 1: When the value of Q is 1, determine a target parameter value of a target adjustable parameter in a first auxiliary register of a target quantum circuit.

[0154] Here, the target quantum circuit also includes the block coding quantum circuit; that is, the target quantum circuit includes a first auxiliary register and the block coding quantum circuit. Here, the first auxiliary register is a parameterized quantum circuit; further, the target quantum circuit also includes a target controlled unitary gate controlled by the first auxiliary register and acting on the target main register and the target auxiliary register, the target controlled unitary gate being used to estimate the block coding unitary operator The corresponding characteristic phase.

[0155] Step 2: Based on the t-1th target interval, obtain the tth Q Target value.

[0156] It is understandable that the execution order of step 1 and step 2 in this method 1 can be swapped or executed in parallel, and the present disclosure does not limit this.

[0157] In this example, since the value of Q is 1, the tth Q The target value may also be recorded as the t1-th target value.

[0158] Furthermore, in a specific example, the following method can be used to utilize the t-1th target interval (ζ l(t-1) ,ζ u(t-1) ), get the tth Q Target value (can be expressed as ),Right now:

[0159]

[0160] That is, in this example, the t-1th target interval (ζ l(t-1) ,ζ u(t-1) ) is taken as the middle value of the t Q Target value It is understandable that the above is only an exemplary description. In actual application, other methods can be used to obtain the t Q The target value is not specifically limited in the present disclosure.

[0161] Step 3: Based on the t Q target value, and the first unitary operator U in the t-1th quantum related information t-1 , construct the specified unitary operator

[0162] Here, the first unitary operator Ut-1 is based on the t-1th phase estimate λ t-1 With the block coded unitary operator Determined; When t is equal to 1, the first unitary operator U0 is the block coding unitary operator

[0163] In a specific example, Here, the first unitary operator U t-1 is the output result of the t-1th phase search process. The first unitary operator U t-1 Specifically, the phase estimation value λ of the t-1th phase search process t-1 , and the output result of the previous phase search process (ie, the t-2th phase search process) of the phase search process (such as U t-2 For example, when t is 1, the output results of the first phase search process include: λ1 and U1; at this time, the Furthermore, when the value of t is 2, the output result of the second phase search process includes: λ2 and U2; at this time, the

[0164] Step 4: The target adjustable parameter is the target parameter value, the input quantum state of the first auxiliary register is the preset initial state, the total input quantum state of the target main register and the target auxiliary register is the t-1th target output quantum state in the t-1th quantum related information, and the target controlled unitary gate is updated to the specified unitary operator In the case of the first auxiliary register, the tth Q The measurement results.

[0165] In a specific example, the preset initial state can be, for example, |0> or |1>, that is, the input quantum state of the first auxiliary register is |0> or |1>. It should be noted that the disclosed solution does not impose any specific limitation on this.

[0166] Here, when the value of t is 1, the 0th target output quantum state is the preset total initial quantum state, or the first characteristic state obtained in the previous process.

[0167] In a specific example, the target controlled unitary gate includes a first controlled unitary gate and a second controlled unitary gate. Here, the first controlled unitary gate is controlled by the first auxiliary register and acts on the target main register and the target auxiliary register. Similarly, the second controlled unitary gate is controlled by the first auxiliary register and acts on the target main register and the target auxiliary register.

[0168] Furthermore, in the case where the target controlled unitary gate includes a first controlled unitary gate and a second controlled unitary gate, the designated unitary operator Specifically, it can include unitary operators and unitary operators The conjugate transpose of At this time, in step 4, the target controlled unitary gate is updated to the specified unitary operator Specifically, the first controlled unitary gate is updated to The second controlled unitary gate is updated to the unitary operator The conjugate transpose of

[0169] In a specific example, the (i is an imaginary number), (i is an imaginary number), at this time, it can be understood that, in this example, in the t-th phase search process, when the interval compression process is performed once, the first controlled unitary gate in the target quantum circuit is The equivalent circuit of the second controlled unitary gate is The equivalent circuit of .

[0170] Step 5: Based on the t Q The measurement result and the interval length of the t-1th target interval are used to perform interval compression processing on the t-1th target interval to obtain the first interval (t-1) Q .

[0171] In a specific example, based on the t Q The measurement result and the interval length of the t-1th target interval are used to calculate the target interval length. Q target value, performing interval compression processing on the t-1th target interval to obtain the first interval (t-1) Q .

[0172] For example, in the t-th phase search process, when the interval compression process is performed once, the following method is used to compress the t-1th target interval (ζ l(t-1) ,ζ u(t-1) ) is updated to obtain the first interval (t-1) Q , recorded as To complete the interval compression process:

[0173] If u(t-1) -ζ l(t-1) When >2π-2Δ, the interval is updated according to the following logic:

[0174]

[0175] If u(t-1)-ζ l(t-1) When ≤2π-2Δ, the interval is updated according to the following logic:

[0176]

[0177] Here, it should be noted that, for the t-th phase search process, when the value of Q is 1, the output result after the interval compression processing includes: the first interval (t-1) Q .

[0178] Furthermore, in a specific example, the target adjustable parameter is a target parameter value, the input quantum state of the first auxiliary register is a preset initial state, the total input quantum state of the target main register and the target auxiliary register is the t-1th target output quantum state in the t-1th quantum related information, and the target controlled unitary gate is updated to the specified unitary operator In the case of , the tth target output quantum state jointly output by the target main register and the target auxiliary register is also obtained.

[0179] Here, the tth target output quantum state is the total input quantum state of the target main register and the target auxiliary register in the next phase search process, i.e., the t+1th phase search process. That is, in this example, for the tth phase search process, when the value of Q is 1, the output result after the interval compression processing includes: the first interval (t-1)1 and the tth target output quantum state.

[0180] Based on this, it can be seen that in the first method, for the t-th phase search process, when the value of Q is 1, the output results of the Q-time interval compression processing include: the first interval (t-1) Q , the t-th target output quantum state. Further, based on the output results of the Q-th compression process, the final output result of the t-th phase search process is obtained, including: the t-th phase estimation value λ t , the first unitary operator U t , the tth target interval, and the tth target output quantum state.

[0181] In a specific example, for each phase search process (i.e., when t takes any value from 1 to T), Q takes the value of 1, that is, an interval compression process is performed in each phase search process. In this case, the block coding unitary operator can be estimated by T training. The corresponding first characteristic phase λ.

[0182] In this way, the disclosed solution can obtain a block coding unitary operator that meets the accuracy requirements with a very high probability. The corresponding first characteristic phase λ; at the same time, the required quantum resources are low, thus increasing the feasibility of solving quantum characteristics in medium-scale quantum computing devices.

[0183] Compression method 2: For the t-th phase search process, the value of Q is greater than 1, that is, it is a positive integer greater than or equal to 2. That is to say, unlike method 1, in method 2, the interval compression processing in the t-th phase search process needs to be cyclically performed multiple times (i.e., Q times).

[0184] Specifically, the above-mentioned t-1th target interval in the t-1th quantum related information is compressed Q times to obtain the first interval (t-1) Q , specifically including:

[0185] Step 1: When the value of Q is greater than or equal to 2, determine a target parameter value of a target adjustable parameter in a first auxiliary register of a target quantum circuit.

[0186] Here, the target quantum circuit also includes the block coding quantum circuit; that is, the target quantum circuit includes a first auxiliary register and the block coding quantum circuit. Here, the first auxiliary register is a parameterized quantum circuit; further, the target quantum circuit also includes a target controlled unitary gate controlled by the first auxiliary register and acting on the target main register and the target auxiliary register, the target controlled unitary gate being used to estimate the block coding unitary operator The corresponding characteristic phase.

[0187] Step 2: After Q interval compression processing for the t-th phase search process, the first interval (t-1) is obtained using the following process: Q .

[0188] Here, the qth interval compression process in the Qth interval compression process of the tth phase search process specifically includes:

[0189] Step 2-1: Based on the first interval (t-1) obtained q-1 , get the tth q Target value.

[0190] Here, the first interval (t-1) q-1 It is the result obtained after the q-1th interval compression processing in the tth phase search process, that is, the output result after the q-1th interval compression processing in the tth phase search process. Correspondingly, it is also the interval targeted by the qth interval compression processing in the tth phase search process.

[0191] Here, q is a natural number greater than or equal to 1 and less than or equal to Q. Furthermore, when q is 1, that is, the first interval (t-1)0 used in the first interval compression process in the t-th phase search process is the t-1th target interval, that is, the output result of the t-1th phase search process.

[0192] Furthermore, in a specific example, the first interval (t-1) can be used based on the following method. q-1 , recorded as Get the tth q Target value (can be expressed as ),Right now:

[0193]

[0194] That is, in this example, the first interval (t-1) q-1 The middle value of the t q Target value It is understandable that the above is only an exemplary description. In actual application, other methods can be used to obtain the t q The target value is not specifically limited in the present disclosure.

[0195] Step 2-2: Based on the t q target value, and the first unitary operator U in the t-1th quantum related information t-1 , construct the specified unitary operator required for the qth interval compression process

[0196] Here, specify the unitary operator Represents the unitary operator required for the qth interval compression process in the tth phase search process.

[0197] Furthermore, the first unitary operator U t-1 is based on the t-1th phase estimate λ t-1 With the block coded unitary operator Determined; when t is equal to 1, the first unitary operator U0 is the block coding unitary operator

[0198] In a specific example, Here, the i is an imaginary number; the first unitary operator U t-1 is the output result of the t-1th phase search process. The first unitary operator U t-1 Specifically, the phase estimation value λ of the t-1th phase search process t-1 , and the output result of the previous phase search process (ie, the t-2th phase search process) of the phase search process (such as U t-2) is related. For example, when t is 1, the output results of the first phase search process include: λ1 and U1; at this time, the Furthermore, when the value of t is 2, the output result of the second phase search process includes: λ2 and U2; at this time, the

[0199] Step 2-3: When the target adjustable parameter is the target parameter value, the input state of the first auxiliary register is the preset initial state, and the total input state of the target main register and the target auxiliary register is the tth q-1 Output quantum state, and the target controlled unitary gate is updated to the specified unitary operator In the case of the first auxiliary register, the tth q The measurement results.

[0200] In a specific example, the preset initial state can be, for example, |0> or |1>. That is, the input quantum state of the first auxiliary register is |0> or |1>. It should be noted that the disclosed solution does not impose any specific limitation on this.

[0201] Here, the t q-1 The output quantum state is the total output quantum state of the target main register and the target auxiliary register after the q-1th interval compression processing in the tth phase search process; further, when q is 1, that is, during the first interval compression processing in the tth phase search process, the total input quantum state of the target main register and the target auxiliary register is the t-1th target output quantum state, that is, the total output quantum state of the target main register and the target auxiliary register after the t-1th phase search process, or after all Q interval compression processing in the t-1th phase search process is completed.

[0202] Furthermore, when the value of q is 1, the t0-th output quantum state is the t-1-th target output quantum state in the t-1-th quantum related information.

[0203] Further, when t=1 and q=1, the 10th output quantum state is the 0th target output quantum state in the 0th quantum-related information, and the 0th target output quantum state is the preset total initial quantum state, or the first characteristic state obtained by the previous process, that is, the 10th output quantum state is the preset total initial quantum state, or the first characteristic state obtained by the previous process.

[0204] Furthermore, after the Q interval compression processes of the t-th phase search process are all completed, the total output quantum state of the target main register and the target auxiliary register is the t-th target output quantum state.

[0205] Here, the t q The measurement result represents the measurement result after the quantum measurement of the first auxiliary register after the qth interval compression processing in the tth phase search process.

[0206] In a specific example, the target controlled unitary gate includes a first controlled unitary gate and a second controlled unitary gate. Here, the first controlled unitary gate is controlled by the first auxiliary register and acts on the target main register and the target auxiliary register. Similarly, the second controlled unitary gate is controlled by the first auxiliary register and acts on the target main register and the target auxiliary register.

[0207] Furthermore, in the case where the target controlled unitary gate includes a first controlled unitary gate and a second controlled unitary gate, the designated unitary operator Specifically, it can include unitary operators and unitary operators The conjugate transpose of At this time, in step 2-3, the target controlled unitary gate is updated to the specified unitary operator Specifically, the first controlled unitary gate is updated to the unitary operator The second controlled unitary gate is updated to the unitary operator The conjugate transpose of .

[0208] In a specific example, the (i is an imaginary number), (i is an imaginary number), at this time, it can be understood that, in this example, in the t-th phase search process, during the q-th interval compression process, the first controlled unitary gate in the target quantum circuit is the The equivalent circuit of the second controlled unitary gate is The equivalent circuit of .

[0209] Step 2-4: Based on the t q The measurement results, and the first interval (t-1) q-1 The length of the interval, for the first interval (t-1) q-1 Perform interval compression processing to obtain the first interval (t-1) q .

[0210] In a specific example, based on the t q The measurement result of the first interval (t-1) q-1 The length of the interval, and using the t q Target value, for the first interval (t-1) q-1 Perform interval compression processing to obtain the first interval (t-1) q .

[0211] For example, in the t-th phase search process, during the q-th interval compression process, the first interval (t-1) is compressed in the following manner: q-1 , recorded as Update and get the first interval (t-1) q , recorded as To complete the interval compression process:

[0212] like , then update according to the following logic:

[0213]

[0214] like , then update according to the following logic:

[0215]

[0216] That is, in the second method, the output result after the qth interval compression process in the tth phase search process includes: the first interval (t-1) q .

[0217] Furthermore, in the case where q is Q, that is, after all Q interval compression processes in the t-th phase search process are completed, the first interval (t-1) can be obtained. Q .

[0218] In this way, the disclosed solution can obtain the first characteristic phase through multiple interval compression processes, thereby further improving the accuracy of the first characteristic phase.

[0219] In a specific example of the disclosed solution, after the qth interval compression process in the tth phase search process, the tth interval will also be output. q Output quantum state. Specifically, the quantum phase search step also includes:

[0220] The target adjustable parameter is the target parameter value, the input state of the first auxiliary register is the preset initial state, and the total input state of the target main register and the target auxiliary register is the tth q-1 Output quantum state, and the target controlled unitary gate in the target quantum circuit is updated to the specified unitary operator In the case of , the tth output of the target main register and the target auxiliary register is obtained q Output quantum state.

[0221] Here, the t qThe output quantum state is the total input quantum state of the target main register and the target auxiliary register during the next interval compression process, that is, the q+1th interval compression process in the tth phase search process.

[0222] That is, in this example, the output result after the qth interval compression process in the tth phase search process includes: the first interval (t-1) q and t q Output quantum state.

[0223] It can be understood that when q is Q, the t Q The output quantum state is the t-th target output quantum state, that is, the final output quantum state after Q-times interval compression processing in the t-th phase search process.

[0224] Based on this, it can be seen that in the second method, the output result of the qth interval compression process in the tth phase search process includes: the first interval (t-1) q , t q Output quantum state. Further, according to the above method, Q interval compression processing is performed. At this time, after the Q interval compression processing of the t-th phase search process is completed, the first interval (t-1) can be obtained. Q and t Q Output quantum state (that is, the tth target output quantum state).

[0225] Furthermore, based on the output results of the Q-th compression process, the final output result of the t-th phase search process can be further obtained, that is, the t-th phase estimation value λ t , the first unitary operator U t , the tth target interval, and the tth target output quantum state.

[0226] In this way, the disclosed solution obtains the t-th q The output quantum state lays the foundation for obtaining the first characteristic state corresponding to the first characteristic phase that meets the accuracy requirements.

[0227] In a specific example of the disclosed solution, after performing T-1 phase search processes according to the above process, the T-1 target output quantum state (i.e. (T-1) Q output quantum state), at this time, the first characteristic state corresponding to the first characteristic phase is the T-1th target output quantum state.

[0228] In this way, the disclosed solution can obtain the first characteristic state corresponding to the first characteristic phase that meets the accuracy requirement with extremely high probability without the need for quantum Fourier transform.

[0229] It should be noted that, in actual applications, in the above compression method 1 or compression method 2, the target parameter value satisfies the first error condition. Accordingly, the final result obtained, and the first characteristic phase, at least satisfies the first error condition.

[0230] In a specific example, the first auxiliary register in the target quantum circuit described above includes at least one quantum bit, for example, one, two, or more than two quantum bits, which is not limited in the present disclosure.

[0231] In a specific example of the disclosed solution, a specific method for determining a target parameter value of a target adjustable parameter in a first auxiliary register of a target quantum circuit is provided. Specifically, determining the target parameter value of the target adjustable parameter in the first auxiliary register of the target quantum circuit in the aforementioned compression method 1 or compression method 2 includes using the target parameter value of the target adjustable parameter in a trained preset parameterized quantum circuit as the target parameter value of the target adjustable parameter in the first auxiliary register.

[0232] In other words, the target adjustable parameter is included in the preset parameterized quantum circuit. Thus, the target parameter value of the target adjustable parameter in the trained preset parameterized quantum circuit is used as the target parameter value of the target adjustable parameter in the first auxiliary register. In other words, in this example, the target parameter value of the target adjustable parameter in the first auxiliary register can be obtained by training other parameterized quantum circuits.

[0233] It should be noted that the preset parameterized quantum circuit may also include other adjustable parameters, and the present disclosure does not impose any specific restrictions on this, as long as the preset parameterized quantum circuit includes the target adjustable parameters required by the first auxiliary register.

[0234] Furthermore, the trained preset parameterized quantum circuit is used to simulate an objective function f(x), which is used to characterize the relationship between a preset value k and an independent variable x.

[0235] Here, the target controlled unitary gate includes a first controlled unitary gate and a second controlled unitary gate; the second controlled unitary gate is the conjugate transpose of the first controlled unitary gate.

[0236] Furthermore, the target quantum circuit is based on the following:

[0237] The preset parameterized quantum circuit is used as the first auxiliary register, and a target main register and a target auxiliary register are expanded. Furthermore, the first target rotation gate in the preset parameterized quantum circuit acting on the first auxiliary register is replaced with the first controlled unitary gate, and the second target rotation gate in the preset parameterized quantum circuit acting on the first auxiliary register is replaced with the second controlled unitary gate. In other words, the target quantum circuit is expanded from the preset parameterized quantum circuit.

[0238] Here, the first rotation parameter of the first target revolving door and the second rotation parameter of the second target revolving door are both the independent variable x of the target function f(x).

[0239] Furthermore, the first auxiliary register includes at least a portion of the circuit in the preset parameterized quantum circuit except the first target revolving gate and the second target revolving gate; here, the first target revolving gate and the second target revolving gate may be collectively referred to as target revolving gates. In this case, the first auxiliary register includes at least a portion of the circuit in the preset parameterized quantum circuit except the target revolving gate.

[0240] It can be understood that since the target quantum circuit is obtained by expanding the preset parameterized quantum circuit, the first auxiliary register can also be understood as being obtained on the basis of the preset parameterized quantum circuit and including a partial circuit structure corresponding to the target adjustable parameter in the preset parameterized quantum circuit. This lays the foundation for obtaining the target parameter value of the target adjustable parameter of the first auxiliary register by training the preset parameterized quantum circuit.

[0241] It can be understood that since the circuit structure of the preset parameterized quantum circuit is simpler than that of the target quantum circuit, the method of obtaining the target parameter value of the target adjustable parameter by training the preset parameterized quantum circuit can effectively reduce the amount of calculation and provide a method for efficiently estimating the block coded unitary operator. The corresponding first characteristic phase lays the foundation.

[0242] Furthermore, in practical applications, the preset parameterized quantum circuit can also be obtained by simulation in a classical computing device. Accordingly, the target parameter value of the target adjustable parameter obtained by training can also be implemented in a classical computing device. Therefore, the method of obtaining the target parameter value of the target adjustable parameter in the disclosed solution does not occupy quantum computing resources. Therefore, in order to obtain the block coded unitary operator for efficient estimation, The corresponding first characteristic phase not only lays the foundation but also effectively reduces the computational cost.

[0243] Moreover, the disclosed scheme is for block coding unitary operators Without any restrictions, in other words, any block coding unitary operator can be implemented The corresponding first characteristic phase estimation has strong versatility. At the same time, the disclosed solution can also be applied to large-scale block coding unitary operators. Therefore, it also has scalability. In summary, it can be seen that the disclosed solution has high efficiency, versatility and scalability.

[0244] It is understandable that in practical applications, any trigonometric polynomial that can approximate the target function with a certain accuracy can also be used to optimize the optimal parameter value of the target adjustable parameter, and the present disclosure does not impose any specific restrictions on this.

[0245] It should be noted that the disclosed solution does not limit the method of training the preset parameterized quantum circuit to obtain the target parameter value of the target adjustable parameter.

[0246] For example, the preset parameterized quantum circuit includes one qubit, as shown in FIG4( a ). The preset parameterized quantum circuit includes L training layers, wherein one training layer of at least two training layers of the L training layers, for example, the i-th training layer of the L training layers, includes, in order of action:

[0247] Rotation angle φ i The first revolving door R corresponding to the angle of the z-axis Z (φ i );

[0248] Rotation angle θ i The second revolving door R is the angle corresponding to the y-axis Y (θ i );

[0249] Rotation parameter x j The target revolving door R is the angle corresponding to the z axis Z (x j ).

[0250] Here, the first revolving door R Z (φ i )’s rotation angle φ i and the second revolving door R Y (θ i )’s rotation angle θ i is the target adjustable parameter in the i-th training layer, where i is an integer greater than or equal to 1 and less than or equal to L.

[0251] It is understood that the structure of the other training layer in the at least two training layers of the L training layers is also the structure shown in FIG4 (a). This is not repeated here. Furthermore, in another specific example, the structure of each training layer in the L training layers is the structure shown in FIG4 (a), which is not repeated here.

[0252] In this way, the disclosed solution effectively improves the expressive power of preset parameterized quantum circuits. At the same time, the types and number of quantum gates used are small, and the number of target adjustable parameters to be trained is small. This lays the foundation for efficiently estimating the first eigenphase corresponding to the block-coded unitary operator.

[0253] Furthermore, in another example, as shown in FIG4( b ), the preset parameterized quantum circuit further includes, after L training layers:

[0254] The third revolving door R with a rotation angle φ0 corresponding to the angle of the z axis Z (φ0);

[0255] The fourth revolving door R with a rotation angle θ0 corresponding to the y-axis Y (θ0).

[0256] Here, the rotation angle φ0 and the rotation angle θ0 are also target adjustable parameters.

[0257] Alternatively, in another example, as shown in FIG4( c ), the preset parameterized quantum circuit further includes, after L training layers:

[0258] The third revolving door R with a rotation angle φ0 corresponding to the angle of the z axis Z (φ0);

[0259] The fourth revolving door R with a rotation angle θ0 corresponding to the y-axis Y (θ0);

[0260] and the fifth revolving door R whose rotation angle α is the angle corresponding to the z axis Z (α).

[0261] Here, the rotation angle φ0, the rotation angle θ0 and the rotation angle α are all target adjustable parameters.

[0262] In this way, the disclosed solution effectively improves the expressive power of preset parameterized quantum circuits. At the same time, the types and number of quantum gates used are small, and the number of target adjustable parameters to be trained is small. This lays the foundation for efficiently estimating the first eigenphase corresponding to the block-coded unitary operator and also lays the foundation for improving the accuracy of the results.

[0263] Furthermore, the target quantum circuit obtained based on the preset parameterized quantum circuit comprises M layers, where M is a positive integer greater than or equal to 1 and less than or equal to L / 2;

[0264] Furthermore, each layer in the M layer is based on the following:

[0265] The first controlled unitary gate is replaced by the first target revolving gate of the first training layer of the two training layers, and the second controlled unitary gate is replaced by the second target revolving gate of the second training layer of the two training layers; wherein the two training layers are two adjacent training layers in the L training layers.

[0266] For example, as shown in FIG5(a), according to the order of action of the quantum gate, the first The layers (i ranges from 1 to L) include:

[0267] The first revolving door R acting on the first auxiliary register Z (φ i+1 ); rotation angle φ i+1 is the angle corresponding to the z-axis;

[0268] The second revolving door R acting on the first auxiliary register Y (θ i+1 ); rotation angle θ i+1 is the angle corresponding to the y-axis

[0269] a first controlled unitary gate controlled by the first auxiliary register and acting on the block-coded quantum circuit (i.e., the target main register and the target auxiliary register);

[0270] The first revolving door R acting on the first auxiliary register Z (φ i ); rotation angle φ i is the angle corresponding to the z-axis;

[0271] The second revolving door R acting on the first auxiliary register Y (θ i ); rotation angle θ i is the angle corresponding to the y-axis;

[0272] A second controlled unitary gate is controlled by the first auxiliary register and acts on the block-coded quantum circuit (ie, the target main register and the target auxiliary register).

[0273] It is understandable that the structure after the M layer of the target quantum circuit can be seen in FIG4( b ) or FIG4( c ), which will not be described in detail here.

[0274] Furthermore, more specifically, as shown in FIG5(b), according to the order of action of the quantum gates, the first The layers (i ranges from 1 to L) include:

[0275] The first revolving door R acting on the first auxiliary register Z (φ i+1 ); rotation angle φ i+1 is the angle corresponding to the z-axis;

[0276] The second revolving door R acting on the first auxiliary register Y (θ i+1 ); rotation angle θ i+1 is the angle corresponding to the y-axis;

[0277] The target unitary operator U acting on the first sub-auxiliary register and the second sub-auxiliary register (ie, the target auxiliary register) ρ ;

[0278] a SWAP gate controlled by the first auxiliary register and acting on the target main register and the first sub-auxiliary register;

[0279] The target unitary operator U acting on the first sub-auxiliary register and the second sub-auxiliary register (that is, acting on the target auxiliary register) ρ The conjugate transpose of

[0280] a reflection operator R controlled by the first auxiliary register and acting on the first sub-auxiliary register and the second sub-auxiliary register (i.e., acting on the target auxiliary register);

[0281] The first revolving door R acting on the first auxiliary register Z (φ i ); rotation angle φ i is the angle corresponding to the z-axis;

[0282] The second revolving door R acting on the first auxiliary register Y (θ i ); rotation angle θ i is the angle corresponding to the y-axis;

[0283] a reflection operator R controlled by the first auxiliary register and acting on the first sub-auxiliary register and the second sub-auxiliary register (i.e., acting on the target auxiliary register);

[0284] The target unitary operator U acting on the first sub-auxiliary register and the second sub-auxiliary register (that is, acting on the target auxiliary register) ρ ;

[0285] a SWAP gate controlled by the first auxiliary register and acting on the target main register and the first sub-auxiliary register;

[0286] The target unitary operator U acting on the first sub-auxiliary register and the second sub-auxiliary register (that is, acting on the target auxiliary register) ρ The conjugate transpose of

[0287] Here, the target unitary operator U ρ , SWAP gate and reflection operator R (Reflector) can be found in the above description and will not be repeated here.

[0288] It is understandable that the structure after the M layer of the target quantum circuit can also be seen in FIG4( b ) or FIG4( c ), which will not be described in detail here.

[0289] It should be noted that in the disclosed solution, as shown in FIG5(b), when the quantum state of the first auxiliary register is |0>, the hollow-core reflection operator R and the hollow-core SWAP gate in the second controlled unitary gate of the target quantum circuit are activated. When the quantum state of the first auxiliary register is |1>, the solid-core reflection operator R and the solid-core SWAP gate in the first controlled unitary gate of the target quantum circuit are activated. In other words, in practical applications, when the current quantum state of the first auxiliary register is determined, the reflection operator R and the SWAP gate in the first controlled unitary gate are either operative or the reflection operator R and the SWAP gate in the second controlled unitary gate are operative.

[0290] In summary, the disclosed solution has the following advantages:

[0291] Strong practicality: It can be implemented on a quantum computer, has a rich range of application scenarios, and does not require quantum Fourier transform technology; moreover, the circuit structure is simpler, the probability of success is higher, and it is easier to implement. In addition, the target quantum state of the disclosed scheme can be a quantum pure state or a quantum mixed state. In other words, the disclosed scheme is applicable to both quantum pure states and quantum mixed states. High efficiency: Quantum circuits can be constructed with low consumption, effectively reducing the required resources. Determinism: Quantum principal components that meet the accuracy requirements are obtained with extremely high probability. Strong scalability, and can be used to analyze the main components of large-scale quantum states. High precision: Effectively guarantees the accuracy requirements. Innovation: Provides a novel and efficient quantum circuit to implement quantum principal component analysis.

[0292] The following describes the disclosed solution in further detail with reference to a specific example. Specifically, this example is designed to extract the principal components of a quantum state generated by a quantum circuit. This example simplifies the quantum circuit used in the solution, effectively reducing the requirements for quantum circuits and making the disclosed solution applicable to near-future quantum computers. Unlike traditional solutions, the disclosed solution uses a quantum phase search scheme to extract the characteristics of quantum systems. This quantum phase search scheme has lower requirements for quantum circuits, resulting in a more efficient and practical solution, making it easier to implement on near-future quantum computing devices.

[0293] Specifically, the disclosed scheme mainly starts from the target quantum state ρ and uses a quantum phase search scheme to extract a block-coded eigenvalue (i.e., a characteristic phase) of the target quantum state ρ. Here, the block code is a unitary operator (which can be called a block-coded unitary operator). The eigenvalue of the block-coded unitary operator and the eigenvalue of the target quantum state ρ can be related to the eigenvalue of the target quantum state ρ through trigonometric functions. In this way, the target eigenvalue of the target quantum state ρ and its corresponding target eigenstate are obtained, thereby realizing quantum principal component analysis of the quantum system represented by the target quantum state ρ (i.e., the first quantum system described above).

[0294] The following is a detailed explanation of this example in several parts: Part 1, the quantum phase search scheme; Part 2, the principal component analysis scheme based on phase search; Part 3, application expansion; Part 4, case presentation.

[0295] Part I: Quantum phase search scheme;

[0296] The first part can be implemented through the following program 1; here, the program 1 includes subroutine 1 and subroutine 2; among them, subroutine 1 is mainly used to perform Q-time interval compression processing, and output a first interval and a target output quantum state. Subroutine 1 is a program that will be called by subroutine 2; subroutine 2 is mainly used to search for characteristic phases, and output a first characteristic phase λ and a first characteristic state corresponding to the first characteristic phase λ.

[0297] Subroutine 1

[0298] It is understandable that in actual applications, without considering the computational cost, this subroutine 1 can also be run in a classical computing device or a quantum computing device, and the present disclosure does not impose any specific restrictions on this.

[0299] Specifically, the specific steps of this subroutine 1 include:

[0300] Step 11-1: Expand the preset parameterized quantum circuit and expand the block coded quantum circuit to obtain the target quantum circuit. Here, the target quantum circuit can estimate the block coded unitary operator The corresponding first characteristic phase λ and its corresponding first characteristic state; the coding quantum circuit is the block coding unitary operator The equivalent circuit of .

[0301] Specifically, in a specific example, the target quantum circuit can be obtained in the following manner:

[0302] A preset parameterized quantum circuit is used as a first auxiliary register in the target quantum circuit, and a block coded quantum circuit including a target main register and a target auxiliary register is expanded. At the same time, a first target rotation gate acting on the first auxiliary register in the preset parameterized quantum circuit is replaced with the first controlled unitary gate, and a second target rotation gate acting on the first auxiliary register in the preset parameterized quantum circuit is replaced with the second controlled unitary gate, thereby obtaining a target quantum circuit including the first auxiliary register, a target main register, and a target auxiliary register.

[0303] Furthermore, in a specific example, as shown in FIG5(b), the target quantum circuit comprises 2n+n'+1 quantum bits; wherein the block coded unitary operator The corresponding number of quantum bits is 2n+n', that is, the block coded quantum circuit contains 2n+n' quantum bits; the number of quantum bits contained in the preset parameterized quantum circuit is 1, that is, the first auxiliary register contains 1 quantum bit.

[0304] Furthermore, the block coding unitary operator is based on the target unitary operator U used to prepare the target quantum state ρ ρ The target quantum state ρ is the quantum state corresponding to a quantum system containing n qubits, that is, the target quantum state ρ corresponds to n qubits. In other words, the block coded unitary operator It can be expressed as:

[0305]

[0306] It should be noted that n is a positive integer greater than or equal to 1, and n′ is a positive integer satisfying 2 n′ ≤ rank(ρ) requires a positive integer.

[0307] It is understandable that in practical applications, the preset parameterized quantum circuit may also include multiple quantum bits, as long as the block coded unitary operator can be estimated based on the target quantum circuit. The corresponding first characteristic phase λ and its corresponding first characteristic state are sufficient. The present disclosure does not limit the circuit structure of the preset parameterized quantum circuit. The relevant content of the preset parameterized quantum circuit can also be found in the above description and will not be repeated here.

[0308] It should be noted that, in the disclosed solution, the first auxiliary register in the target quantum circuit is equivalent to the auxiliary register of the block coding quantum circuit in the target quantum circuit; here, the relevant content of the block coding quantum circuit can be found in the above description, and correspondingly, the relevant content of the target quantum circuit can also be found in the above description, and no further details will be given here.

[0309] Step 11-2: For the t-th phase search process, input parameter Q (the total number of interval compression processes), preset constant Δ>0, and the target parameter value obtained after training the preset parameterized quantum circuit and And the result obtained by inputting the last phase search process, that is, the first unitary operator U in the t-1th quantum related information t-1 , the t-1th target interval (denoted as (ζ l(t-1) ,ζ u(t-1) )) and the t-1th target output quantum state |χ t-1 >.

[0310] Here, for t=1, the first unitary operator U0 is the initial unitary operator U0. Furthermore, the initial unitary operator U0 is the block coding unitary operator Right now The 0th target interval is a preset initial interval, such as (-π, π).

[0311] Here, in this example, Q is a positive integer greater than or equal to 2.

[0312] Step 11-3: Loop Q times as follows:

[0313] It is understandable that the qth interval compression process in the Q-time process depends on the output result of the q-1th interval compression process. Here, the output result of the q-1th interval compression process is recorded as:

[0314] First interval (t-1) q-1 , for t not equal to 1 and q = 1, the first interval (t-1)0 is the t-1th target interval, and for t = 1 and q = 1, the interval is a preset initial interval, such as (-π, π);

[0315] No. t q-1 Output quantum state, that is, the total output quantum state of the target main register and the target auxiliary register after the q-1th interval compression process in the tth phase search process; for t is not equal to 1, q = 1, the t0th output quantum state is the t-1th target output quantum state |χ t-1 >.

[0316] Here, it can be understood that for t = 1 and q = 1, the input quantum state of this step is the total initial quantum state |χ0>, such as Alternatively, |χ0> = the first characteristic state obtained in the previous process.

[0317] Here, the qth interval compression process in the Q interval compression processes includes the following steps:

[0318] Step (a): Calculate the tth q Target value

[0319] Step (b): Construction (i is an imaginary number), (i is an imaginary number), and use and The target quantum circuit is constructed as shown in Figure 5(b). The construction method is as described above and will not be repeated here.

[0320] It should be noted that for the qth interval compression process in the tth phase search process, the first controlled unitary gate in Figure 5(b) is The equivalent circuit of the second controlled unitary gate is The equivalent circuit of the target main register and the target auxiliary register in Figure 5(b) is the total input quantum state of the tth q-1 Output quantum state, the input quantum state of the first auxiliary register is a preset initial state, for example, |0>.

[0321] Compared to existing solutions, the disclosed solution effectively reduces the required quantum computing resources and enhances the feasibility of solving quantum features using medium-scale quantum computing devices. Furthermore, the disclosed solution is applicable to arbitrary block-coded unitary operators and has a wide range of application scenarios.

[0322] Step (c): Run the target quantum circuit obtained in step (b), and perform quantum measurement on the first auxiliary register to obtain the corresponding measurement result. Here, for the qth interval compression process in the tth phase search process, the measurement result can be recorded as the tth q The measurement results.

[0323] Step (d): For the first interval (t-1) q-1 Update as follows to get the first interval (t-1) q :

[0324] if Then update according to the following logic:

[0325]

[0326] like Then update according to the following logic:

[0327]

[0328] Step (e): Get the total output quantum state of the target main register and the target auxiliary register, and record it as t q Output quantum state. q The output quantum state serves as the total input quantum state of the target main register and the target auxiliary register for the q+1th interval compression process in the tth phase estimation process.

[0329] Here, when q = Q, t Q The output quantum state is the tth target output quantum state.

[0330] After Q cycles, the first interval (t-1) is obtained. Q and the tth target output quantum state.

[0331] Step 11-4: Output the first interval (t-1) Q and the tth target output quantum state |χ t >.

[0332] Subroutine 2

[0333] The function of the second subroutine is to find the initial unitary operator U0, that is, the block coding unitary operator, through the binary search algorithm. The phase interval is obtained, and the length of the interval is compressed to output the first characteristic phase that meets the accuracy requirement.

[0334] It is understandable that in actual applications, without considering the computational cost, the second subroutine can also be run in a classical computing device or a quantum computing device, and the present disclosure does not impose any specific restrictions on this.

[0335] Specifically, the specific steps of the second subroutine include:

[0336] Step 12-1: Input the initial unitary operator Total initial quantum state Preset constants Error tolerance value∈,δ>0.

[0337] Here, the total initial quantum state |χ0> is the initial quantum state of the block-coded quantum system corresponding to the block-coded quantum circuit. It can be any quantum state of the block-coded quantum system, such as an eigenstate or a non-eigenstate, and the disclosed solution does not impose any restrictions on this. δ is the phase estimation accuracy, which is used to constrain the accuracy of the final output result.

[0338] Step 12-2: Based on the preset constant Δ and error tolerance value ∈, the target adjustable parameters in the preset parameterized quantum circuit are trained to obtain the optimal parameter value (i.e., the target parameter value) and

[0339] here,

[0340] Step 12-3: Determine the values ​​of T and Q based on the preset constant Δ and phase estimation accuracy δ. The specific setting method is as follows:

[0341]

[0342] Here, the Where T represents the number of phase search steps, and Q represents the number of interval compression steps. The larger T and Q are, the more accurate the final output result will be.

[0343] Step 12-4: Initialization, setting the preset initial interval ζ l0 = -π and ζ u0 =π.

[0344] Step 12-5: For t=1,…,T, loop through the following steps:

[0345] For the t-th phase search process, the following steps are performed:

[0346] (a) Call subroutine 1, input parameter Q, preset constant Δ>0, target parameter value and And the output result of the t-1th phase search process, that is, the first unitary operator U t-1 , the t-1th target interval (denoted as (ζ l(t-1) ,ζ u(t-1) )) and the t-1th target output quantum state |χ t-1 >.

[0347] For t=1, the first unitary operator U0 is the block coding unitary operator The 0th target interval is the preset initial interval, such as (-π, π), and the 0th target output quantum state is the total initial quantum state, such as Or |χ0> = the first characteristic state obtained in the previous process.

[0348] (b) For the t-th phase search process, obtain the output result of subroutine 1, that is, the first interval (t-1) Q (denoted as ), and the t-th target output quantum state |χ t >.

[0349] (c) Obtain the tth phase estimate

[0350] (d) Update the first interval (t-1) Q , get the tth target interval (ζ lt ,ζ ut ), and update the first unitary operator U t-1 , get the first unitary operator U t ;in,

[0351]

[0352]

[0353]

[0354] Here, the

[0355] After T cycles, T phase estimation values ​​are obtained, and at the same time, the target output quantum state |χ T-1 >.

[0356] Step 12-6: Output the first characteristic phase and T-1 target output quantum state |χ T-1 >, where the first characteristic phase λ is the block coding unitary operator The estimated value of the corresponding characteristic phase, T-1 target output quantum state |χ T-1 > is the characteristic quantum state (also known as the first characteristic state) corresponding to the first characteristic phase λ.

[0357] Part II: Quantum Principal Component Analysis Scheme

[0358] This can be achieved through the following program 2, which is the main program of the disclosed solution.

[0359] Program 2: The main idea of ​​this program is to use quantum phase search to extract the larger eigenvalue and corresponding eigenstate of the target quantum state ρ.

[0360] Assume that the target quantum state ρ can be represented by a known target unitary operator U ρ Preparation, at this time, as Figure 6 As shown in Figure 2, the core steps of quantum principal component analysis include:

[0361] Step 21: Determine the target unitary operator U used to prepare the target quantum state ρ ρ .

[0362] Here, the target quantum state ρ is the quantum state of a quantum system containing n quantum bits.

[0363] Step 22: Use the target unitary operator Uρ Get the block coded unitary operator of the target quantum state ρ

[0364] Here, the block coded unitary operator It can be realized by an equivalent circuit, in this case, it is used to realize the block coding unitary operator The equivalent circuit of can be called a block-coded quantum circuit. Furthermore, the quantum system corresponding to the block-coded quantum circuit can be called a block-coded quantum system.

[0365] Furthermore, in a specific example, Figure 3 As shown, the block-coded quantum system corresponding to the block-coded quantum circuit includes a first quantum system and a total auxiliary quantum system. The first quantum system contains n qubits and corresponds to the target main register in the block-coded quantum circuit. Here, the first quantum system is the main quantum system in the block-coded quantum system. Correspondingly, the total auxiliary quantum system is the auxiliary quantum system of the first quantum system.

[0366] Furthermore, in a specific example, the total auxiliary quantum system may specifically include a first subsystem (i.e., subsystem A, corresponding to the first sub-auxiliary register) and a second subsystem (i.e., subsystem B, corresponding to the second sub-auxiliary register); wherein, the first subsystem includes n quantum bits, and correspondingly, the second subsystem includes n' quantum bits. The n is a positive integer greater than or equal to 1, and the n' is a positive integer satisfying 2 n’ A positive integer ≥rank(ρ); the values ​​of n and n' may be the same or different, and the present disclosure does not impose any specific limitation on this.

[0367] Step 23: Use the target unitary operator U ρ Prepare the target quantum state ρ; further, prepare the preset total initial quantum state required for the block coding quantum circuit

[0368] Here, the target quantum state ρ is the initial quantum state of the first quantum system; the quantum state is the initial quantum state of the total auxiliary quantum system formed by subsystem A and subsystem B in the block coded quantum circuit. Further, for subsystem A, its initial quantum state can be specifically Correspondingly, for subsystem B, its initial quantum state can be specifically expressed as

[0369] Based on this, the total initial quantum state That is the initial input quantum state of the block-coded quantum system corresponding to the block-coded quantum circuit in program one.

[0370] Step 24: Block Encoding Unitary Operator As the initial unitary operator U0 in program 1, and the preset total initial quantum state Input them into program 1 and get the output of program 1, that is, get the block coding unitary operator The corresponding first characteristic phase λ and T-1 target output quantum state |χ T-1 >.

[0371] Here, the first characteristic phase λ is the block coding unitary operator The estimated value of the corresponding characteristic phase, T-1 target output quantum state |χ T-1 > is the characteristic quantum state (also known as the first characteristic state) corresponding to the first characteristic phase λ.

[0372] Step 25: Initialize the quantum state And perform the following steps:

[0373] Step 25.1: Measure the total auxiliary quantum system, i.e., the subsystem A and subsystem B, to obtain a measurement result; if the measurement result is a zero state, directly execute step 26; otherwise, execute step 25.2.

[0374] Step 25.2: Update the total initial quantum state |χ0> so that Recall procedure 1. Specifically, continue to encode the unitary operator As the initial unitary operator U0 in program 1 (that is, ), and the total initial quantum state |χ0> is updated to the current quantum state In the case of , re-obtain the output of program 1, that is, obtain the block coding unitary operator The corresponding new first characteristic phase λ and the new T-1 target output quantum state |χ T-1 >. Proceed to step 25.3.

[0375] Step 25.3: Update the current quantum state The updated quantum state is the new T-1 target output quantum state |χ obtained in step 25.2 T-1 > and return to step 25.1 to remeasure.

[0376] Step 26: Based on the measurement results, it can be known that the output quantum state of subsystem B and the total auxiliary quantum system corresponding to subsystem B is zero state. At this time, based on the current quantum state The quantum pure state on the first quantum system is obtained, denoted as |χ ρ >, that is In other words, after removing the system quantum state of the total auxiliary quantum system corresponding to subsystems A and B from the system quantum state of the block coded quantum system, the target characteristic state corresponding to the target quantum state ρ can be obtained, that is, |χ ρ >. Accordingly, based on the current first characteristic phase λ, the target eigenvalue of the target quantum state ρ, i.e., cos(λ), is obtained.

[0377] Here, |χ ρ > satisfy ρ|χ ρ >=cos(λ)|χ ρ >.

[0378] Step 27: Output the target eigenvalue cos(λ) of the target quantum state ρ and the target eigenstate corresponding to the target eigenvalue |χ ρ >.

[0379] Part III: Application Expansion: Quantum State Entanglement Spectrum Estimation

[0380] Specifically, execute the above main program (i.e., program 2) S times to obtain S target eigenvalues, sort the S target eigenvalues ​​in descending order, and select the top k target eigenvalues ​​from them. At this time, the top k target eigenvalues ​​are recorded as That is the estimated value of the entanglement spectrum of the two-component quantum state corresponding to the target quantum state ρ.

[0381] Here, the bipartite quantum state refers to the system quantum state of a bipartite quantum system consisting of the quantum system corresponding to the target quantum state ρ (i.e., the first quantum system described above) and another quantum system (which can be referred to as the second quantum system). For example, assuming the bipartite quantum state of the two quantum systems (i.e., the first quantum system and the second quantum system) is denoted by |ψ>, then the target quantum state ρ = Tr2(|ψ><ψ|), that is, the target quantum state ρ is equal to the partial trace of the bipartite quantum state |ψ> in the second quantum system.

[0382] Based on this, it can be seen that when the entanglement spectrum is estimated based on the disclosed solution, its input is: target quantum state ρ, number of executions S, number of eigenvalues ​​k. Correspondingly, its output is That is, the estimated value of the entanglement spectrum of the two-component quantum state |ψ>.

[0383] Part 4, Case Presentation:

[0384] In order to demonstrate the effect of the disclosed solution, the following numerical simulation experiment was conducted: Here, a random 4-qubit unitary matrix is ​​selected as the target unitary operator U for preparing a 2-qubit target quantum state ρ ρ , among which, through U ρ The matrix expression of the target quantum state ρ is numerically calculated as follows:

[0385]

[0386] The four eigenvalues ​​range from small to approximately 0.004, 0.027, 0.319, and 0.650. The goal of this experiment is to demonstrate that the disclosed solution can find the larger eigenvalue and corresponding eigenstate of the target quantum state ρ with a high probability in actual use.

[0387] First, the target unitary operator U ρ Enter the main program (also known as Program 2), then repeat the main program 100 times. Finally, the 100 eigenvalues ​​obtained are counted. The statistical results are shown in the figure below:

[0388] Specifically, if Figure 7 As shown, in 100 runs, the probability of returning 0.004 is 1%, the probability of returning 0.027 is 1%, the probability of returning 0.319 is 31%, and the probability of returning 0.650 is 67%. This verifies that the disclosed scheme can correctly return the principal component of the target quantum state ρ.

[0389] This public solution is designed to adapt to the near-term practical quantum computers and has the following features:

[0390] First, only a single auxiliary qubit (i.e., the first auxiliary register) is used, which reduces the required quantum resources and enhances the feasibility of solving quantum features in medium-scale quantum computing devices.

[0391] Second, rich application scenarios, block coding unitary operator No restriction is imposed, that is, no restriction is imposed on the target unitary operator.

[0392] In summary, the disclosed solution has the following advantages:

[0393] (1) Practicality: It can be implemented on a quantum computer, has a wide range of application scenarios, and does not require quantum Fourier transform technology. Moreover, the circuit structure is simpler, the probability of success is higher, and it is easier to implement. In addition, the target quantum state of the disclosed solution can be a quantum pure state or a quantum mixed state. In other words, the disclosed solution is applicable to both quantum pure states and quantum mixed states.

[0394] (2) High efficiency: Quantum circuits can be constructed with low consumption, effectively reducing the required resources;

[0395] (3) Certainty: The quantum principal component that meets the accuracy requirements is obtained with extremely high probability;

[0396] (4) Scalability: It has strong scalability and can be used to analyze the main components of large-scale quantum states;

[0397] (5) High precision: effectively ensures the accuracy requirements;

[0398] (6) Innovation: A novel and efficient quantum circuit is provided to implement quantum principal component analysis.

[0399] The disclosed solution also provides a device for determining quantum state components, such as Figure 8 Shown, including:

[0400] The component processing unit 801 is used to perform the component analysis step; wherein, the component analysis step includes: in the current sub-process, the total initial quantum state is used as the simulated block coded unitary operator Given the total input quantum state of the corresponding block-coded quantum circuit, the block-coded unitary operator is obtained The first characteristic phase λ corresponding to the first characteristic phase λ, and the first characteristic state corresponding to the first characteristic phase λ; wherein the first characteristic state corresponding to the first characteristic phase λ is the block coding unitary operator The block coded quantum system includes a first quantum system and a total auxiliary quantum system; the block coded quantum circuit includes a target auxiliary register corresponding to the total auxiliary quantum system, and a target main register corresponding to the first quantum system; the total initial quantum state is obtained based on the target quantum state ρ of the first quantum system, which is a preset total initial quantum state or a first eigenstate obtained in a previous process; when it is determined that the measurement result corresponding to the target auxiliary register in the block coded quantum circuit meets a preset requirement, first component information of the target quantum state ρ is obtained based on the first eigenphase λ and the first eigenstate corresponding to the first eigenphase λ;

[0401] The output unit 802 is used to output the first component information of the target quantum state ρ; wherein the first component information includes at least one of the following: a target eigenvalue of the target quantum state ρ, and a target eigenstate corresponding to the target eigenvalue.

[0402] In a specific example of the disclosed solution, the component processing unit 801 is further configured to:

[0403] Performing the component analysis step multiple times to obtain multiple pieces of first component information of the target quantum state ρ; obtaining principal component information of the target quantum state ρ based on the multiple pieces of first component information of the target quantum state ρ;

[0404] Among them, the target eigenvalue corresponding to the principal component information of the target quantum state ρ is greater than the target eigenvalue corresponding to other first component information.

[0405] In a specific example of the disclosed solution, the apparatus further comprises: an entanglement spectrum determining unit; wherein,

[0406] The entanglement spectrum determination unit is used to perform the entanglement spectrum determination step, which includes: when multiple target eigenvalues ​​are obtained, selecting at least two target eigenvalues ​​that meet the numerical requirements from the multiple target eigenvalues, and obtaining the entanglement spectrum of the two-component quantum state corresponding to the target quantum state ρ based on the at least two selected target eigenvalues.

[0407] In a specific example of the present disclosure, the component processing unit 801 is specifically configured to:

[0408] Obtaining a target eigenvalue of the target quantum state ρ based on the first eigenphase λ;

[0409] Based on the first eigenstate corresponding to the first eigenphase λ, a target eigenstate corresponding to the target eigenvalue of the target quantum state ρ is obtained.

[0410] In a specific example of the present disclosure, the component processing unit 801 is specifically configured to:

[0411] Based on the first characteristic phase λ, an eigenvalue cos(λ) is obtained; wherein the eigenvalue cos(λ) is a target eigenvalue of the target quantum state ρ.

[0412] In a specific example of the present disclosure, the component processing unit 801 is specifically configured to:

[0413] Based on a first eigenstate corresponding to the first eigenphase λ, a deflection trace of the first eigenstate on the total auxiliary quantum system is obtained; wherein the deflection trace is a target eigenstate corresponding to a target eigenvalue of the target quantum state ρ.

[0414] In a specific example of the disclosed solution, the component processing unit 801 is further configured to:

[0415] When it is determined that the measurement result corresponding to the target auxiliary register in the block coded quantum circuit does not meet the preset requirements, the total initial quantum state is updated to the first characteristic state obtained by the current process, and the next process is executed to obtain the block coded unitary operator The corresponding new first characteristic phase λ, and the first characteristic state corresponding to the new first characteristic phase λ.

[0416] In a specific example of the disclosed solution, the apparatus further includes: a phase processing unit;

[0417] The phase processing unit is used to perform a quantum phase search step, wherein the quantum phase search step includes: obtaining a block coded unitary operator of a block coded quantum system T phase estimation values; the T phase estimation values ​​meet the phase estimation accuracy requirement, and the value of T is at least related to the phase estimation accuracy requirement;

[0418] The component processing unit is specifically configured to obtain the block coding unitary operator based on the T phase estimation values. The corresponding first characteristic phase λ.

[0419] In a specific example of the disclosed solution, the phase processing unit is further configured to:

[0420] Obtaining a t-th phase estimation value among the T phase estimation values ​​based on the t-th phase search process;

[0421] The t-th phase search process includes:

[0422] Determining the t-1th quantum related information required for the t-th phase search process; the t-1th quantum related information is based on the t-1th phase search process;

[0423] Perform Q interval compression processing on the t-1th target interval in the t-1th quantum related information to obtain the first interval (t-1) Q ; Wherein, Q is a positive integer greater than or equal to 1;

[0424] Based on the first interval (t-1) Q Get the tth phase estimate λ t .

[0425] In a specific example of the disclosed solution, the phase processing unit is further configured to:

[0426] Based on the t-th phase estimation value λ t , for the first interval (t-1) Q Update to obtain the t-th target interval; wherein the t-th target interval is the interval obtained after the t-th phase search process, which is used as the t-th quantum related information required for the t+1-th phase search process.

[0427] In a specific example of the disclosed solution, the phase processing unit is further configured to:

[0428] Based on the t-th phase estimation value, the first unitary operator U in the t-1-th quantum related information is t-1 Update and get the first unitary operator U t ; The first unitary operator U tThe unitary operator obtained after the t-th phase search process is used as the t-th quantum related information required for the t+1-th phase search process;

[0429] Wherein, the first unitary operator U t-1 is based on the t-1th phase estimate and the block coding unitary operator Determined; When t is equal to 1, the first unitary operator U0 is the block coding unitary operator

[0430] In a specific example of the disclosed solution, the phase processing unit is specifically configured to:

[0431] When the value of Q is 1, a target parameter value of a target adjustable parameter in a first auxiliary register of a target quantum circuit is determined; wherein the target quantum circuit also includes the block coded quantum circuit; the first auxiliary register is a parameterized quantum circuit; the target quantum circuit further includes a target controlled unitary gate controlled by the first auxiliary register and acting on the target main register and the target auxiliary register, the target controlled unitary gate being used to estimate the block coded unitary operator The corresponding characteristic phase;

[0432] Based on the t-1th target interval, the tth Q target value;

[0433] Based on the Q target value, and the first unitary operator U in the t-1th quantum related information t-1 , construct the specified unitary operator The first unitary operator U t-1 is based on the t-1th phase estimate and the block coding unitary operator Determined; When t is equal to 1, the first unitary operator U0 is a block coding unitary operator

[0434] The target adjustable parameter is the target parameter value, the input quantum state of the first auxiliary register is the preset initial state, the total input quantum state of the target main register and the target auxiliary register is the t-1th target output quantum state in the t-1th quantum related information, and the target controlled unitary gate is updated to the specified unitary operator In the case of the first auxiliary register, the tth Q measurement results; where, when t is 1, the 0th target output quantum state is the preset total initial quantum state, or the first characteristic state obtained in the previous process;

[0435] Based on the QThe measurement result and the interval length of the t-1th target interval are used to perform interval compression processing on the t-1th target interval to obtain the first interval (t-1) Q .

[0436] In a specific example of the disclosed solution, the phase processing unit is further configured to:

[0437] The target adjustable parameter is the target parameter value, the input quantum state of the first auxiliary register is the preset initial state, the total input state of the target main register and the target auxiliary register is the t-1th target output quantum state in the t-1th quantum related information, and the target controlled unitary gate is updated to the specified unitary operator In the case of , the tth target output quantum state jointly output by the target main register and the target auxiliary register is obtained.

[0438] In a specific example of the disclosed solution, the phase processing unit is specifically configured to:

[0439] When the value of Q is greater than or equal to 2, a target parameter value of a target adjustable parameter in a first auxiliary register of a target quantum circuit is determined; wherein the target quantum circuit also includes the block coded quantum circuit; the first auxiliary register is a parameterized quantum circuit; the target quantum circuit further includes a target controlled unitary gate controlled by the first auxiliary register and acting on the target main register and the target auxiliary register, the target controlled unitary gate being used to estimate the block coded unitary operator The corresponding characteristic phase;

[0440] After the Q-time interval compression process for the t-th phase search process is performed using the following process, the first interval (t-1) is obtained: Q ;

[0441] The qth interval compression process in the Qth interval compression process of the tth phase search process includes:

[0442] Based on the first interval (t-1) obtained q-1 , get the tth q Target value; the first interval (t-1) q-1 is obtained by the q-1th interval compression process in the tth phase search process. When q is 1, the first interval (t-1)0 is the t-1th target interval; q is a natural number greater than or equal to 1 and less than or equal to Q;

[0443] Based on the q target value, and the first unitary operator U in the t-1th quantum related information t-1 , construct the specified unitary operator required for the qth interval compression process The first unitary operator U t-1 is based on the t-1th phase estimate and the block coding unitary operator Determined; When t is equal to 1, the first unitary operator U0 is the block coding unitary operator

[0444] The target adjustable parameter is the target parameter value, the input state of the first auxiliary register is the preset initial state, and the total input state of the target main register and the target auxiliary register is the tth q-1 Output quantum state, and the target controlled unitary gate in the target quantum circuit is updated to the specified unitary operator In the case of the first auxiliary register, the tth q The measurement result of the tth time; wherein, the tth time q-1 The output quantum state is the total output quantum state of the target main register and the target auxiliary register after the q-1th interval compression process for the tth phase search process; when q is 1, the t0th output quantum state is the t-1th target output quantum state in the t-1th quantum-related information; when t is 1 and q is 1, the 10th output quantum state is the 0th target output quantum state in the 0th quantum-related information, and the 0th target output quantum state is the preset total initial quantum state, or the first characteristic state obtained in the previous process;

[0445] Based on the q The measurement results, and the first interval (t-1) q-1 The length of the interval, for the first interval (t-1) q-1 Perform interval compression processing to obtain the first interval (t-1) q .

[0446] In a specific example of the disclosed solution, the phase processing unit is further configured to:

[0447] The target adjustable parameter is the target parameter value, the input state of the first auxiliary register is the preset initial state, and the total input state of the target main register and the target auxiliary register is the tth q-1 Output quantum state, and the target controlled unitary gate in the target quantum circuit is updated to the specified unitary operator In the case of , the tth output of the target main register and the target auxiliary register is obtained q Output quantum state;

[0448] Wherein, when the value of q is Q, the tth Q The output quantum state is the t-th target output quantum state.

[0449] In a specific example of the presently disclosed solution, the first characteristic state corresponding to the first characteristic phase is the T-1th target output quantum state.

[0450] In a specific example of the disclosed solution, the phase processing unit is specifically configured to:

[0451] using the target parameter value of the target adjustable parameter in the trained preset parameterized quantum circuit as the target parameter value of the target adjustable parameter in the first auxiliary register;

[0452] Wherein, the target controlled unitary gate includes a first controlled unitary gate and a second controlled unitary gate; the second controlled unitary gate is the conjugate transpose of the first controlled unitary gate;

[0453] The target quantum circuit is obtained by using the preset parameterized quantum circuit as a first auxiliary register, extending a target main register and a target auxiliary register, replacing a first target rotation gate in the preset parameterized quantum circuit that acts on the first auxiliary register with the first controlled unitary gate, and replacing a second target rotation gate in the preset parameterized quantum circuit that acts on the first auxiliary register with the second controlled unitary gate.

[0454] 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.

[0455] 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.

[0456] The disclosed solution also provides a computer program product, including a computer program, which, when executed by at least one quantum processing unit, implements the method described in the application to a quantum computing device.

[0457] The present disclosure also provides a computing device, comprising:

[0458] At least one quantum processing unit (QPU);

[0459] a memory coupled to the at least one QPU and configured to store executable instructions,

[0460] 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.

[0461] It is understood that the QPU element used in the solution of the present disclosure, which may also be called a quantum processor or quantum chip, may involve a physical chip including multiple quantum bits interconnected in a specific manner.

[0462] 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.

[0463] 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.

[0464] Figure 9 A schematic block diagram of an example computing device 900 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.

[0465] like Figure 9 As shown, the device 900 includes a computing unit 901, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 902 or a computer program loaded from a storage unit 908 into a random access memory (RAM) 903. Various programs and data required for the operation of the device 900 can also be stored in the RAM 903. The computing unit 901, the ROM 902, and the RAM 903 are connected to each other via a bus 904. An input / output (I / O) interface 905 is also connected to the bus 904.

[0466] Various components in the device 900 are connected to the I / O interface 905, including an input unit 906, such as a keyboard, a mouse, etc.; an output unit 907, such as various types of displays, speakers, etc.; a storage unit 908, such as a magnetic disk, an optical disk, etc.; and a communication unit 909, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 909 allows the device 900 to exchange information / data with other devices via a computer network such as the Internet and / or various telecommunication networks.

[0467] The computing unit 901 can be a variety of general-purpose and / or specialized processing components with processing and computing capabilities. Some examples of the computing unit 901 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 901 performs the various methods and processes described above, such as the method for determining the quantum state composition. For example, in some embodiments, the method for determining the quantum state composition can be implemented as a computer software program that is tangibly contained in a machine-readable medium, such as the storage unit 908. In some embodiments, part or all of the computer program can be loaded and / or installed on the device 900 via the ROM 902 and / or the communication unit 909. When the computer program is loaded into the RAM 903 and executed by the computing unit 901, one or more steps of the method for determining the quantum state composition described above can be performed. Alternatively, in other embodiments, the computing unit 901 can be configured to perform the method for determining the quantum state composition by any other suitable means (e.g., by means of firmware).

[0468] 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.

[0469] 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.

[0470] 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.

[0471] 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).

[0472] 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.

[0473] 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.

[0474] 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.

[0475] 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 determining quantum state components, comprising: Component analysis step; wherein the component analysis step includes: In the current subprocess, the total initial quantum state is used as the simulated block coded unitary operator Given the total input quantum state of the corresponding block-coded quantum circuit, the block-coded unitary operator is obtained The first characteristic phase λ corresponding to the first characteristic phase λ, and the first characteristic state corresponding to the first characteristic phase λ; wherein the first characteristic state corresponding to the first characteristic phase λ is the block coding unitary operator The system quantum state of the corresponding block-coded quantum system; the block-coded quantum system includes a first quantum system and a total auxiliary quantum system; the block-coded quantum circuit includes a target auxiliary register corresponding to the total auxiliary quantum system, and a target main register corresponding to the first quantum system; the total initial quantum state is obtained based on the target quantum state ρ of the first quantum system, and is a preset total initial quantum state, or the first characteristic state obtained in the previous process; In a case where it is determined that the measurement result corresponding to the target auxiliary register in the block coded quantum circuit is a preset state, first component information of the target quantum state ρ is obtained based on the first characteristic phase λ and the first characteristic state corresponding to the first characteristic phase λ; wherein the first component information includes at least one of the following: a target eigenvalue of the target quantum state ρ, and a target eigenstate corresponding to the target eigenvalue.

2. The method according to claim 1, further comprising: Performing the component analysis step multiple times to obtain multiple pieces of first component information of the target quantum state ρ; Obtaining principal component information of the target quantum state ρ based on the plurality of first component information of the target quantum state ρ; Among them, the target eigenvalue corresponding to the principal component information of the target quantum state ρ is greater than the target eigenvalue corresponding to other first component information.

3. The method according to claim 2, further comprising: The entanglement spectrum determining step comprises: When multiple target eigenvalues ​​are obtained, at least two target eigenvalues ​​that meet the numerical requirements are selected from the multiple target eigenvalues, and based on the at least two selected target eigenvalues, the entangled spectrum of the two-component quantum state corresponding to the target quantum state ρ is obtained.

4. The method according to claim 1, wherein The obtaining, based on the first characteristic phase λ and the first characteristic state corresponding to the first characteristic phase λ, first component information of the target quantum state ρ includes: Obtaining a target eigenvalue of the target quantum state ρ based on the first eigenphase λ; Based on the first eigenstate corresponding to the first eigenphase λ, a target eigenstate corresponding to the target eigenvalue of the target quantum state ρ is obtained.

5. The method according to claim 4, wherein The obtaining, based on the first characteristic phase λ, a target characteristic value of the target quantum state ρ, comprises: Based on the first characteristic phase λ, an eigenvalue cos(λ) is obtained; wherein the eigenvalue cos(λ) is a target eigenvalue of the target quantum state ρ.

6. The method according to claim 4, wherein: Obtaining a target eigenstate corresponding to a target eigenvalue of the target quantum state ρ based on the first eigenstate corresponding to the first eigenphase λ includes: Based on a first eigenstate corresponding to the first eigenphase λ, a deflection trace of the first eigenstate on the total auxiliary quantum system is obtained; wherein the deflection trace is a target eigenstate corresponding to a target eigenvalue of the target quantum state ρ.

7. The method according to any one of claims 4 to 6, wherein: The component analysis step further comprises: When it is determined that the measurement result corresponding to the target auxiliary register in the block coded quantum circuit is not the preset state, the total initial quantum state is updated to the first characteristic state obtained by the current process, and the next process is executed to obtain the block coded unitary operator The corresponding new first characteristic phase λ, and the first characteristic state corresponding to the new first characteristic phase λ.

8. The method according to any one of claims 1 to 6, further comprising: A quantum phase search step, wherein the quantum phase search step comprises: Obtaining the block-coded unitary operator of a block-coded quantum system T phase estimation values; the T phase estimation values ​​meet the phase estimation accuracy requirement, and the value of T is at least related to the phase estimation accuracy requirement; Among them, the block coding unitary operator is obtained The corresponding first characteristic phase λ includes: Based on the T phase estimation values, the block coding unitary operator is obtained The corresponding first characteristic phase λ.

9. The method according to claim 8, wherein The quantum phase search step further comprises: Obtaining a t-th phase estimation value among the T phase estimation values ​​based on the t-th phase search process; The t-th phase search process includes: Determining the t-1th quantum related information required for the t-th phase search process; the t-1th quantum related information is based on the t-1th phase search process; Perform Q interval compression processing on the t-1th target interval in the t-1th quantum related information to obtain the first interval (t-1) Q ; Wherein, Q is a positive integer greater than or equal to 1; Based on the first interval (t-1) Q Get the tth phase estimate λ t .

10. The method according to claim 9, wherein: The quantum phase search step further comprises: Based on the t-th phase estimation value λ t , for the first interval (t-1) Q Update to obtain the t-th target interval; wherein the t-th target interval is the interval obtained after the t-th phase search process, which is used as the t-th quantum related information required for the t+1-th phase search process.

11. The method according to claim 9, wherein The quantum phase search step further comprises: Based on the t-th phase estimation value, the first unitary operator U in the t-1-th quantum related information is t-1 Update and get the first unitary operator U t ; The first unitary operator U t The unitary operator obtained after the t-th phase search process is used as the t-th quantum related information required for the t+1-th phase search process; Wherein, the first unitary operator U t-1 is based on the t-1th phase estimate and the block coding unitary operator Determined; When t is equal to 1, the first unitary operator U0 is the block coding unitary operator 12. The method according to claim 9, wherein The t-1th target interval in the t-1th quantum related information is compressed Q times to obtain the first interval (t-1) Q ,include: When the value of Q is 1, a target parameter value of a target adjustable parameter in a first auxiliary register of a target quantum circuit is determined; wherein the target quantum circuit also includes the block coded quantum circuit; the first auxiliary register is a parameterized quantum circuit; the target quantum circuit further includes a target controlled unitary gate controlled by the first auxiliary register and acting on the target main register and the target auxiliary register, the target controlled unitary gate being used to estimate the block coded unitary operator The corresponding characteristic phase; Based on the t-1th target interval, the tth Q target value; Based on the Q target value, and the first unitary operator U in the t-1th quantum related information t-1 , construct the specified unitary operator The first unitary operator U t-1 is based on the t-1th phase estimate and the block coding unitary operator Determined; When t is equal to 1, the first unitary operator U0 is a block coding unitary operator The target adjustable parameter is the target parameter value, the input quantum state of the first auxiliary register is the preset initial state, the total input quantum state of the target main register and the target auxiliary register is the t-1th target output quantum state in the t-1th quantum related information, and the target controlled unitary gate is updated to the specified unitary operator In the case of the first auxiliary register, the tth Q measurement results; where, when t is 1, the 0th target output quantum state is the preset total initial quantum state, or the first characteristic state obtained in the previous process; Based on the Q The measurement result and the interval length of the t-1th target interval are used to perform interval compression processing on the t-1th target interval to obtain the first interval (t-1) Q .

13. The method according to claim 12, wherein: The quantum phase search step further comprises: The target adjustable parameter is the target parameter value, the input quantum state of the first auxiliary register is the preset initial state, the total input state of the target main register and the target auxiliary register is the t-1th target output quantum state in the t-1th quantum related information, and the target controlled unitary gate is updated to the specified unitary operator In the case of , the tth target output quantum state jointly output by the target main register and the target auxiliary register is obtained.

14. The method according to claim 9, wherein The t-1th target interval in the t-1th quantum related information is compressed Q times to obtain the first interval (t-1) Q ,include: When the value of Q is greater than or equal to 2, a target parameter value of a target adjustable parameter in a first auxiliary register of a target quantum circuit is determined; wherein the target quantum circuit also includes the block coded quantum circuit; the first auxiliary register is a parameterized quantum circuit; the target quantum circuit further includes a target controlled unitary gate controlled by the first auxiliary register and acting on the target main register and the target auxiliary register, the target controlled unitary gate being used to estimate the block coded unitary operator The corresponding characteristic phase; After the Q-time interval compression process for the t-th phase search process is performed using the following process, the first interval (t-1) is obtained: Q ; The qth interval compression process in the Qth interval compression process of the tth phase search process includes: Based on the first interval (t-1) obtained q-1 , get the tth q Target value; the first interval (t-1) q-1 is obtained by the q-1th interval compression process in the tth phase search process. When q is 1, the first interval (t-1)0 is the t-1th target interval; q is a natural number greater than or equal to 1 and less than or equal to Q; Based on the q target value, and the first unitary operator U in the t-1th quantum related information t-1 , construct the specified unitary operator required for the qth interval compression process The first unitary operator U t-1 is based on the t-1th phase estimate and the block coding unitary operator Determined; When t is equal to 1, the first unitary operator U0 is the block coding unitary operator The target adjustable parameter is the target parameter value, the input state of the first auxiliary register is the preset initial state, and the total input state of the target main register and the target auxiliary register is the tth q-1 Output quantum state, and the target controlled unitary gate in the target quantum circuit is updated to the specified unitary operator In the case of the first auxiliary register, the tth q The measurement result of the tth time; wherein, the tth time q-1 The output quantum state is the total output quantum state of the target main register and the target auxiliary register after the q-1th interval compression process for the tth phase search process; when q is 1, the t0th output quantum state is the t-1th target output quantum state in the t-1th quantum-related information; when t is 1 and q is 1, the 10th output quantum state is the 0th target output quantum state in the 0th quantum-related information, and the 0th target output quantum state is the preset total initial quantum state, or the first characteristic state obtained in the previous process; Based on the q The measurement results, and the first interval (t-1) q-1 The length of the interval, for the first interval (t-1) q-1 Perform interval compression processing to obtain the first interval (t-1) q .

15. The method according to claim 14, wherein the quantum phase search step further comprises: The target adjustable parameter is the target parameter value, the input state of the first auxiliary register is the preset initial state, and the total input state of the target main register and the target auxiliary register is the tth q-1 Output quantum state, and the target controlled unitary gate in the target quantum circuit is updated to the specified unitary operator In the case of , the tth output of the target main register and the target auxiliary register is obtained q Output quantum state; Among them, when the value of q is Q, the tth Q The output quantum state is the tth target output quantum state.

16. The method according to claim 13, wherein: The first characteristic state corresponding to the first characteristic phase is the T-1th target output quantum state.

17. The method according to claim 12, wherein: Determining a target parameter value of a target adjustable parameter in a first auxiliary register of a target quantum circuit includes: using the target parameter value of the target adjustable parameter in the trained preset parameterized quantum circuit as the target parameter value of the target adjustable parameter in the first auxiliary register; Wherein, the target controlled unitary gate includes a first controlled unitary gate and a second controlled unitary gate; the second controlled unitary gate is the conjugate transpose of the first controlled unitary gate; The target quantum circuit is obtained by using the preset parameterized quantum circuit as a first auxiliary register, extending a target main register and a target auxiliary register, replacing a first target rotation gate in the preset parameterized quantum circuit that acts on the first auxiliary register with the first controlled unitary gate, and replacing a second target rotation gate in the preset parameterized quantum circuit that acts on the first auxiliary register with the second controlled unitary gate.

18. A device for determining quantum state components, comprising: A component processing unit is used to perform a component analysis step; wherein the component analysis step includes: in the current sub-process, the total initial quantum state is used as a simulated block coding unitary operator Given the total input quantum state of the corresponding block-coded quantum circuit, the block-coded unitary operator is obtained The first characteristic phase λ corresponding to the first characteristic phase λ, and the first characteristic state corresponding to the first characteristic phase λ; wherein the first characteristic state corresponding to the first characteristic phase λ is the block coding unitary operator The block coded quantum system includes a first quantum system and a total auxiliary quantum system; the block coded quantum circuit includes a target auxiliary register corresponding to the total auxiliary quantum system, and a target main register corresponding to the first quantum system; the total initial quantum state is obtained based on the target quantum state ρ of the first quantum system, which is a preset total initial quantum state or a first eigenstate obtained in a previous process; when it is determined that the measurement result corresponding to the target auxiliary register in the block coded quantum circuit is a preset state, first component information of the target quantum state ρ is obtained based on the first eigenphase λ and the first eigenstate corresponding to the first eigenphase λ; An output unit is used to output the first component information of the target quantum state ρ; wherein the first component information includes at least one of the following: a target eigenvalue of the target quantum state ρ, and a target eigenstate corresponding to the target eigenvalue.

19. The device according to claim 18, wherein The component processing unit is further configured to perform the component analysis step multiple times to obtain multiple pieces of first component information of the target quantum state ρ; Obtaining principal component information of the target quantum state ρ based on the plurality of first component information of the target quantum state ρ; Among them, the target eigenvalue corresponding to the principal component information of the target quantum state ρ is greater than the target eigenvalue corresponding to other first component information.

20. The device according to claim 19, wherein The device further comprises: an entanglement spectrum determining unit; wherein, The entanglement spectrum determination unit is used to perform the entanglement spectrum determination step, which includes: when multiple target eigenvalues ​​are obtained, selecting at least two target eigenvalues ​​that meet the numerical requirements from the multiple target eigenvalues, and obtaining the entanglement spectrum of the two-component quantum state corresponding to the target quantum state ρ based on the at least two selected target eigenvalues.

21. The apparatus according to claim 18, wherein The component processing unit is specifically used for: Obtaining a target eigenvalue of the target quantum state ρ based on the first eigenphase λ; Based on the first eigenstate corresponding to the first eigenphase λ, a target eigenstate corresponding to the target eigenvalue of the target quantum state ρ is obtained.

22. The device according to claim 21, wherein The component processing unit is specifically used for: Based on the first characteristic phase λ, an eigenvalue cos(λ) is obtained; wherein the eigenvalue cos(λ) is a target eigenvalue of the target quantum state ρ.

23. The device according to claim 21, wherein The component processing unit is specifically used for: Based on a first eigenstate corresponding to the first eigenphase λ, a deflection trace of the first eigenstate on the total auxiliary quantum system is obtained; wherein the deflection trace is a target eigenstate corresponding to a target eigenvalue of the target quantum state ρ.

24. The device according to any one of claims 21 to 23, wherein: The component processing unit is further used for: When it is determined that the measurement result corresponding to the target auxiliary register in the block coded quantum circuit is not the preset state, the total initial quantum state is updated to the first characteristic state obtained by the current process, and the next process is executed to obtain the block coded unitary operator The corresponding new first characteristic phase λ, and the first characteristic state corresponding to the new first characteristic phase λ.

25. The apparatus according to any one of claims 18 to 23, further comprising: Phase processing unit; The phase processing unit is used to perform a quantum phase search step, wherein the quantum phase search step includes: obtaining a block coded unitary operator of a block coded quantum system T phase estimation values; the T phase estimation values ​​meet the phase estimation accuracy requirement, and the value of T is at least related to the phase estimation accuracy requirement; The component processing unit is specifically configured to obtain the block coding unitary operator based on the T phase estimation values. The corresponding first characteristic phase λ.

26. The device according to claim 25, wherein The phase processing unit is further configured to: Obtaining a t-th phase estimation value among the T phase estimation values ​​based on the t-th phase search process; The t-th phase search process includes: Determining the t-1th quantum related information required for the t-th phase search process; the t-1th quantum related information is based on the t-1th phase search process; Perform Q interval compression processing on the t-1th target interval in the t-1th quantum related information to obtain the first interval (t-1) Q ; Wherein, Q is a positive integer greater than or equal to 1; Based on the first interval (t-1) Q Get the tth phase estimate λ t .

27. The device according to claim 26, wherein The phase processing unit is further configured to: Based on the t-th phase estimation value λ t , for the first interval (t-1) Q Update to obtain the t-th target interval; wherein the t-th target interval is the interval obtained after the t-th phase search process, which is used as the t-th quantum related information required for the t+1-th phase search process.

28. The apparatus according to claim 26, wherein The phase processing unit is further configured to: Based on the t-th phase estimation value, the first unitary operator U in the t-1-th quantum related information is t-1 Update and get the first unitary operator U t ; The first unitary operator U t The unitary operator obtained after the t-th phase search process is used as the t-th quantum related information required for the t+1-th phase search process; Wherein, the first unitary operator U t-1 is based on the t-1th phase estimate and the block coding unitary operator Determined; When t is equal to 1, the first unitary operator U0 is the block coding unitary operator 29. The apparatus according to claim 26, wherein The phase processing unit is specifically configured to: When the value of Q is 1, a target parameter value of a target adjustable parameter in a first auxiliary register of a target quantum circuit is determined; wherein the target quantum circuit also includes the block coded quantum circuit; the first auxiliary register is a parameterized quantum circuit; the target quantum circuit further includes a target controlled unitary gate controlled by the first auxiliary register and acting on the target main register and the target auxiliary register, the target controlled unitary gate being used to estimate the block coded unitary operator The corresponding characteristic phase; Based on the t-1th target interval, the tth Q target value; Based on the Q target value, and the first unitary operator U in the t-1th quantum related information t-1 , construct the specified unitary operator The first unitary operator U t-1 is based on the t-1th phase estimate and the block coding unitary operator Determined; When t is equal to 1, the first unitary operator U0 is a block coding unitary operator The target adjustable parameter is the target parameter value, the input quantum state of the first auxiliary register is the preset initial state, the total input quantum state of the target main register and the target auxiliary register is the t-1th target output quantum state in the t-1th quantum related information, and the target controlled unitary gate is updated to the specified unitary operator In the case of the first auxiliary register, the tth Q measurement results; where, when t is 1, the 0th target output quantum state is the preset total initial quantum state, or the first characteristic state obtained in the previous process; Based on the Q The measurement result and the interval length of the t-1th target interval are used to perform interval compression processing on the t-1th target interval to obtain the first interval (t-1) Q .

30. The apparatus according to claim 29, wherein The phase processing unit is further configured to: The target adjustable parameter is the target parameter value, the input quantum state of the first auxiliary register is the preset initial state, the total input state of the target main register and the target auxiliary register is the t-1th target output quantum state in the t-1th quantum related information, and the target controlled unitary gate is updated to the specified unitary operator In the case of , the tth target output quantum state jointly output by the target main register and the target auxiliary register is obtained.

31. The apparatus according to claim 26, wherein The phase processing unit is specifically configured to: When the value of Q is greater than or equal to 2, a target parameter value of a target adjustable parameter in a first auxiliary register of a target quantum circuit is determined; wherein the target quantum circuit also includes the block coded quantum circuit; the first auxiliary register is a parameterized quantum circuit; the target quantum circuit further includes a target controlled unitary gate controlled by the first auxiliary register and acting on the target main register and the target auxiliary register, the target controlled unitary gate being used to estimate the block coded unitary operator The corresponding characteristic phase; After the Q-time interval compression process for the t-th phase search process is performed using the following process, the first interval (t-1) is obtained: Q ; The qth interval compression process in the Qth interval compression process of the tth phase search process includes: Based on the first interval (t-1) obtained q-1 , get the tth q Target value; the first interval (t-1) q-1 is obtained by the q-1th interval compression process in the tth phase search process. When q is 1, the first interval (t-1)0 is the t-1th target interval; q is a natural number greater than or equal to 1 and less than or equal to Q; Based on the q target value, and the first unitary operator U in the t-1th quantum related information t-1 , construct the specified unitary operator required for the qth interval compression process The first unitary operator U t-1 is based on the t-1th phase estimate and the block coding unitary operator Determined; When t is equal to 1, the first unitary operator U0 is the block coding unitary operator The target adjustable parameter is the target parameter value, the input state of the first auxiliary register is the preset initial state, and the total input state of the target main register and the target auxiliary register is the tth q-1 Output quantum state, and the target controlled unitary gate in the target quantum circuit is updated to the specified unitary operator In the case of the first auxiliary register, the tth q The measurement result of the tth time; wherein, the tth time q-1 The output quantum state is the total output quantum state of the target main register and the target auxiliary register after the q-1th interval compression process for the tth phase search process; when q is 1, the t0th output quantum state is the t-1th target output quantum state in the t-1th quantum-related information; when t is 1 and q is 1, the 10th output quantum state is the 0th target output quantum state in the 0th quantum-related information, and the 0th target output quantum state is the preset total initial quantum state, or the first characteristic state obtained in the previous process; Based on the q The measurement results, and the first interval (t-1) q-1 The length of the interval, for the first interval (t-1) q-1 Perform interval compression processing to obtain the first interval (t-1) q .

32. The apparatus according to claim 31, wherein the phase processing unit is further configured to: The target adjustable parameter is the target parameter value, the input state of the first auxiliary register is the preset initial state, and the total input state of the target main register and the target auxiliary register is the tth q-1 Output quantum state, and the target controlled unitary gate in the target quantum circuit is updated to the specified unitary operator In the case of , the tth output of the target main register and the target auxiliary register is obtained q Output quantum state; in, When the value of q is Q, the tth Q The output quantum state is the tth target output quantum state.

33. The apparatus according to claim 30, wherein The first characteristic state corresponding to the first characteristic phase is the T-1th target output quantum state.

34. The apparatus of claim 29, wherein: The phase processing unit is specifically configured to: using the target parameter value of the target adjustable parameter in the trained preset parameterized quantum circuit as the target parameter value of the target adjustable parameter in the first auxiliary register; Wherein, the target controlled unitary gate includes a first controlled unitary gate and a second controlled unitary gate; the second controlled unitary gate is the conjugate transpose of the first controlled unitary gate; The target quantum circuit is obtained by using the preset parameterized quantum circuit as a first auxiliary register, extending a target main register and a target auxiliary register, replacing a first target rotation gate in the preset parameterized quantum circuit that acts on the first auxiliary register with the first controlled unitary gate, and replacing a second target rotation gate in the preset parameterized quantum circuit that acts on the first auxiliary register with the second controlled unitary gate.

35. 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 17; 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 17.

36. 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 17; Alternatively, the computer instructions are used to cause the computer to execute the method according to any one of claims 1-17.

37. 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 17; Or the computer program implements the method according to any one of claims 1 to 17 when executed by a processor.

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