Quantum computing method for expectation estimation capable of reducing depth of quantum computing device

Abstract

The application provides a quantum computing method for expectation estimation, which can reduce the depth of a quantum computing device, and comprises the following steps: encoding the variable value and its probability of a system in a quantum state with n quantum bits; constructing an observation quantity according to a return function of the system; expanding the observation quantity under a set of information complete parameterized generalized observations (ICPOVM) by using an adaptive measurement algorithm, and adjusting parameters according to the expansion result to minimize measurement error; and outputting the expectation of the obtained observation quantity with minimized measurement error as the expectation value of the return function of the system. The method of the application only needs constant-level circuit depth while effectively reducing error, and thus can be implemented in a quantum computer with lower complexity and only needs a small number of measurements.

Description

Technical Field

[0001] This invention relates to the technical field of system analysis using quantum technology, and more specifically, to a quantum computing method for expectation estimation that can reduce the depth of quantum computing devices. Background Technology

[0002] Current quantum statistical estimation techniques are based on the quantum Monte Carlo method. First, a quantum oracle encodes the probability distribution of the system variables under analysis onto the quantum state amplitude, where the quantum state amplitude is the square root of the probability. Then, a circuit calculating the reward function transforms the amplitude into the product of the square root of the probability and the square root of the reward function value. The amplitude is then measured using amplitude estimation techniques in quantum computing to calculate the expected value of the reward function. Compared to the classical Monte Carlo method, the sampling error can be reduced from O(1 / √N) to O(1 / N), where N is the number of samples. Therefore, the sampling complexity is reduced under the same error conditions. In the quantum amplitude estimation algorithm, the quantum state amplitude is obtained by calling the quantum phase estimation algorithm. Current quantum statistical estimation techniques require large-scale quantum circuits. Quantum phase estimation requires quantum Fourier transforms and multiple calls to the quantum oracle. These factors necessitate deep quantum circuits, which are not feasible on current hardware. Therefore, a quantum computing method and device that can also reduce errors and the number of measurements, but with shallower quantum circuit depth, is needed. Summary of the Invention

[0003] To address the aforementioned technical problems, a first aspect of the present invention provides a quantum computing method for expectation estimation that can reduce the depth of quantum computing devices, comprising:

[0004] Take the values ​​of the system variables and its probability Encoded in a quantum state with n qubits middle;

[0005] Construct an observation based on the system's reward function. ;

[0006] The observations are measured using an adaptive measurement algorithm. In a set of parameters Expanding under Information Complete Generalized Measurement (ICPOVM) and adjusting the parameters based on the expansion results. To minimize measurement error, the observed measurement with the smallest possible measurement error is obtained. The expected value is output as the expected value of the system's reward function.

[0007] Preferably, the adaptive measurement algorithm is used to measure the observations. In a set of parameters Expanding under Information Complete Generalized Measurement (ICPOVM) and adjusting the parameters based on the expansion results. To minimize measurement error, the following are included:

[0008] The observation Expanded under a set of information-complete generalized measurements with parameters (ICPOVM) as In the form of, The elements representing the information-complete generalized measurement (ICPOVM) are... for The corresponding expansion coefficients;

[0009] The observation Expectations Defined by the following formula: ,in This represents the probability of obtaining m under the Information Completeness Generalized Measurement (ICPOVM);

[0010] The result was obtained by calculation using the Monte Carlo method. (m from 1 to 4) n variance The variance Simultaneously for the parameters The function, i.e. ;

[0011] According to the variance Obtain the For the parameters The gradient;

[0012] The variance and stated For the parameters The gradient is provided as input to the classical optimizer to obtain updated parameters. and According to the updated parameters and Adjust the parameters Information complete generalized measurement (ICPOVM) up to the variance or convergence.

[0013] Preferably, the method calculated using the Monte Carlo method yields the following results. (m from 1 to 4) n variance include:

[0014] Using the Monte Carlo method to analyze probability Sampling is performed, wherein the probability By the observation In the parameter Obtained by expansion under Information Completeness Generalized Measurement (ICPOVM); and

[0015] The variance Obtained through the following formula:

[0016]

[0017] Preferably, based on the variance Obtain the For the parameters The gradients include:

[0018] The gradient is calculated according to the parameter translation rule, which includes:

[0019] For parameters The partial derivative of the k-th component can be calculated by the following formula:

[0020]

[0021] in It is the unit vector of the kth component.

[0022] Preferably, the and It is obtained by calculation using the Monte Carlo method.

[0023] Preferably, based on the variance Obtain the For the parameters The gradients include:

[0024] The difference method is used to obtain the aforementioned... For the parameters The gradient.

[0025] Preferably, the elements of the Information Completeness Generalized Measurement (ICPOVM) From the parameterized unitary matrix Given:

[0026]

[0027] in It is a computational basis. It is a single-bit identity matrix.

[0028] Preferably, the quantum state with n qubits is encoded by a quantum generative adversarial network. .

[0029] A second aspect of the present invention provides a quantum computing device for desired estimation that can reduce the depth of quantum computing devices, comprising:

[0030] The encoding input module is configured to input the system's variable values. and its probability Encoded in a quantum state with n qubits middle;

[0031] An observation configuration module is configured to construct an observation based on the system's reward function. ;

[0032] An adaptive measurement module, configured to use an adaptive measurement algorithm to measure the observations... In a set of parameters Expanding under Information Complete Generalized Measurement (ICPOVM) and adjusting the parameters based on the expansion results. To minimize measurement error, and to obtain the observation with the minimum measurement error. The expected value is output as the expected value of the system's reward function.

[0033] A third aspect of the present invention provides a storage medium storing a computer program, wherein the computer program is configured to execute the method provided in the first aspect of the present invention when it is run.

[0034] A fourth aspect of the present invention provides an electronic device including a memory and a processor, the memory storing a computer program and the processor being configured to run the computer program to perform the method described in the first aspect of the present invention.

[0035] The quantum computing method for desired estimation according to the present invention, which reduces the depth of quantum computing devices, can be implemented in... While avoiding the use of circuits for calculating the return function and the quantum amplitude estimation algorithm and its numerous quantum oracles, this approach requires only a constant-level circuit depth and can be quickly and easily applied to existing quantum computers. In other words, this technical solution greatly reduces the dependence on the quantum circuit depth of quantum computing devices. Attached Figure Description

[0036] The embodiments of the present invention will be further described below with reference to the accompanying drawings, wherein:

[0037] Figure 1 An exemplary quantum circuit for preparing quantum states using a quantum generative adversarial network is shown.

[0038] Figure 2An example is shown of the quantum circuitry used in the ICPOVM, a generalized measurement of information completeness for a single qubit.

[0039] Figure 3 An example is shown for Figure 1 Each generated qubit is subjected to Figure 2 The overall quantum circuit diagram for adaptive measurement is shown. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Those skilled in the art can make appropriate adjustments to the components, parameters, etc., in the embodiments of the present invention based on the inventive concept. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention. In other cases, well-known methods, apparatuses, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of the present invention.

[0041] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to give a full understanding of embodiments of the invention. However, those skilled in the art will recognize that the technical solutions of the invention can be practiced without one or more of the specific details, or other methods, components, apparatuses, steps, etc., can be employed. In other instances, well-known methods, apparatuses, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of the invention. The processes in the embodiments are merely illustrative and do not necessarily include all contents and operations / steps, nor do they necessarily have to be performed in the described order. For example, some operations / steps can be broken down, while others can be combined or partially combined; therefore, the actual order of execution may change depending on the actual situation.

[0042] In estimating statistical results for quantum systems, the inventors discovered that the core principle is to reduce measurement errors using a quantum amplitude estimation algorithm, decreasing the error from O(1 / √N) to O(1 / N). The inventors found that adaptive measurement techniques can also achieve the same effect of reducing measurement errors, requiring only a constant-level circuit depth. Therefore, they considered applying adaptive measurement techniques to the estimation of statistical results for systems. Furthermore, the original scheme for estimating quantum statistical results requires first encoding the probability distribution of system variables into quantum states and constructing the reward function as a quantum circuit. The inventors found that it is only necessary to set the observation as a diagonal Hermitian matrix and use the reward function as a matrix element. By measuring this observation using adaptive measurement techniques, the statistical results of the system can be estimated. The reward function here can be any form of reward function commonly used in the general mathematical field or various technical fields. Its specific expression varies in different fields such as medicine, electricity, and applied physics research, but all are within the scope of protection of this application.

[0043] Specifically, the method described in this application should follow these principles: 1. Expectation estimation is performed using adaptive measurement techniques. Compared to existing quantum amplitude estimation algorithms, the inventors believe this can significantly reduce the quantum circuit depth. 2. The reward function is constructed as a diagonal element of the observation, which is equivalent to parameterizing the measurement rather than parameterizing the quantum circuit that calculates the reward function. This quantum computing structure eliminates the need for calculating the quantum circuit corresponding to the reward function in existing quantum statistical result estimation algorithms. 3. In a further preferred embodiment, adaptive measurement and updating of the observable can be performed using the parameter translation rule, the technical effect of which is to calculate the gradient more accurately.

[0044] Example 1

[0045] This embodiment provides an exemplary quantum computing method for estimating systematic statistical results according to the present invention, based on the principles described above. It is merely illustrative and not intended to limit the scope of the invention.

[0046] First, a predetermined quantum state with n qubits is prepared. For a general system statistical result estimation problem in this field, the given variables are assigned values... and its probability Encoded in the quantum state amplitude, in this embodiment we exemplarily employ a quantum generative adversarial network to prepare the following predetermined quantum state. :

[0047]

[0048] Where n is the number of qubits, n qubits can represent... A variable that takes one value.

[0049] Figure 1 An exemplary quantum circuit for preparing a quantum state using a quantum generative adversarial network (GAN) is shown. While the GAN method can rapidly obtain the desired quantum state, it can also be prepared using other methods conventional in the art.

[0050] Next, an observation is constructed based on the system's reward function. For example, the following observations are constructed:

[0051]

[0052] It can be seen that in the state The expectation of measuring this observation is the expectation of the reward function. .

[0053] Next, an adaptive measurement algorithm is used to process the observed measurements. In a set of parameters This is unfolded under Information Complete Generalized Measurement (ICPOVM). The steps include first constructing a set of parameters before measuring the observation using adaptive measurement techniques. Information Complete Positive Operator-Valued Measure (ICPOVM).

[0054] Figure 2 An example is shown of the quantum circuitry used for the information-complete generalized measurement of a single qubit using ICPOVM. For a single qubit, this set of ICPOVMs has four elements. The parameters are given by the parameterized unitary matrix.

[0055]

[0056] in, It is a two-bit joint operation. This means that the measurement in adaptive measurement technology is parameterized, making it easier to adjust the parameter during later optimization. ; It is a computational basis of two qubits , It is a single-bit identity matrix.

[0057] Similar to the information-complete generalized measurement ICPOVM for a single qubit, we can also give the information-complete generalized measurement ICPOVM for n qubits, whose elements The quantity is 4 n indivual.

[0058] Having obtained the parameterized information-complete generalized measurement ICPOVM, the following section presents the decomposition of the constructed observations under a set of information-complete generalized measurement ICPOVMs.

[0059]

[0060] Figure 3 An example is shown for Figure 1 Each generated qubit is subjected to Figure 2 The diagram shows the overall quantum circuitry for adaptive measurement. Therefore, the expectation of the observed quantity can be expressed as:

[0061]

[0062] A quantum state with a probability distribution. Encoded Hamiltonian, This is the expected value of the results of systematic statistics.

[0063] However, in actual calculations, the above formula has a total of Item, calculated directly The feasibility is low. The inventors analyzed that, as shown in the above formula, the expected value of the system statistical results can be expressed as a random variable. With probability Therefore, it is proposed that the Monte Carlo method can be used for sampling to estimate the expectation. For example, by performing S measurements on the measurand substate under this set of information-complete generalized measurement ICPOVM, the observation can be obtained. Estimated value

[0064]

[0065] Specifically, for a given measurement of the measured substate under this information-complete generalized measurement ICPOVM, based on the measured... The dimension m of this measurement can be determined. Therefore, after S measurements, the probability corresponding to each dimension m can be determined. Each dimension m corresponds to a random variable (Right now The expansion coefficients were not modified in this round. The value is known in the measurement.

[0066] The goal of adaptive measurement is to construct an objective function and minimize it through iterative parameter tuning. In this embodiment, random variables are used. The variance 1 is determined as the objective function and minimized for optimization. variance It can be written as,

[0067]

[0068] The latter term is the expectation of a random variable, which is independent of the parameterized POVM and can be considered as a measurement obtained by sampling using the Monte Carlo method. Therefore, it is sufficient to minimize the first term. Since the parameters in the information-complete generalized measurement ICPOVM... The variable is adjustable, and the variance corresponding to the adjustment result is... The numerical change of , therefore the above formula can be written as . .

[0069] Based on the above formula and the measurement results from multiple measurements in the Information Completeness Generalized Measurement ICPOVM, the parameter translation rule is used to calculate... For the parameters The gradient, due to It is an m-dimensional vector; therefore, in gradient calculation, for the parameters... The partial derivative of the k-th component can be calculated by the following formula:

[0070]

[0071] in It is the unit vector of the kth component.

[0072] Similar to estimating the expectation, the Monte Carlo method can be used to calculate... and This includes: in information-complete generalized measurement ICPOVM, The kth component is adjusted and updated as follows: Then we take measurements. At this point, we obtain... variance ,as well as For the parameters The gradient can be obtained by substituting these two quantities into the classical optimizer to get the updated gradient. and the corresponding .

[0073] Updated parameters and As a parameter Adjust the information-complete generalized measurement (ICPOVM) and repeat the previous steps to calculate the new variance. as well as For the parameters The gradient, up to the variance. or Convergence. At this point, the optimal measurement is obtained, and the variance is sufficiently small to achieve [the desired result]. Level of error.

[0074] The method described in this embodiment, due to the use of adaptive measurement technology, can achieve... While achieving a level of error, it avoids the use of circuits for calculating the reward function; it also avoids the quantum oracle used extensively in quantum amplitude estimation algorithms, requiring only constant-level circuit depth, thus enabling implementation in less complex quantum computers.

[0075] Example 2

[0076] This embodiment provides a quantum computing device for estimating the system statistical results (e.g., expectations) according to the present invention, comprising: an encoding input module, an observation configuration module, and an adaptive measurement module.

[0077] The encoding module is configured to take values ​​for the system's variables through a quantum generative adversarial network. and its probability Encoded in a quantum state with n qubits middle.

[0078] The observation configuration module is configured to construct an observation based on the system's reward function. :

[0079] In state The observation was measured in the middle. The expectation is the expected value of the return function. .

[0080] The adaptive measurement module is configured to use an adaptive measurement algorithm to measure the observations. In a set of parameters Expanding under Information Complete Generalized Measurement (ICPOVM) and adjusting the parameters based on the expansion results. To minimize measurement error, and to obtain the observation with the minimum measurement error. The expected value is output as the expected value of the system's reward function. This includes:

[0081] The observation Expanded under a set of information-complete generalized measurements with parameters (ICPOVM) as The form;

[0082] The observation Expectations Defined by the following formula:

[0083] ;

[0084] The result was obtained by calculation using the Monte Carlo method. (m from 1 to 4) n variance The variance Simultaneously for the parameters The function, i.e. Among them, the probability is determined by the Monte Carlo method. Sampling is performed, wherein the probability By the observation In the parameter Obtained by expansion under Information Completeness Generalized Measurement (ICPOVM); and

[0085] The variance Obtained through the following formula:

[0086] ;

[0087] According to the variance Obtain the For the parameters The gradient includes:

[0088] The gradient is calculated according to the parameter translation rule, where the parameters are... The partial derivative of the k-th component can be calculated by the following formula:

[0089]

[0090] in It is the unit vector of the kth component.

[0091] The variance and stated For the parameters The gradient is provided as input to the classical optimizer to obtain updated parameters. and According to the updated parameters and Adjust the parameters Information complete generalized measurement (ICPOVM) up to the variance or convergence.

[0092] In other embodiments of this application, the gradient may be calculated using other methods than the parametric translation rule, such as the interpolation method.

[0093] In other embodiments of this application, for optimization variance The classical optimizer can also be any suitable optimizer known in the art that can run on a classical computer or a quantum computer.

[0094] In other embodiments of this application, a storage medium is provided in which a computer program is stored, including a quantum computer program and a classical computer program. The computer program is configured to execute the method described in Embodiment 1 when run.

[0095] In other embodiments of this application, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program and the processor is configured to run the computer program to perform the method described in Embodiment 1.

[0096] The quantum computing methods for expectation estimation described in various embodiments of the present invention, which can reduce the depth of quantum computing devices, can be effectively applied in multiple fields. The following are only examples of several classical fields, but this is not a limitation of the present invention:

[0097] Logistics and Supply Chain Management: In logistics and supply chain management, statistical results, such as those from expected estimates, can be used to forecast demand, manage inventory, and predict delivery times. This helps optimize transportation and storage strategies, improve efficiency, and reduce costs.

[0098] Healthcare: In the medical field, statistical results, such as expected estimates, can be used to analyze patient population survival rates, treatment outcomes, and risk factors. It is crucial for clinical trials, epidemiological studies, and healthcare policy development.

[0099] Telecommunications and Communications: In the telecommunications industry, for example, statistical results of expectation estimation can be applied to network performance analysis, data transmission rate prediction, and signal processing problems, such as the estimation of signal-to-noise ratio;

[0100] Engineering and Manufacturing: In engineering and manufacturing, statistical results, such as expected estimates, can be used to assess product reliability, lifespan, and quality. It is crucial for design optimization and quality control.

[0101] In the financial field, for example, statistical results of expectation estimation can be applied to option estimation.

[0102] While the present invention has been described through preferred embodiments, it is not limited to the embodiments described herein, and various changes and modifications are made without departing from the scope of the invention.

Claims

1. A quantum computing method for expectation estimation that reduces the depth of quantum computing devices, wherein the expectation estimation is directed at variables of the system, including: Take the values ​​of the system variables and its probability Encoded in a quantum state with n qubits middle; Construct an observation based on the system's reward function. The expectation of the reward function is the output of the quantum computing method. The observations are measured using an adaptive measurement algorithm. In a set of parameters Expanding under Information Complete Generalized Measurement (ICPOVM) and adjusting the parameters based on the expansion results. To minimize measurement error, the observed measurement with the smallest possible measurement error is obtained. The expected value is output as the expected value of the system's reward function.

2. The method according to claim 1, wherein, The adaptive measurement algorithm is used to measure the observations. In a set of parameters Expanding under Information Complete Generalized Measurement (ICPOVM) and adjusting the parameters based on the expansion results. To minimize measurement error, the following are included: The observation Expanded under a set of information-complete generalized measurements with parameters (ICPOVM) as In the form of, The elements representing the information-complete generalized measurement (ICPOVM) are... for The corresponding expansion coefficients; The observation Expectations Defined by the following formula: ,in This represents the probability of obtaining m under the Information Completeness Generalized Measurement (ICPOVM); The result was obtained by calculation using the Monte Carlo method. variance Where m ranges from 1 to 4 n The variance Simultaneously for the parameters The function, i.e. ; According to the variance Obtain the For the parameters The gradient; The variance and stated For the parameters The gradient is provided as input to the classical optimizer to obtain updated parameters. and According to the updated parameters and Adjust the parameters Information complete generalized measurement (ICPOVM) up to the variance or convergence.

3. The method according to claim 2, wherein, The result obtained by calculation using the Monte Carlo method variance include: Using the Monte Carlo method to analyze probability Sampling is performed, wherein the probability By the observation In the parameter Obtained by expansion under Information Completeness Generalized Measurement (ICPOVM); and The variance Obtained through the following formula:

4. The method according to claim 2, wherein, According to the variance Obtain the For the parameters The gradients include: The gradient is calculated according to the parameter translation rule, which includes: For parameters The partial derivative of the k-th component can be calculated by the following formula: in It is the unit vector of the kth component.

5. The method according to claim 4, wherein, The and It is obtained by calculation using the Monte Carlo method.

6. The method according to claim 2, wherein, According to the variance Obtain the For the parameters The gradients include: The difference method is used to obtain the aforementioned... For the parameters The gradient.

7. The method according to claim 2, wherein, The elements of the Information Completeness Generalized Measurement (ICPOVM) From the parameterized unitary matrix Given: in It is a computational basis. It is a single-bit identity matrix.

8. The method according to claim 1, wherein, The quantum state with n qubits is encoded using a quantum generative adversarial network. .

9. A quantum computing device for the expectation estimation of system variables, characterized in that, include: The encoding input module is configured to input the system's variable values. and its probability Encoded in a quantum state with n qubits middle; An observation configuration module is configured to construct an observation based on the system's reward function. ; An adaptive measurement module, configured to use an adaptive measurement algorithm to measure the observations... In a set of parameters Expanding under Information Complete Generalized Measurement (ICPOVM) and adjusting the parameters based on the expansion results. To minimize measurement error, and to obtain the observation with the minimum measurement error. The expected value is output as the expected value of the system's reward function.

10. A storage medium, characterized in that, The storage medium stores a computer program, wherein the computer program is configured to execute the method described in any one of claims 1 to 8 when it is run.

11. An electronic device comprising a memory and a processor, characterized in that, The memory stores a computer program, and the processor is configured to run the computer program to perform the method as described in any one of claims 1 to 8.

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