Unitary operator property analysis method and device in distributed scenarios

Abstract

The present invention provides a method and device for analyzing the properties of unitary operators in a distributed scenario, and relates to the field of quantum information technology. The method includes: using the unitary operator of a quantum terminal to perform a rotation transformation on the initial quantum state of the quantum terminal to obtain the intermediate quantum state of the quantum terminal; using a plurality of unitary matrices included in a unitary matrix set to synchronously measure the intermediate quantum states of the plurality of quantum terminals to obtain a plurality of inner product results, wherein each inner product result is obtained based on a set of measurement results of the plurality of quantum terminals; based on the plurality of inner product results, obtaining the property analysis results of the quantum terminal, wherein the property analysis results of the quantum terminal characterize the similarity between the unitary operators included in the plurality of quantum terminals.

Description

Technical Field

[0001] The present invention relates to the field of quantum information technology, and more specifically, to a method and device for analyzing unitary operator properties in a distributed scenario. Background Art

[0002] Cross-platform verification is an important task that has been raised as small quantum computers have become increasingly popular on different physical platforms. Due to the diversity and limitations of quantum computer hardware, different quantum computers may use different physical implementations (such as superconducting, ion traps, optics, etc.), and these differences make it difficult to directly implement quantum communication between them. Currently, research on cross-platform verification mainly focuses on the sample complexity required to estimate the inner product of quantum states. This method estimates the properties of quantum states only through local operations and classical communications to ensure accurate estimation results with a limited number of samples.

[0003] However, the above method can only estimate the inner product of the quantum state on one device at a time, and mainly focuses on the input model based on sampling, while other types of input models are less studied. Therefore, in a distributed scenario, the estimation of the inner product is affected by multiple factors such as the synchronization of the quantum state and measurement errors, making it difficult to accurately estimate the inner product properties of the unitary operator. Summary of the invention

[0004] In view of this, the present invention provides a method and device for analyzing unitary operator properties in a distributed scenario.

[0005] One aspect of the present invention provides a method for analyzing the properties of unitary operators in a distributed scenario, the method comprising: using the unitary operator of a quantum terminal to perform a rotational transformation on the initial quantum state of the quantum terminal to obtain an intermediate quantum state of the quantum terminal; using a plurality of unitary matrices included in a unitary matrix set to synchronously measure the intermediate quantum states of the plurality of quantum terminals to obtain a plurality of inner product results; based on the plurality of inner product results, obtaining a property analysis result of the quantum terminal, wherein the property analysis result of the quantum terminal characterizes the degree of similarity between the unitary operators included in each of the plurality of quantum terminals.

[0006] According to an embodiment of the present invention, the above-mentioned use of multiple unitary matrices included in the unitary matrix set to synchronously measure the intermediate quantum states of each of the multiple quantum terminals to obtain multiple inner product results includes: for a target unitary matrix among the multiple unitary matrices, using the target unitary matrix to synchronously measure the intermediate quantum states of each of the multiple quantum terminals for multiple times to obtain a set of measurement results of each of the multiple quantum terminals in the measurement basis corresponding to the target unitary matrix; based on the set of measurement results of each of the multiple quantum terminals in the measurement basis corresponding to the target unitary matrix, determining the above-mentioned inner product result.

[0007] According to an embodiment of the present invention, the target unitary matrix is ​​used to synchronously perform multiple measurements on the intermediate quantum states of the multiple quantum terminals to obtain a set of measurement results of the multiple quantum terminals under the measurement basis corresponding to the target unitary matrix, including: for any one of the quantum terminals, based on the target unitary matrix and the standard basis, determining the measurement basis of the quantum terminal; projecting the intermediate quantum states of the quantum terminal onto multiple basis vectors included in the measurement basis to obtain multiple projection components; based on the probabilities of the multiple projection components, obtaining the probability distribution of the multiple projection components; based on the probability distribution of the multiple projection components, determining the measurement results of the quantum terminal under the measurement basis; based on the multiple measurement results obtained by the quantum terminal after multiple tests under the measurement basis, obtaining a set of measurement results of the quantum terminal under the measurement basis corresponding to the target unitary matrix.

[0008] According to an embodiment of the present invention, the inner product result is determined based on a set of measurement results of each of the multiple quantum terminals in the measurement basis corresponding to the target unitary matrix, including: performing intersection calculation on a set of measurement results of each of the multiple quantum terminals in the measurement basis corresponding to the target unitary matrix to obtain a target measurement result set; and determining the inner product result based on the number of elements included in the target measurement result set.

[0009] According to an embodiment of the present invention, the above-mentioned property analysis results of the quantum terminal are obtained based on multiple inner product results, including: based on the above-mentioned multiple inner product results and the dimension of the above-mentioned unitary matrix set, calculating an unbiased estimation result corresponding to each of the above-mentioned inner product results; based on the unbiased estimation result corresponding to each of the above-mentioned inner product results, obtaining the property analysis results of the above-mentioned quantum terminal.

[0010] According to an embodiment of the present invention, the property analysis result of the quantum terminal is obtained based on the unbiased estimation result corresponding to each of the inner product results, including: performing mean calculation on the unbiased estimation results corresponding to each of the multiple inner product results to obtain the average value of the unbiased estimation results; and obtaining the property analysis result of the quantum terminal based on the average value of the unbiased estimation results.

[0011] According to an embodiment of the present invention, the initial quantum states of the above-mentioned multiple quantum terminals are the same, wherein the above-mentioned initial quantum states are used to characterize the quantum states generated by the above-mentioned quantum terminals using multiple quantum gates.

[0012] According to an embodiment of the present invention, the above-mentioned use of the unitary operator of the above-mentioned quantum terminal to rotate the initial quantum state of the above-mentioned quantum terminal to obtain the intermediate quantum state of the above-mentioned quantum terminal includes: using the unitary operator of the above-mentioned quantum terminal to rotate the initial quantum state of the above-mentioned quantum terminal to obtain a rotated quantum state; converting the above-mentioned rotated quantum state into a density matrix to obtain the intermediate quantum state of the above-mentioned quantum terminal.

[0013] Another aspect of the present invention provides a unitary operator property analysis device in a distributed scenario, the device comprising: a transformation module, used to use the unitary operator of the quantum terminal to perform a rotational transformation on the initial quantum state of the quantum terminal to obtain the intermediate quantum state of the quantum terminal; a measurement module, used to respectively use a plurality of unitary matrices included in a unitary matrix set to synchronously measure the intermediate quantum states of the plurality of quantum terminals to obtain a plurality of inner product results, wherein each of the inner product results is obtained based on a measurement result set of the plurality of quantum terminals; a determination module, used to obtain a property analysis result of the quantum terminal based on the plurality of inner product results, wherein the property analysis result of the quantum terminal characterizes the degree of similarity between the unitary operators included in the plurality of quantum terminals.

[0014] According to an embodiment of the present invention, the above-mentioned measurement module includes: a synchronous measurement submodule, which is used to synchronously perform multiple measurements on the intermediate quantum states of each of the above-mentioned multiple quantum terminals using the target unitary matrix among the above-mentioned multiple unitary matrices, so as to obtain a set of measurement results of each of the above-mentioned multiple quantum terminals in the measurement basis corresponding to the above-mentioned target unitary matrix; and an inner product result determination submodule, which is used to determine the above-mentioned inner product result based on the set of measurement results of each of the above-mentioned multiple quantum terminals in the above-mentioned measurement basis corresponding to the above-mentioned target unitary matrix.

[0015] According to an embodiment of the present invention, based on the unitary operator on each quantum terminal, the quantum state of the quantum terminal is processed, and the quantum states of multiple quantum terminals are synchronously measured through multiple unitary matrices, so that the similarity between the unitary operators included in the multiple quantum terminals is obtained by calculating the inner product result of the unitary operator, thereby ensuring unbiased estimation of the properties of the unitary operators included in the multiple quantum terminals in a distributed scenario. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The above and other objects, features and advantages of the present invention will become more apparent through the following description of the embodiments of the present invention with reference to the accompanying drawings.

[0017] Figure 1 A flow chart of a method for analyzing unitary operator properties in a distributed scenario according to an embodiment of the present invention is shown.

[0018] Figure 2A block diagram of a device for analyzing unitary operator properties in a distributed scenario according to an embodiment of the present invention is shown.

[0019] Figure 3 A block diagram of an electronic device suitable for implementing a unitary operator property analysis method in a distributed scenario according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0020] Below, embodiments of the present invention will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the present invention. In the following detailed description, for ease of explanation, many specific details are set forth to provide a comprehensive understanding of embodiments of the present invention. However, it is apparent that one or more embodiments may also be implemented without these specific details. In addition, in the following description, descriptions of known structures and technologies are omitted to avoid unnecessary confusion of concepts of the present invention.

[0021] The terms used herein are only for describing specific embodiments and are not intended to limit the present invention. The terms "comprise", "include", etc. used herein indicate the existence of the features, steps, operations and / or components, but do not exclude the existence or addition of one or more other features, steps, operations or components.

[0022] All terms (including technical and scientific terms) used herein have the meanings commonly understood by those skilled in the art unless otherwise defined. It should be noted that the terms used herein should be interpreted as having a meaning consistent with the context of this specification and should not be interpreted in an idealized or overly rigid manner.

[0023] When using expressions such as "at least one of A, B, and C, etc.", they should generally be interpreted according to the meaning of the expression commonly understood by those skilled in the art (for example, "a system having at least one of A, B, and C" should include but is not limited to a system having A alone, B alone, C alone, A and B, A and C, B and C, and / or A, B, C, etc.).

[0024] Cross-platform verification is an important task that has been proposed as small quantum computers become increasingly popular on different physical platforms. Cross-platform verification refers to the verification of the same quantum state or quantum operation on different quantum computers or different physical platforms to ensure its consistency and reliability.

[0025] However, due to the diversity and limitations of quantum computer hardware, different quantum computers may use different physical implementations (such as superconductivity, ion traps, optics, etc.). These differences make it difficult to directly implement quantum communication between them. Therefore, traditional methods such as joint SWAP testing cannot be directly applied to cross-platform verification. In addition, since quantum states have characteristics such as superposition and entanglement, it is difficult to directly observe and verify them. At the same time, quantum states on different quantum computers may be affected by different noise and environmental factors, which further increases the difficulty of verification. Noise and environmental factors may cause decoherence and error accumulation of quantum states, thereby affecting the accuracy of the verification results.

[0026] Currently, research on cross-platform verification focuses on the sample complexity required to estimate the inner product of quantum states. For example, Alice and Bob each have multiple copies of an unknown quantum state, and their goal is to estimate the properties of the quantum state only through local operations and classical communication, and to ensure that the error between the estimated value and the true value does not exceed a given threshold. This scheme usually involves complex quantum measurement and data processing techniques to ensure accurate estimation results with a limited number of samples. Among them, Alice and Bob can be represented as receiving terminals on two different physical platforms.

[0027] However, the above method can only estimate the inner product of the quantum state on one device at a time, and mainly focuses on the input model based on sampling, while other types of input models are less studied. Therefore, in a distributed scenario, the estimation of the inner product is affected by multiple factors such as the synchronization of the quantum state and measurement errors, making it difficult to accurately estimate the inner product properties of the unitary operator.

[0028] In view of this, an embodiment of the present invention processes the quantum state of the quantum terminal through the unitary operator on each quantum terminal, and synchronously measures the quantum states of multiple quantum terminals through multiple unitary matrices, so as to obtain the similarity between the unitary operators included in the multiple quantum terminals through the calculated inner product result of the unitary operators, thereby ensuring unbiased estimation of the properties of the unitary operators included in the multiple quantum terminals in a distributed scenario.

[0029] Specifically, an embodiment of the present invention provides a method for analyzing the properties of unitary operators in a distributed scenario, including: using the unitary operator of the quantum terminal to rotate the initial quantum state of the quantum terminal to obtain an intermediate quantum state of the quantum terminal; using multiple unitary matrices included in a unitary matrix set to synchronously measure the intermediate quantum states of multiple quantum terminals to obtain multiple inner product results, wherein each inner product result is obtained based on a set of measurement results of each of the multiple quantum terminals; based on the multiple inner product results, obtaining a property analysis result of the quantum terminal, wherein the property analysis result of the quantum terminal characterizes the degree of similarity between the unitary operators included in each of the multiple quantum terminals.

[0030] It should be noted that the method and device for analyzing the properties of unitary operators in a distributed scenario determined by the embodiment of the present invention can be used in the field of quantum information technology, such as the field of quantum circuit mapping technology and the field of quantum computing technology. The method and device for analyzing the properties of unitary operators in a distributed scenario determined by the embodiment of the present invention can also be used in any field other than the field of quantum information technology, and the application field of the method and device for analyzing the properties of unitary operators in a distributed scenario determined by the embodiment of the present invention is not limited.

[0031] According to an embodiment of the present invention, a unitary operator is a linear operator acting on a Hilbert space that satisfies the unitary condition. For example, let U be a linear operator on a Hilbert space H. If U satisfies ,in is the adjoint matrix (or conjugate transposed matrix) of U, and I is the identity matrix, then U is called a unitary operator.

[0032] According to an embodiment of the present invention, in quantum computing, unitary transformation, as one of the basic operations, is the key to realizing quantum algorithms and quantum communications. Quantum gates are represented by unitary operators, and the collection of quantum gates forms a unitary group, which are used to manipulate quantum bits to realize quantum computing. Common quantum gates (such as Hadamard gates, Pauli gates, and CNOT gates) are all elements of the unitary group.

[0033] Figure 1 A flow chart of a method for analyzing unitary operator properties in a distributed scenario according to an embodiment of the present invention is shown.

[0034] like Figure 1 As shown, the method includes operations S101 to S103.

[0035] In operation S101, the initial quantum state of the quantum terminal is rotationally transformed using the unitary operator of the quantum terminal to obtain an intermediate quantum state of the quantum terminal.

[0036] In operation S102, the intermediate quantum states of the plurality of quantum terminals are synchronously measured using the plurality of unitary matrices included in the unitary matrix set to obtain a plurality of inner product results.

[0037] In operation S103, a property analysis result of the quantum terminal is obtained based on the plurality of inner product results.

[0038] According to an embodiment of the present invention, a quantum terminal can be used to represent a device or system for performing quantum computing and quantum communication. For example, in a distributed scenario, a quantum terminal includes two parts, a first quantum terminal and a second quantum terminal, which respectively own and operate their own quantum resources and algorithms. The first quantum terminal and the second quantum terminal can be actual physical devices or virtual entities representing different stakeholders or computing nodes.

[0039] According to an embodiment of the present invention, the initial quantum state can be used to indicate the uniform random quantum state of the quantum terminal to simulate the uncertainty in quantum computing. is a d-dimensional complex vector whose components (or amplitudes) are randomly and uniformly distributed and can be expressed as .

[0040] Specifically, if the quantum terminal includes a first quantum terminal and a second quantum terminal, the first quantum terminal uses its unitary operator U to convert its initial quantum state By performing a rotation transformation, we can obtain the intermediate quantum state of the first quantum terminal. , and the intermediate quantum state can be recorded as Similarly, the second quantum terminal uses its unitary operator V to its initial quantum state By performing a rotation transformation, we can obtain the intermediate quantum state of the second quantum terminal. , and the intermediate quantum state can be recorded as .in, can be expressed as the conjugate transpose of the unitary operator U, can be expressed as the conjugate transpose of the unitary operator V.

[0041] According to an embodiment of the present invention, the unitary matrix set includes multiple unitary matrices, wherein the dimension of the unitary matrix set can be In quantum computing, unitary matrices can be used to represent the transformation of quantum operations or quantum gates, and the dimension of the matrix set can be related to the number of quantum bits.

[0042] According to an embodiment of the present invention, a unitary matrix set may be randomly selected from Randomly select any unitary matrix , each time a unitary matrix is ​​selected, the intermediate quantum states of multiple quantum terminals can be synchronously measured, thereby obtaining an inner product result. The inner product result is the estimated intermediate value of the inner product between two discrete probability distributions, and the inner product estimation result of the unitary operator can be obtained through the estimated intermediate value of the inner product. The inner product result can be used to characterize the similarities or differences between different quantum states.

[0043] According to an embodiment of the present invention, before conducting an experiment, a randomly selected unitary matrix The intermediate quantum state of the first quantum terminal and the intermediate quantum state of the second quantum terminal The measurements are performed to obtain the estimated inner product value of the first quantum terminal and the estimated inner product value of the second quantum terminal in the distributed scenario, as shown below:

[0044] (1);

[0045] (2);

[0046] In the formula, represents the inner product estimate of the first quantum terminal, represents the inner product estimate of the second quantum terminal, W represents a randomly selected unitary matrix, and b represents a standard basis, where .

[0047] According to an embodiment of the present invention, the inner product relationship between the first quantum terminal and the second quantum terminal may be defined as follows:

[0048] (3);

[0049] In the formula, represents the inner product relationship between the first quantum terminal and the second quantum terminal, and d represents the dimension of the unitary matrix set.

[0050] According to an embodiment of the present invention, the inner product relationship can be calculated based on a symmetric subspace algorithm. Solve to get the inner product relationship The corresponding expected value. In quantum information theory, a symmetric subspace usually refers to a subspace consisting of all permutation-invariant quantum states. Here, "permutation-invariant" means that for any permutation operation (i.e., any unitary matrix W), the quantum states in the subspace remain unchanged after permutation. Specifically, it is related to the inner product relationship The corresponding expected value expression is as follows:

[0051] (4);

[0052] (5);

[0053] In the formula, Represents the inner product relationship The corresponding expectation value, f, represents the property of the unitary operator and can be expressed as the inner product of the conjugate transpose of the unitary operator U at the first quantum terminal and the trace of the unitary operator V at the second quantum terminal.

[0054] According to an embodiment of the present invention, the expected value can be used to synchronously measure the intermediate quantum states of multiple quantum terminals based on the following operations.

[0055] According to an embodiment of the present invention, multiple inner product results can be obtained based on multiple synchronous measurements, and the property analysis result of the quantum terminal is calculated based on the multiple inner product results, wherein the property analysis result can also be expressed as an unbiased estimation result of the inner product obtained based on the unitary operator definition.

[0056] According to an embodiment of the present invention, the property analysis result can be used to characterize the similarity between the unitary operators included in each quantum terminal. For example, the closer the value of the unbiased estimation result of the inner product is to 1, the higher the similarity between the unitary operators of all quantum terminals. The closer the value of the unbiased estimation result of the inner product is to 0, the lower the similarity between the unitary operators of all quantum terminals.

[0057] Based on this, an embodiment of the present invention processes the quantum state of the quantum terminal based on the unitary operator on each quantum terminal, and synchronously measures the quantum states of multiple quantum terminals through multiple unitary matrices, so as to obtain the similarity between the unitary operators included in the multiple quantum terminals through the calculated inner product result of the unitary operator, so as to ensure unbiased estimation of the properties of the unitary operators included in the multiple quantum terminals in a distributed scenario.

[0058] According to an embodiment of the present invention, a plurality of unitary matrices included in a unitary matrix set are respectively used to synchronously measure the intermediate quantum states of a plurality of quantum terminals to obtain a plurality of inner product results, including: for a target unitary matrix among the plurality of unitary matrices, the target unitary matrix is ​​used to synchronously measure the intermediate quantum states of the plurality of quantum terminals for multiple times to obtain a set of measurement results of the plurality of quantum terminals in a measurement basis corresponding to the target unitary matrix; and the inner product result is determined based on the set of measurement results of the plurality of quantum terminals in a measurement basis corresponding to the target unitary matrix.

[0059] According to an embodiment of the present invention, a target unitary matrix is ​​used to synchronously perform multiple measurements on the intermediate quantum states of multiple quantum terminals to obtain a set of measurement results of each of the multiple quantum terminals under the measurement basis corresponding to the target unitary matrix, including: for any quantum terminal, based on the target unitary matrix and the standard basis, determining the measurement basis of the quantum terminal; projecting the intermediate quantum states of the quantum terminal onto multiple basis vectors included in the measurement basis to obtain multiple projection components; based on the probabilities of each of the multiple projection components, obtaining the probability distribution of the multiple projection components; based on the probability distribution of the multiple projection components, determining the measurement result of the quantum terminal under the measurement basis; based on multiple measurement results obtained by multiple tests of the quantum terminal under the measurement basis, obtaining a set of measurement results of the quantum terminal under the measurement basis corresponding to the target unitary matrix.

[0060] According to an embodiment of the present invention, an inner product result is determined based on a measurement result set of each of the multiple quantum terminals in a measurement basis corresponding to a target unitary matrix, including: performing intersection calculation on a measurement result set of each of the multiple quantum terminals in a measurement basis corresponding to the target unitary matrix to obtain a target measurement result set; and determining the inner product result based on the number of elements included in the target measurement result set.

[0061] According to an embodiment of the present invention, for multiple unitary matrices in the unitary matrix set, a unitary matrix can be randomly selected as a target unitary matrix for the first quantum terminal and the second quantum terminal in each round of multiple rounds of experiments.

[0062] According to an embodiment of the present invention, for each target unitary matrix selected in a multi-round experiment, an inner product result corresponds to each of them. When calculating the inner product result corresponding to each target unitary matrix in the round, the intermediate quantum state of each of the multiple quantum terminals is measured m times synchronously using the target unitary matrix to obtain a set of measurement results of each of the multiple quantum terminals in the measurement basis corresponding to the target unitary matrix. Each set of measurement results includes m measurement results.

[0063] According to an embodiment of the present invention, for a set of measurement results obtained in each round of calculations during multiple rounds of experiments, the set of measurement results of each of the multiple quantum terminals in the measurement basis corresponding to the target unitary matrix is ​​calculated through operations such as statistical value taking, and the inner product results between the unitary operators included in each of the multiple quantum terminals are obtained.

[0064] For example, in any distributed scenario, the quantum terminal includes a first quantum terminal and a second quantum terminal, wherein the first quantum terminal and the second quantum terminal have a unitary operator U and a unitary operator V, respectively, and the initial quantum states of the first quantum terminal and the second quantum terminal are the same, both of which are .

[0065] According to an embodiment of the present invention, the unitary operator of the quantum terminal is used to perform a rotational transformation on the initial quantum state of the quantum terminal to obtain an intermediate quantum state of the quantum terminal, including: using the unitary operator of the quantum terminal to perform a rotational transformation on the initial quantum state of the quantum terminal to obtain a rotated quantum state; converting the rotated quantum state into a density matrix to obtain an intermediate quantum state of the quantum terminal.

[0066] According to an embodiment of the present invention, the first quantum terminal unitary operator Acting on the initial quantum state The intermediate quantum state of the first quantum terminal is obtained , specifically including the following operations: the first quantum terminal unitary operator Acting on the initial quantum state The transformed rotational quantum state is obtained The first quantum terminal converts the transformed rotational quantum state into a density matrix form to obtain the intermediate quantum state of the first quantum terminal. Similarly, the second quantum terminal converts the unitary operator Acting on the initial quantum state The intermediate quantum state of the second quantum terminal can also be obtained .

[0067] The following operation is repeated N times to determine the property analysis result between the unitary operators U and V respectively included in the first quantum terminal and the second quantum terminal.

[0068] Specifically, in the i-th round, from the unitary matrix set A target unitary matrix W is randomly selected for the first quantum terminal and the second quantum terminal i .in, , N is a positive integer greater than or equal to 2.

[0069] Based on the target unitary matrix W i The measurement basis of the first quantum terminal and the second quantum terminal can be determined In the measurement base The intermediate quantum state of the first quantum terminal is and the intermediate quantum state of the second quantum terminal Perform m synchronous measurements to obtain the first set of measurement results. and the second measurement result set Each set of measurement results includes the quantum terminal in the target unitary matrix W i The corresponding m measurement results under the measurement basis.

[0070] For the first measurement result set and the second measurement result set Perform intersection calculation, count the number of elements with equal values ​​in the two measurement result sets, and determine the inner product result between the unitary operators U and V based on the number of elements in the intersection and the number of synchronous measurements. The specific calculation method is as follows:

[0071] (6);

[0072] In the formula, g i represents the inner product result between unitary operators U and V, m represents the number of synchronous measurements, It means the number of elements with equal values. represents the measurement result of the first quantum terminal in the lth round during the jth synchronous measurement, represents the measurement result of the second quantum terminal in the kth round during the jth synchronous measurement. , .

[0073] According to an embodiment of the present invention, during the above N rounds of experiments, the measurement basis of the quantum terminal It can be obtained by the following operations: Based on the target unitary matrix W i and the standard basis of round i The measurement basis of the first quantum terminal and the second quantum terminal in the i-th round can be obtained .in, represents the i-th vector in the standard basis, Represents the i-th vector in the standard basis through the target unitary matrix W i The new vector after the conjugate transpose transformation.

[0074] According to an embodiment of the present invention, in the i-th round of the N-round experiment, the quantum terminal is in the same position as the target unitary matrix W i The corresponding measurement basis The following m measurement results can be obtained based on the following operations:

[0075] During the jth synchronous measurement, the intermediate quantum state of the first quantum terminal is and projected onto the measurement basis On each basis vector of , multiple projection components are obtained; the probability of projecting multiple projection components onto any basis vector, and based on the probability distribution of multiple projection components, a basis vector is randomly sampled as the first quantum terminal in relation to the target unitary matrix W i The corresponding measurement result under the measurement basis can be recorded as ,in ; Similarly, the intermediate quantum state of the second quantum terminal and projected onto the measurement basis On each basis vector of , we get the second quantum terminal in the same matrix as the target unitary matrix Wi The corresponding measurement result under the measurement basis can be recorded as ,in .

[0076] According to an embodiment of the present invention, based on m times of synchronous measurement, the first quantum terminal can be obtained respectively in relation to the target unitary matrix W i The corresponding set of measurement results under the measurement basis is recorded as , and the second quantum terminal is in the same unitary matrix as the target matrix W i The corresponding set of measurement results under the measurement basis is recorded as .

[0077] According to an embodiment of the present invention, based on multiple inner product results, a property analysis result of a quantum terminal is obtained, including: based on multiple inner product results and the dimension of a unitary matrix set, calculating an unbiased estimation result corresponding to each inner product result; based on the unbiased estimation result corresponding to each inner product result, obtaining the property analysis result of the quantum terminal.

[0078] According to an embodiment of the present invention, based on the unbiased estimation result corresponding to each inner product result, a property analysis result of the quantum terminal is obtained, including: performing mean calculation on the unbiased estimation results corresponding to each of the multiple inner product results to obtain an average value of the unbiased estimation results; and obtaining the property analysis result of the quantum terminal based on the average value of the unbiased estimation results.

[0079] According to an embodiment of the present invention, if the expected value of an estimator is equal to the true value of the estimated parameter, then the estimator can be considered unbiased. The unbiased estimation result can be used to characterize the final estimation result obtained by estimating the inner product value of the unitary operator based on multiple inner product result intermediate values. The inner product result g between the unitary operators U and V obtained based on formula (6) is i And the unitary matrix set The dimension d can be obtained by the inner product relationship in the above formulas (4) and (5): Under the support of the principle of corresponding expected value, the result g of each inner product is calculated i The corresponding unbiased estimation result is expressed as follows:

[0080] (7);

[0081] Where, T i Represents the inner product result g with the i-th inner product result g i The corresponding unbiased estimation result.

[0082] According to an embodiment of the present invention, after obtaining the inner product results of N rounds, the n unbiased estimation results are accumulated and the mean is calculated to obtain the average value of the unbiased estimation results. The specific expression is as follows:

[0083] (8);

[0084] Where T represents the average value of the unbiased estimation results.

[0085] According to an embodiment of the present invention, the average value of the unbiased estimation result calculated by the above formula (8) can be used as the property of the unitary operator The results of property analysis.

[0086] According to an embodiment of the present invention, considering the estimated value of the unitary operator in the additive error The probability of being within the range of is not less than 2 / 3, then at least unbiased estimation results. Among them, K represents the required unbiased estimation results, N represents the number of experimental rounds, m represents the number of synchronous measurements, and C represents the constant coefficient. Therefore, the number of experimental rounds and the number of synchronous measurements can be determined based on this relationship to obtain the properties of the unitary operator with a probability of not less than 2 / 3 by ensuring sufficient unbiased estimation results. Within the error range Unbiased estimate of .

[0087] Figure 2 A block diagram of a device for analyzing unitary operator properties in a distributed scenario according to an embodiment of the present invention is shown.

[0088] like Figure 2 As shown, the unitary operator property analysis device in a distributed scenario includes a transformation module 210 , a measurement module 220 , and a determination module 230 .

[0089] The transformation module 210 is used to perform a rotation transformation on the initial quantum state of the quantum terminal using the unitary operator of the quantum terminal to obtain an intermediate quantum state of the quantum terminal.

[0090] The measurement module 220 is used to synchronously measure the intermediate quantum states of the multiple quantum terminals using the multiple unitary matrices included in the unitary matrix set, and obtain multiple inner product results, wherein each inner product result is obtained based on the measurement result set of the multiple quantum terminals.

[0091] The determination module 230 is used to obtain a property analysis result of the quantum terminal based on the multiple inner product results, wherein the property analysis result of the quantum terminal represents the similarity between the unitary operators respectively included in the multiple quantum terminals.

[0092] According to an embodiment of the present invention, the measurement module 220 includes a synchronous measurement submodule and an inner product result determination submodule.

[0093] The synchronous measurement submodule is used to synchronously perform multiple measurements on the intermediate quantum states of multiple quantum terminals using the target unitary matrix among the multiple unitary matrices, and obtain a set of measurement results of each of the multiple quantum terminals under the measurement basis corresponding to the target unitary matrix.

[0094] The inner product result determination submodule is used to determine the inner product result based on a set of measurement results of each of the multiple quantum terminals under a measurement basis corresponding to the target unitary matrix.

[0095] According to an embodiment of the present invention, the synchronous measurement submodule includes a measurement basis determination unit, a projection unit, a probability distribution unit, a measurement result determination unit, and a measurement result set determination unit.

[0096] The measurement basis determination unit is used to determine the measurement basis of any quantum terminal based on the target unitary matrix and the standard basis.

[0097] The projection unit is used to project the intermediate quantum state of the quantum terminal onto a plurality of basis vectors included in the measurement basis to obtain a plurality of projection components.

[0098] The probability distribution unit is used to obtain the probability distribution of the multiple projection components based on the respective probabilities of the multiple projection components.

[0099] The measurement result determination unit is used to determine the measurement result of the quantum terminal under the measurement basis based on the probability distribution of multiple projection components.

[0100] The measurement result set determination unit is used to obtain a measurement result set of the quantum terminal in a measurement basis corresponding to the target unitary matrix based on multiple measurement results obtained by multiple tests of the quantum terminal in the measurement basis.

[0101] According to an embodiment of the present invention, the inner product result determination submodule includes a calculation unit and an inner product result determination unit.

[0102] The calculation unit is used to perform intersection calculation on the measurement result sets of each of the multiple quantum terminals under the measurement basis corresponding to the target unitary matrix to obtain the target measurement result set.

[0103] The inner product result determination unit is used to determine the inner product result based on the number of elements included in the target measurement result set.

[0104] According to an embodiment of the present invention, the determination module 230 includes a calculation submodule and an analysis result determination submodule.

[0105] The calculation submodule is used to calculate an unbiased estimation result corresponding to each inner product result based on multiple inner product results and the dimensions of the unitary matrix set.

[0106] The analysis result determination submodule is used to obtain the property analysis result of the quantum terminal based on the unbiased estimation result corresponding to each inner product result.

[0107] According to an embodiment of the present invention, the analysis result determination submodule includes a mean value calculation unit and an analysis result determination unit.

[0108] The mean calculation unit is used to perform mean calculation on multiple unbiased estimation results corresponding to each inner product result to obtain an average value of the unbiased estimation results.

[0109] The analysis result determination unit is used to obtain the property analysis result of the quantum terminal based on the average value of the unbiased estimation result.

[0110] According to an embodiment of the present invention, the transformation module 210 includes a rotation submodule and a conversion submodule.

[0111] The rotator module is used to use the unitary operator of the quantum terminal to perform a rotation transformation on the initial quantum state of the quantum terminal to obtain a rotational quantum state.

[0112] The conversion submodule is used to convert the rotation quantum state into a density matrix to obtain the intermediate quantum state of the quantum terminal.

[0113] According to the embodiments of the present invention, any one or more of the modules, submodules, units, and subunits, or at least part of the functions of any one of them can be implemented in one module. According to the embodiments of the present invention, any one or more of the modules, submodules, units, and subunits can be split into multiple modules for implementation. According to the embodiments of the present invention, any one or more of the modules, submodules, units, and subunits can be at least partially implemented as hardware circuits, such as field programmable gate arrays (FPGAs), programmable logic arrays (PLAs), systems on chips, systems on substrates, systems on packages, application specific integrated circuits (ASICs), or can be implemented by hardware or firmware in any other reasonable way of integrating or packaging the circuit, or by any one of the three implementation methods of software, hardware, and firmware, or by a proper combination of any of them. Alternatively, according to the embodiments of the present invention, one or more of the modules, submodules, units, and subunits can be at least partially implemented as computer program modules, and when the computer program modules are run, the corresponding functions can be executed.

[0114] For example, any multiple of the transformation module 210, the measurement module 220, and the determination module 230 can be combined in one module / unit / sub-unit for implementation, or any one of the modules / units / sub-units can be split into multiple modules / units / sub-units. Alternatively, at least part of the functions of one or more of these modules / units / sub-units can be combined with at least part of the functions of other modules / units / sub-units and implemented in one module / unit / sub-unit. According to an embodiment of the present invention, at least one of the transformation module 210, the measurement module 220, and the determination module 230 can be at least partially implemented as a hardware circuit, such as a field programmable gate array (FPGA), a programmable logic array (PLA), a system on a chip, a system on a substrate, a system on a package, an application specific integrated circuit (ASIC), or can be implemented by hardware or firmware such as any other reasonable way of integrating or packaging the circuit, or implemented in any one of the three implementation methods of software, hardware, and firmware, or in any appropriate combination of any of them. Alternatively, at least one of the transformation module 210 , the measurement module 220 , and the determination module 230 may be at least partially implemented as a computer program module, and when the computer program module is executed, the corresponding function may be performed.

[0115] It should be noted that the unitary operator property analysis device in a distributed scenario in the embodiment of the present invention corresponds to the unitary operator property analysis method in a distributed scenario in the embodiment of the present invention. The description of the unitary operator property analysis device in a distributed scenario specifically refers to the unitary operator property analysis method in a distributed scenario, which will not be repeated here.

[0116] Figure 3 A block diagram of an electronic device suitable for implementing a unitary operator property analysis method in a distributed scenario according to an embodiment of the present invention is shown. Figure 3 The electronic device shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present invention.

[0117] like Figure 3 As shown, the electronic device according to an embodiment of the present invention includes a processor 301, which can perform various appropriate actions and processes according to the program stored in the read-only memory ROM 302 or the program loaded from the storage part 308 to the random access memory RAM 303. The processor 301 may include, for example, a general-purpose microprocessor (such as a CPU), an instruction set processor and / or a related chipset and / or a special-purpose microprocessor (for example, an application-specific integrated circuit (ASIC)), etc. The processor 301 may also include an on-board memory for caching purposes. The processor 301 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present invention.

[0118] In RAM 303, various programs and data required for the operation of the electronic device are stored. The processor 301, ROM 302 and RAM 303 are connected to each other through a bus 304. The processor 301 performs various operations of the method flow according to the embodiment of the present invention by executing the program in ROM 302 and / or RAM 303. It should be noted that the program can also be stored in one or more memories other than ROM 302 and RAM 303. The processor 301 can also perform various operations of the method flow according to the embodiment of the present invention by executing the program stored in the one or more memories.

[0119] According to an embodiment of the present invention, the electronic device may further include an input / output (I / O) interface 305, which is also connected to the bus 304. The electronic device may further include one or more of the following components connected to the input / output (I / O) interface 305: an input portion 306 including a keyboard, a mouse, etc.; an output portion 307 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc., and a speaker, etc.; a storage portion 308 including a hard disk, etc.; and a communication portion 309 including a network interface card such as a LAN card, a modem, etc. The communication portion 309 performs communication processing via a network such as the Internet. A drive 310 is also connected to the input / output (I / O) interface 305 as needed. A removable medium 311, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 310 as needed, so that a computer program read therefrom is installed into the storage portion 308 as needed.

[0120] According to an embodiment of the present invention, the method flow according to an embodiment of the present invention can be implemented as a computer software program. For example, an embodiment of the present invention includes a computer program product, which includes a computer program carried on a computer-readable storage medium, and the computer program contains a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 309, and / or installed from the removable medium 311. When the computer program is executed by the processor 301, the above-mentioned functions defined in the system of the embodiment of the present invention are executed. According to an embodiment of the present invention, the system, equipment, device, module, unit, etc. described above can be implemented by a computer program module.

[0121] The present invention also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiment; or may exist independently without being assembled into the device / apparatus / system. The above computer-readable storage medium carries one or more programs, and when the above one or more programs are executed, the method according to the embodiment of the present invention is implemented.

[0122] According to an embodiment of the present invention, the computer-readable storage medium may be a non-volatile computer-readable storage medium. For example, it may include but is not limited to: 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), a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present invention, the computer-readable storage medium may be any tangible medium containing or storing a program, which may be used by or in combination with an instruction execution system, an apparatus or a device.

[0123] For example, according to an embodiment of the present invention, the computer-readable storage medium may include the ROM 302 and / or the RAM 303 described above and / or one or more memories other than the ROM 302 and the RAM 303 .

[0124] An embodiment of the present invention also includes a computer program product, which includes a computer program, which contains program code for executing the method provided by the embodiment of the present invention. When the computer program product runs on an electronic device, the program code is used to enable the electronic device to implement the quantum circuit generation method based on balanced Boolean functions provided by the embodiment of the present invention.

[0125] When the computer program is executed by the processor 301, the above functions defined in the system / device of the embodiment of the present invention are executed. According to the embodiment of the present invention, the system, device, module, unit, etc. described above can be implemented by a computer program module.

[0126] In one embodiment, the computer program may rely on tangible storage media such as optical storage devices, magnetic storage devices, etc. In another embodiment, the computer program may also be transmitted and distributed in the form of signals on a network medium, and downloaded and installed through the communication part 309, and / or installed from the removable medium 311. The program code contained in the computer program may be transmitted using any appropriate network medium, including but not limited to: wireless, wired, etc., or any suitable combination of the above.

[0127] According to an embodiment of the present invention, the program code for executing the computer program provided by the embodiment of the present invention can be written in any combination of one or more programming languages. Specifically, these computing programs can be implemented using high-level process and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, Java, C++, python, "C" language or similar programming languages. The program code can be executed entirely on the user computing device, partially on the user device, partially on the remote computing device, or entirely on the remote computing device or server. In the case of a remote computing device, the remote computing device can be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computing device (e.g., using an Internet service provider to connect through the Internet).

[0128] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present invention. In this regard, each box in the flowchart or block diagram may represent a module, a program segment, or a part of a code, and the above-mentioned module, program segment, or a part of the code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box may also occur in an order different from the order marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram or flowchart, and the combination of boxes in the block diagram or flowchart, can be implemented with a dedicated hardware-based system that performs the specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions. It can be understood by those skilled in the art that the features recorded in the various embodiments of the present invention can be combined and / or combined in various ways, even if such a combination or combination is not explicitly recorded in the present invention. In particular, without departing from the spirit and teachings of the present invention, the features recorded in the various embodiments of the present invention can be combined and / or combined in various ways. All these combinations and / or combinations fall within the scope of the present invention.

[0129] The embodiments of the present invention are described above. However, these embodiments are only for the purpose of illustration, and are not intended to limit the scope of the present invention. Although each embodiment is described above, it does not mean that the measures in each embodiment cannot be used in combination advantageously. Without departing from the scope of the present invention, those skilled in the art may make various substitutions and modifications, which should all fall within the scope of the present invention.

Claims

1. A method for analyzing the properties of unitary operators in a distributed scenario, characterized in that: The method comprises: Using a unitary operator of a quantum terminal to perform a rotation transformation on an initial quantum state of the quantum terminal to obtain an intermediate quantum state of the quantum terminal; Using a plurality of unitary matrices included in the unitary matrix set, respectively, to synchronously measure the intermediate quantum states of the plurality of quantum terminals, to obtain a plurality of inner product results, wherein each of the inner product results is obtained based on the measurement result set of the plurality of quantum terminals, including: For a target unitary matrix among the multiple unitary matrices, using the target unitary matrix to synchronously perform multiple measurements on the intermediate quantum states of the multiple quantum terminals to obtain a set of measurement results of the multiple quantum terminals under a measurement basis corresponding to the target unitary matrix; Determining the inner product result based on a set of measurement results of each of the plurality of quantum terminals under the measurement basis corresponding to the target unitary matrix; Based on the multiple inner product results, a property analysis result of the quantum terminal is obtained, wherein the property analysis result of the quantum terminal characterizes the similarity between the unitary operators included in each of the multiple quantum terminals, including: Based on the multiple inner product results and the dimensions of the unitary matrix set, an unbiased estimation result corresponding to each of the inner product results is calculated; Calculating the mean of the unbiased estimation results corresponding to each of the plurality of inner product results to obtain an average value of the unbiased estimation results; Based on the average value of the unbiased estimation results, a property analysis result of the quantum terminal is obtained.

2. The unitary operator property analysis method according to claim 1, characterized in that: The method of synchronously measuring the intermediate quantum states of the plurality of quantum terminals multiple times by using the target unitary matrix to obtain a set of measurement results of the plurality of quantum terminals in a measurement basis corresponding to the target unitary matrix includes: For any of the quantum terminals, determining the measurement basis of the quantum terminal based on the target unitary matrix and a standard basis; Projecting the intermediate quantum state of the quantum terminal onto a plurality of basis vectors included in the measurement basis to obtain a plurality of projection components; Based on the respective probabilities of the multiple projection components, obtaining a probability distribution of the multiple projection components; Determining a measurement result of the quantum terminal under the measurement basis based on the probability distribution of the multiple projection components; Based on the multiple measurement results obtained by the quantum terminal through multiple tests under the measurement basis, a set of measurement results of the quantum terminal under the measurement basis corresponding to the target unitary matrix is ​​obtained.

3. The unitary operator property analysis method according to claim 2, characterized in that: The determining the inner product result based on a set of measurement results of each of the plurality of quantum terminals under the measurement basis corresponding to the target unitary matrix comprises: Performing intersection calculation on measurement result sets of each of the multiple quantum terminals under the measurement basis corresponding to the target unitary matrix to obtain a target measurement result set; The inner product result is determined based on the number of elements included in the target measurement result set.

4. The unitary operator property analysis method according to claim 1, characterized in that: The initial quantum states of the multiple quantum terminals are the same, wherein the initial quantum states are used to characterize quantum states generated by the quantum terminals using multiple quantum gates.

5. The unitary operator property analysis method according to claim 1, characterized in that: The step of using the unitary operator of the quantum terminal to perform a rotation transformation on the initial quantum state of the quantum terminal to obtain an intermediate quantum state of the quantum terminal includes: Using the unitary operator of the quantum terminal to perform a rotational transformation on the initial quantum state of the quantum terminal to obtain a rotational quantum state; The rotational quantum state is converted into a density matrix to obtain an intermediate quantum state of the quantum terminal.

6. A unitary operator property analysis device in a distributed scenario, characterized in that: The device comprises: A transformation module, used to perform a rotation transformation on the initial quantum state of the quantum terminal using the unitary operator of the quantum terminal to obtain an intermediate quantum state of the quantum terminal; A measurement module is used to synchronously measure the intermediate quantum states of the plurality of quantum terminals using the plurality of unitary matrices included in the unitary matrix set, respectively, to obtain a plurality of inner product results, wherein each of the inner product results is obtained based on the measurement result set of the plurality of quantum terminals, wherein the measurement module is configured as follows: For a target unitary matrix among the multiple unitary matrices, using the target unitary matrix to synchronously perform multiple measurements on the intermediate quantum states of the multiple quantum terminals to obtain a set of measurement results of the multiple quantum terminals under a measurement basis corresponding to the target unitary matrix; Determining the inner product result based on a set of measurement results of each of the plurality of quantum terminals under the measurement basis corresponding to the target unitary matrix; A determination module is used to obtain a property analysis result of the quantum terminal based on the multiple inner product results, wherein the property analysis result of the quantum terminal characterizes the similarity between the unitary operators respectively included in the multiple quantum terminals, wherein the determination module is configured to: Based on the multiple inner product results and the dimensions of the unitary matrix set, an unbiased estimation result corresponding to each of the inner product results is calculated; Calculating the mean of the unbiased estimation results corresponding to each of the plurality of inner product results to obtain an average value of the unbiased estimation results; Based on the average value of the unbiased estimation results, a property analysis result of the quantum terminal is obtained.

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