Sparse principal component analysis method, quantum computing device and medium

Abstract

The invention relates to a sparse principal component analysis method, a quantum computing device and a medium, belongs to the technical field of data dimension reduction, and solves the problem that the sparse principal component analysis method is low in efficiency. According to the technical scheme, the method mainly comprises the steps that a target data matrix is obtained, and a covariance matrix is determined based on the target data matrix; setting a to-be-solved principal component vector, and determining an original objective function and a vector constraint condition; expressing each component of the to-be-solved principal component vector through a binary system, and defining a plurality of second binary variables to respectively express whether each component of the to-be-solved principal component vector is zero or not; determining constraint conditions of the first binary variable and the second binary variable according to the vector constraint conditions and the definition of the second binary variable; forming a secondary unconstrained binary optimization model; and solving the quadratic unconstrained binary optimization model to determine the value of each first binary variable.

Description

Technical Field

[0001] The present invention belongs to the technical field of data dimensionality reduction, and specifically relates to a sparse principal component analysis method, a quantum computing device and a medium. Background Art

[0002] In the field of data science and machine learning, dimensionality reduction of high-dimensional data is an important issue. The traditional PCA method can map high-dimensional data to low-dimensional space through linear transformation. However, in practical applications, due to the high dimension of the data and the correlation between the data, the traditional PCA method often produces overly dense principal components that are difficult to interpret and understand. In contrast, sparse principal component analysis (Sparse PCA) can generate sparse principal components while retaining the main features of the data, better describing the structure and characteristics of the data.

[0003] The sparse principal component analysis method can effectively process high-dimensional data, retain the main features of the data, and generate sparse principal components, thus having important application value in data processing and analysis.

[0004] However, the sparse principal component analysis method involves a non-convex optimization problem, which is an NP-hard problem. The conflict between optimizing sparsity (i.e. minimizing the number of non-zero coefficients) and optimizing variance (i.e. maximizing the explained variance) makes the problem very difficult to solve. Due to the complexity of the optimization problem of sparse PCA, commonly used solution algorithms (such as coordinate descent, gradient descent, etc.) may become unstable or computationally inefficient on large-scale data sets. In addition, in high-dimensional data, it is necessary to design an algorithm that can both ensure the stability of the solution and effectively reduce the computational complexity.

[0005] In summary, the sparse principal component analysis method in the prior art has the problem of low efficiency that needs to be solved. Summary of the invention

[0006] In view of the above analysis, the embodiment of the present invention aims to provide a sparse principal component analysis method, a quantum computing device and a medium to solve the problem of low efficiency of the sparse principal component analysis method. The method comprises the following steps: Obtaining a target data matrix, and determining a covariance matrix based on the target data matrix; Setting a principal component vector to be solved, and determining an original objective function and vector constraint conditions of the sparse principal component analysis based on the principal component vector to be solved and the covariance matrix; Each component of the principal component vector to be solved is represented as a binary representation through a plurality of first binary variables, and a plurality of second binary variables are defined to respectively represent whether each component of the principal component vector to be solved is zero; Determining constraints of the first binary variable and the second binary variable according to the vector constraint and the definition of the second binary variable; Converting the original objective function into a quadratic objective function of a plurality of binary variables according to the binary representation, forming a quadratic penalty term of the binary variable according to the constraint condition, and adding the quadratic penalty term to the quadratic objective function to form a quadratic unconstrained binary optimization model; The quadratic unconstrained binary optimization model is solved to determine the value of each of the first binary variables, and the principal component vector is determined according to the value of the first binary variable.

[0007] In some embodiments, solving the quadratic unconstrained binary optimization model to determine the value of each first binary variable includes: Converting the quadratic unconstrained binary optimization model into an Ising model and a maximum cut problem; Quantum computing is used to obtain the ground state of the Ising model, and a solution to the maximum cut problem is found to obtain the value of each of the first binary variables.

[0008] In some embodiments, solving the quadratic unconstrained binary optimization model to determine the value of each first binary variable includes: The quadratic unconstrained binary optimization model is solved using a QAOA quantum circuit to obtain a value of each of the first binary variables.

[0009] In some embodiments, the original objective function and vector constraints of the sparse principal component analysis are determined based on the principal component vector to be solved and the covariance matrix, wherein the objective function is expressed as: ,in v represents the principal component vector to be solved, represents the covariance matrix of the target data matrix; The vector constraints include: The principal component vector to be solved is a unit vector; The number of non-zero components in the principal component vector to be solved is less than or equal to k, where k is a preset integer.

[0010] In some embodiments, the binary representation comprises: ,in Represents the principal component vector to be solved v No. iQuantity, and are all first binary variables, express No. j The value of an integer digit, express No. j The value of decimal places, m represents the upper limit of integer and decimal places.

[0011] In some embodiments, determining the constraint conditions of the first binary variable and the second binary variable according to the vector constraint condition and the definition of the second binary variable includes: The first constraint condition determined according to the principal component vector to be solved being a unit vector is expressed as: ,in Represents the principal component vector to be solved v No. i components, where p represents the dimension of the principal component vector v to be solved; The second constraint condition determined according to the number of non-zero components in the principal component vector to be solved is less than or equal to k is expressed as: , ,in Represents the principal component vector to be solved v of norm, represents the second binary variable; The third constraint condition determined according to the definition of the second binary variable is expressed as: .

[0012] In some embodiments, adding the quadratic penalty term to the quadratic objective function to form a quadratic unconstrained binary optimization model includes: The quadratic unconstrained binary optimization model is expressed as: , in represents the quadratic objective function, expressed as: ; and are all quadratic penalty terms formed based on the third constraint condition, expressed as: ; is a quadratic penalty term formed based on the second constraint, expressed as: ; is a quadratic penalty term formed based on the first constraint condition, expressed as: , In the above formula and Each represents a slack variable represented by binary when the inequality constraint is converted into a penalty term; All non-binary variables in the quadratic unconstrained binary optimization model are converted into a combination representation of several binary variables through binary representation.

[0013] In some embodiments, forming a quadratic unconstrained binary optimization model further comprises: Converting the high-order polynomial into a quadratic polynomial using Rosenberg polynomials; For any two binary variables The product of replace , add a polynomial to the objective function: -2 y- , to ensure .

[0014] In some embodiments, after determining the principal component vector, the method further includes: The covariance matrix is ​​reduced based on the principal component vector, a new principal component vector is determined based on the reduced covariance matrix, and more principal component vectors are obtained through iteration.

[0015] The present invention also provides a quantum computing device, comprising: a quantum processing unit, an electronic processing unit and a storage unit; Wherein, the storage unit stores a computer program, and when the computer program is executed by the quantum processing unit and the electronic processing unit, the sparse principal component analysis method as described in any of the above embodiments is implemented.

[0016] The present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the sparse principal component analysis method described in any of the above embodiments is implemented.

[0017] The present invention also provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the sparse principal component analysis method as described in any of the above embodiments is implemented.

[0018] The embodiments of the present invention have at least the following beneficial effects: 1. By taking the principal component vector to be solved as the solution target by establishing a combination of the first binary variables in binary representation, and assigning the second binary variable as the intermediate variable according to whether each component of the principal component vector to be solved is zero, it is beneficial to the representation of the optimization model and to the construction of a quadratic unconstrained binary optimization model through binary variables.

[0019] 2. By constructing the sparse principal component analysis problem into a quadratic unconstrained binarization model, the model can be solved by a quantum computer, solving the problem of poor stability and effectiveness of the solution results of traditional computer optimization algorithms due to the large complexity scale, and improving the efficiency of solving the sparse principal component analysis problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of this specification or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the embodiments of this specification. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0021] Figure 1 A schematic flow chart of a sparse principal component analysis method provided by the present invention; Figure 2 This is a schematic diagram of the electronic device architecture provided by the present invention. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. It should be noted that, in the absence of conflict, the embodiments and features in the embodiments disclosed in this disclosure can be combined, separated, interchanged and / or rearranged with each other. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0023] The terms used here are for the purpose of describing specific embodiments, and are not intended to be restrictive. As used here, unless the context clearly indicates otherwise, the singular forms "one (kind, person)" and "said (the)" are also intended to include plural forms. In addition, when the terms "comprise" and / or "include" and their variations are used in this specification, it is explained that there are stated features, integral bodies, steps, operations, parts, assemblies and / or their groups, but it is not excluded that there are or add one or more other features, integral bodies, steps, operations, parts, assemblies and / or their groups. It should also be noted that, as used here, the terms "substantially", "approximately" and other similar terms are used as approximate terms and not as degree terms, so that they are used to explain the inherent deviations of the measured values, calculated values ​​and / or the values ​​provided that will be recognized by those of ordinary skill in the art.

[0024] The embodiment of the present invention provides a sparse principal component analysis method, such as Figure 1 As shown, the following steps are included: S1. Obtain a target data matrix, and determine a covariance matrix based on the target data matrix.

[0025] Specifically, for example, the present invention is applied to the Hamiltonian path problem to perform sparse principal component analysis, and a data matrix is ​​considered, denoted as X, in which each column represents an input variable, and each row represents an independent sample in the data population, and each column of X has a zero mean. Then, the covariance matrix determined based on the target data matrix is ​​expressed as: , represents the covariance matrix of the target data matrix X, whose dimension is p×p, where n represents the number of samples in X.

[0026] In some embodiments, if the mean of each column of X is not zero, preprocessing may be performed to subtract the column mean from each element of X.

[0027] S2. Setting a principal component vector to be solved, and determining an original objective function and vector constraints of the sparse principal component analysis based on the principal component vector to be solved and the covariance matrix.

[0028] Given an integer k, where 1≤k≤p, the sparse principal component analysis (Sparse PCA) problem can be described as maximizing the variance in the direction represented by the vector v while limiting its cardinality, that is, considering the following optimization problem:

[0029] The first constraint states that v is a unit vector. In the second constraint, Indicates v norm, which is defined as the number of its nonzero components. Therefore, the second constraint states that the number of nonzero components in v is less than or equal to k, where k is usually an integer much smaller than the dimension p.

[0030] In some embodiments, the original objective function and vector constraints of the sparse principal component analysis are determined based on the principal component vector to be solved and the covariance matrix, wherein the objective function is expressed as: ,in v represents the principal component vector to be solved, represents the covariance matrix of the target data matrix; The vector constraints include: The principal component vector to be solved is a unit vector; The number of non-zero components in the principal component vector to be solved is less than or equal to k, where k is a preset integer. In some embodiments, the value of k is 1 or 2.

[0031] S3. Represent each component of the principal component vector to be solved as a binary representation through a plurality of first binary variables, and define a plurality of second binary variables to respectively represent whether each component of the principal component vector to be solved is zero.

[0032] In some embodiments, the binary representation comprises: ,in Represents the principal component vector to be solved v No. i Quantity, and are all first binary variables, express No. j The value of an integer digit, express No. j The value of decimal places, m represents the upper limit of integer and decimal places.

[0033] For the second binary variable, for example, Indicates whether the i-th category in v is 0, then the 0 norm of vector v can be expressed as: , is the second binary variable.

[0034] S4. Determine constraints on the first binary variable and the second binary variable according to the vector constraints and the definition of the second binary variable.

[0035] In some embodiments, determining the constraint conditions of the first binary variable and the second binary variable according to the vector constraint condition and the definition of the second binary variable includes: The first constraint condition determined according to the principal component vector to be solved being a unit vector is expressed as: ,in Represents the principal component vector to be solved v No. i components, where p represents the dimension of the principal component vector v to be solved; The second constraint condition determined according to the number of non-zero components in the principal component vector to be solved is less than or equal to k is expressed as: , ,in Represents the principal component vector to be solved v of norm, represents the second binary variable; In order to make The value of is correct. According to the definition of the second binary variable, the third constraint is expressed as: .

[0036] S5. Convert the original objective function into a number of quadratic target functions of binary variables according to the binary representation, form a quadratic penalty term of the binary variable according to the constraint condition, and add the quadratic penalty term to the quadratic target function to form a quadratic unconstrained binary optimization model.

[0037] Combinatorial optimization is a mathematical optimization technique that consists of discrete decision variables, objective functions, and constraints, with the goal of solving the optimal value of the objective function and the corresponding optimal solution. If the objective function is quadratic, there are no constraints, and the decision variables can only be 0 or 1, then this combinatorial optimization is called a quadratic unconstrained binary optimization model (QUBO). The QUBO model form can be solved by dedicated quantum computers such as quantum annealing machines or coherent Ising machines. Using quantum computers to accelerate the solution of problems improves computing efficiency and solves the problem that existing technologies are difficult to calculate or take a long time to calculate for complex scheduling problems.

[0038] In some embodiments, adding the quadratic penalty term to the quadratic objective function to form a quadratic unconstrained binary optimization model includes: The quadratic unconstrained binary optimization model is expressed as: , in represents the quadratic objective function, expressed as: ; and are all quadratic penalty terms formed based on the third constraint condition, expressed as: ; is a quadratic penalty term formed based on the second constraint, expressed as: ; is a quadratic penalty term formed based on the first constraint condition, expressed as: , In the above formula and Each represents a slack variable represented by binary when the inequality constraint is converted into a penalty term; All non-binary variables in the quadratic unconstrained binary optimization model are converted into a combination representation of several binary variables through binary representation.

[0039] In some embodiments, forming a quadratic unconstrained binary optimization model further comprises: Converting the high-order polynomial into a quadratic polynomial using Rosenberg polynomials; For any two binary variables The product of replace , add a polynomial to the objective function: -2 y- , to ensure .

[0040] S6. Solve the quadratic unconstrained binary optimization model to determine the value of each of the first binary variables, and determine the principal component vector according to the value of the first binary variable.

[0041] The QUBO model is applicable to special quantum computers such as quantum annealing machines and coherent Ising machines (CIM). The implementation of the physical machine is based on the CIM based on the degenerate optical parametric oscillator (DOPO), which is a hybrid quantum computing system consisting of an optical part and an electrical part. The optical part includes lasers, amplifiers, periodically poled lithium niobate crystals (PPLN) and fiber loops. The laser uses a femtosecond pulse fiber laser and an amplifier system. The amplified laser is first frequency-doubled using a PPLN crystal. The frequency-doubled laser is used as a pump source to synchronously pump a PPLN crystal in a fiber loop to form a degenerate optical parametric oscillation. Hundreds of oscillation pulses can exist simultaneously in the fiber loop. The electrical part includes FPGA (Field Programmable Gate Array), AD / DA (digital analog / analog digital conversion), and phase detection. The laser output from the optical fiber loop and the base frequency laser are measured by a phase detector, and the phase of the output light can be tested. FPGA is used with high-speed AD / DA to measure and feedback control the optical pulse.

[0042] In some embodiments, solving the quadratic unconstrained binary optimization model to determine the value of each first binary variable includes: Converting the quadratic unconstrained binary optimization model into an Ising model and a maximum cut problem; Quantum computing is used to obtain the ground state of the Ising model, and a solution to the maximum cut problem is found to obtain the value of each of the first binary variables.

[0043] The objective function can be expressed as maximizing . Define two rotation unitary matrices and After repeating the operation p times, the following new state can be obtained: .

[0044] This embodiment can use a data processing device for neural network training to solve the QUBO model. Among them, the data processing device for neural network training can be a computer. As an optional implementation, the computer can be a quantum computer. The quantum computer can be implemented using an optical quantum computer or a coherent Ising machine. It is understandable that other quantum computers can also be used to solve. Of course, the QAOA quantum circuit can also be used to solve the QUBO model, which does not affect the implementation of this application.

[0045] In some embodiments, solving the quadratic unconstrained binary optimization model to determine the value of each first binary variable includes: The quadratic unconstrained binary optimization model is solved using a QAOA quantum circuit to obtain a value of each of the first binary variables.

[0046] Then follow the steps below to get the approximate solution: 1. Build a QAOA quantum circuit, which contains trainable parameters.

[0047] 2. Initialize the parameters in the circuit. Initialize the quantum state in the quantum computer.

[0048] 3. Run the quantum circuit to obtain the quantum state.

[0049] 4. Use quantum states to calculate the target function value and the expected value of the Hamiltonian in a classical computer.

[0050] 5. Repeat steps 2-4 several times, that is, measure the same set of parameters γ and β multiple times to obtain the distribution of quantum states.

[0051] 6. Use grid search to optimize the parameters in the circuit. For a new set of parameters γ, β, repeat the results of steps 2-5. After obtaining the distribution of quantum states, select the one with the largest target value.

[0052] 7. Based on the results of step 4, calculate the approximate solution to the target problem.

[0053] In some embodiments, after determining the principal component vector, the method further includes: The covariance matrix is ​​reduced based on the principal component vector, a new principal component vector is determined based on the reduced covariance matrix, and more principal component vectors are obtained through iteration.

[0054] Quantum computers with ultra-large bit numbers can be introduced into sparse principal component analysis problems to better solve practical problems and study the computational characteristics in the context of large instances.

[0055] The present invention also provides a quantum computing device, comprising: a quantum processing unit, an electronic processing unit and a storage unit; Wherein, the storage unit stores a computer program, and when the computer program is executed by the quantum processing unit and the electronic processing unit, the sparse principal component analysis method as described in any of the above embodiments is implemented.

[0056] The present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the sparse principal component analysis method described in any of the above embodiments is implemented.

[0057] The present invention also provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the sparse principal component analysis method as described in any of the above embodiments is implemented.

[0058] Computer readable storage media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include temporary computer readable media (transitory media), such as modulated data signals and carrier waves.

[0059] The professionals should further realize that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in the above description according to the function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0060] The steps of the method or algorithm described in conjunction with the embodiments disclosed herein may be implemented using hardware, a software module executed by a processor, or a combination of the two. The software module may be placed in a random access memory (RAM), a memory, a read-only memory (ROM), an electrically programmable ROM, an electrically erasable programmable ROM, a register, a hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.

[0061] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A sparse principal component analysis method, characterized in that: The following steps are involved: Obtaining a target data matrix, and determining a covariance matrix based on the target data matrix; Setting a principal component vector to be solved, and determining an original objective function and vector constraint conditions of the sparse principal component analysis based on the principal component vector to be solved and the covariance matrix; Each component of the principal component vector to be solved is represented as a binary representation through a plurality of first binary variables, and a plurality of second binary variables are defined to respectively represent whether each component of the principal component vector to be solved is zero; Determining constraints of the first binary variable and the second binary variable according to the vector constraint and the definition of the second binary variable; Converting the original objective function into a quadratic objective function of a plurality of binary variables according to the binary representation, forming a quadratic penalty term of the binary variable according to the constraint condition, and adding the quadratic penalty term to the quadratic objective function to form a quadratic unconstrained binary optimization model; The quadratic unconstrained binary optimization model is solved to determine the value of each of the first binary variables, and the principal component vector is determined according to the value of the first binary variable.

2. The sparse principal component analysis method according to claim 1, characterized in that: The solving the quadratic unconstrained binary optimization model to determine the value of each of the first binary variables includes: Converting the quadratic unconstrained binary optimization model into an Ising model and a maximum cut problem; Quantum computing is used to obtain the ground state of the Ising model, and a solution to the maximum cut problem is found to obtain the value of each of the first binary variables.

3. The sparse principal component analysis method according to claim 1, characterized in that: The solving the quadratic unconstrained binary optimization model to determine the value of each of the first binary variables includes: The quadratic unconstrained binary optimization model is solved using a QAOA quantum circuit to obtain a value of each of the first binary variables.

4. The sparse principal component analysis method according to claim 1, characterized in that: The original objective function and vector constraint conditions of the sparse principal component analysis are determined based on the principal component vector to be solved and the covariance matrix, wherein the objective function is expressed as: ,in v represents the principal component vector to be solved, represents the covariance matrix of the target data matrix; The vector constraints include: The principal component vector to be solved is a unit vector; The number of non-zero components in the principal component vector to be solved is less than or equal to k, where k is a preset integer.

5. The sparse principal component analysis method according to claim 4, characterized in that: The binary representation includes: ,in Represents the principal component vector to be solved v No. i Quantity, and are all first binary variables, express No. j The value of an integer digit, express No. j The value of decimal places, m represents the upper limit of integer and decimal places.

6. The sparse principal component analysis method according to claim 5, characterized in that: The determining the constraint conditions of the first binary variable and the second binary variable according to the vector constraint condition and the definition of the second binary variable comprises: The first constraint condition determined according to the principal component vector to be solved being a unit vector is expressed as: ,in Represents the principal component vector to be solved v No. i components, where p represents the dimension of the principal component vector v to be solved; The second constraint condition determined according to the number of non-zero components in the principal component vector to be solved is less than or equal to k is expressed as: , ,in Represents the principal component vector to be solved v of norm, represents the second binary variable; The third constraint condition determined according to the definition of the second binary variable is expressed as: 。 7. The sparse principal component analysis method according to claim 6, characterized in that: The step of adding the quadratic penalty term to the quadratic objective function to form a quadratic unconstrained binary optimization model comprises: The quadratic unconstrained binary optimization model is expressed as: ， in represents the quadratic objective function, expressed as: ; and are all quadratic penalty terms formed based on the third constraint condition, expressed as: ； is a quadratic penalty term formed based on the second constraint, expressed as: ； is a quadratic penalty term formed based on the first constraint condition, expressed as: ， In the above formula and Each represents a slack variable represented by binary when the inequality constraint is converted into a penalty term; All non-binary variables in the quadratic unconstrained binary optimization model are converted into a combination representation of several binary variables through binary representation.

8. The sparse principal component analysis method according to claim 7, characterized in that: The forming of the quadratic unconstrained binary optimization model further includes: Use Rosenberg polynomials to convert high-order polynomials into quadratic polynomials; For any two binary variables The product of replace , add a polynomial to the objective function: -2 y- , to ensure .

9. The sparse principal component analysis method according to claim 1, characterized in that: After determining the principal component vector, the method further includes: The covariance matrix is ​​reduced based on the principal component vector, a new principal component vector is determined based on the reduced covariance matrix, and more principal component vectors are obtained through iteration.

10. A quantum computing device, characterized in that include: Quantum processing units, electronic processing units, and storage units; Wherein, the storage unit stores a computer program, and when the computer program is executed by the quantum processing unit and the electronic processing unit, the sparse principal component analysis method according to any one of claims 1 to 9 is implemented.

11. An electronic device, characterized in that: include: Quantum processing units, electronic processing units, and storage units; Wherein, the storage unit stores a computer program, and when the computer program is executed by the quantum processing unit and the electronic processing unit, the sparse principal component analysis method according to any one of claims 1 to 9 is implemented.

12. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the computer program is executed by a processor, the sparse principal component analysis method according to any one of claims 1 to 9 is implemented.

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