Distributed Quantum Computing Method, Apparatus, Device, and Medium for Simon's Problem

Abstract

The present invention relates to a distributed quantum computing method, apparatus, device, and medium for the Simon problem. Among them, the method includes: determining the number of computing nodes and the number of domain qubits of each computing node, where the sum of the number of domain qubits of all computing nodes is equal to the number of binary bits in the domain of the Simon problem function to be solved; constructing a sub-Simon problem function corresponding to each computing node based on the number of domain qubits of each computing node and the original domain and range of the Simon problem function to be solved; constructing a quantum circuit for solving the sub-Simon problem function corresponding to each computing node, and respectively running the corresponding quantum circuit for solving the sub-Simon problem function to obtain the corresponding substring to be obtained; combining the corresponding substrings to obtain the substring to be obtained of the Simon problem function to be solved. The present invention has high efficiency, less quantum resources required, and high computing accuracy when solving the Simon problem.

Description

Technical Field

[0001] The present invention relates to the field of quantum computing technology, and in particular to a distributed quantum computing method, apparatus, device and medium for Simon problem. Background Art

[0002] Quantum algorithms are algorithms that run on quantum computers and represent a cutting-edge computing technology. They use properties such as quantum superposition and quantum entanglement in quantum mechanics to solve problems that are difficult to solve with traditional algorithms. Compared with classical algorithms, quantum algorithms use quantum bits (Qubit) as the basic carrier of information and can explore multiple possible solutions at the same time, thereby achieving significant superiority over classical computing on specific problems.

[0003] So far, researchers have developed a series of quantum algorithms and achieved remarkable results in many fields. Among them, the Simon algorithm not only promoted the development of Fourier transform algorithms based on quantum computing, but also laid the foundation for the famous Shor algorithm. With the advantage of quantum parallelism, the Shor algorithm can theoretically efficiently decompose large integers in polynomial time, which has brought disruptive changes to the field of cryptography. The Simon algorithm has also shown great potential in solving practical problems, especially in cryptography and coding. For example, the Simon algorithm can effectively crack encryption schemes based on Simon functions.

[0004] The Simon algorithm was proposed by Daniel Simon in 1994 to solve a specific problem, namely, to determine whether a black box function is a one-to-one function or a two-to-one function and find the corresponding binary string. Specifically, given a Boolean function f: {0, 1} n →{0, 1} m , where m ≥ n-1, {0, 1} n is the range of values of the independent variable, called the domain, {0, 1} m is the range of the dependent variable value, called the range. The function satisfies the following properties: there exists an unknown string s∈{0,1} n , so that for all independent variable values x, y∈{0,1} n , f(x)=f(y) if and only if x=y or ( represents modulo 2 addition, or XOR operation).

[0005] The solution objective of the Simon problem is to determine the string s based on the given domain and range. Currently, there are two main methods to solve the Simon problem: one is the classical algorithm, and the other is the Simon algorithm proposed by Daniel Simon based on quantum computing. Among them, the query complexity of solving the Simon problem using the classical algorithm is O(2 n ), and the query complexity of solving the Simon problem using the Simon algorithm is O(n). Compared with the classical computing method, the computing speed of the existing Simon algorithm is exponentially accelerated.

[0006] However, when the domain and range of the Simon problem are given, the number of qubits required to solve the Simon problem using the existing Simon algorithm is n + m. When n and m are large, the required number of qubits will increase significantly, which means that a large-scale general-purpose quantum computer is needed to complete the calculation. For today's quantum technology, there are many problems in solving the Simon problem using a large-scale general-purpose quantum computer. First, building and running such a computer requires a large amount of financial support; second, the computing efficiency is low because the increase in the number of qubits will lead to a significant increase in the depth and complexity of the quantum circuit, thus slowing down the computing speed; in addition, the quantum fidelity will also be limited, and qubits are vulnerable to noise and errors during operation, which will have a greater negative impact on the accuracy of the calculation. Summary of the Invention

[0007] In view of the technical problems existing in the prior art, the present invention proposes a distributed quantum computing method, device, equipment and medium for the Simon problem, which reduces the computing cost and improves the solution accuracy and computing efficiency.

[0008] To solve the technical problems in the prior art, according to one aspect of the present invention, a distributed quantum computing method for the Simon problem is proposed, including the following steps:

[0009] Obtain the function of the Simon problem to be solved, the number of computing nodes, and the number of domain qubits of each computing node, where the sum of the number of domain qubits of all computing nodes is equal to the number of binary bits of the original domain of the Simon problem function to be solved;

[0010] Construct a sub-Simon problem function corresponding to each computing node based on the number of domain qubits of each computing node and the original domain and range of the Simon problem function to be solved, where the original domain of the Simon problem function to be solved includes the domains of all sub-Simon problem functions combined in a preset combination order, the range of each sub-Simon problem function is a sub-range of the original range of the Simon problem function to be solved, and each sub-Simon problem function includes a corresponding substring to be solved;

[0011] Construct a quantum circuit for solving the sub-Simon problem function corresponding to each computing node;

[0012] Run the quantum circuits for solving the sub-Simon problem functions respectively to obtain the corresponding substrings to be solved;

[0013] Combine the substrings to be solved in the preset combination order of the domain of the sub-Simon problem function in the original domain of the Simon problem function to be solved to obtain the string to be solved of the Simon problem function to be solved.

[0014] Optionally, the steps of constructing the sub-Simon problem function corresponding to each computing node include:

[0015] According to the number of domain qubits of the computing node, determine the same number of second bits from the bits of the original domain of the Simon problem function to be solved as the domain bits of the sub-Simon problem function, and the remaining bits as the first bits of the first domain;

[0016] Sequentially extract the second-bit values from each original independent variable value in the original domain to form each sub-independent variable value of the sub-Simon problem function, and all the sub-independent variable values form the domain of the sub-Simon problem function of the computing node;

[0017] Sequentially extract the first-bit values from each original independent variable value in the original domain to form each first independent variable value, and all the first independent variable values form the first domain;

[0018] Combine each sub-independent variable value of the sub-Simon problem function with each first independent variable value in the order of their bits in the original domain to form an original independent variable value in the original domain;

[0019] Obtain the original dependent variable value corresponding to the original independent variable value from the original range of the Simon problem function to be solved as the first dependent variable value;

[0020] Determine a first dependent variable value from multiple first dependent variable values corresponding to each sub-independent variable value according to the same value-taking function as the sub-dependent variable value corresponding to the sub-independent variable value. Among them, the sub-dependent variable values corresponding to each sub-independent variable value constitute the value range of the sub-Simon problem function of the computing node.

[0021] Optionally, the value-taking function is a maximum value function or a minimum value function; correspondingly, determine the largest or smallest first dependent variable value from multiple first dependent variable values corresponding to each sub-independent variable value as the sub-dependent variable value corresponding to the sub-independent variable value.

[0022] Optionally, when constructing the sub-Simon problem function corresponding to each computing node, the following steps are further included:

[0023] Sort all computing nodes;

[0024] When determining the same number of second bits as the function domain bits of the sub-Simon problem from the bits of the original domain of the Simon problem function to be solved according to the number of domain qubits of each computing node, cut out the second bits with the same number as the number of domain qubits of each computing node from the bits of the original domain in the order from high to low or from low to high according to the sorting of the computing nodes to obtain the function domain bits of the sub-Simon problem function corresponding to each computing node.

[0025] Optionally, when separately running the quantum circuit for solving the sub-Simon problem function to obtain the corresponding substring to be solved, run the quantum circuit for solving the sub-Simon problem function in a serial and / or parallel manner to solve the corresponding sub-Simon problem function.

[0026] According to another aspect of the present invention, the present invention also provides a distributed quantum computing device for Simon's problem, including a parameter acquisition module, a sub-Simon's problem function construction module, a quantum circuit construction module, an operation module, and a calculation module. Among them, the parameter acquisition module is configured to acquire the Simon's problem function to be solved, the number of computing nodes, and the number of domain qubits of each computing node, where the sum of the number of domain qubits of all computing nodes is equal to the number of binary bits of the original domain of the Simon's problem function to be solved; the sub-Simon's problem function construction module is configured to construct sub-Simon's problem functions corresponding to each computing node based on the number of domain qubits of each computing node, the original domain and range of the Simon's problem function to be solved, where when the domains of all sub-Simon's problem functions are combined together in a preset combination order, they constitute the original domain of the Simon's problem function to be solved, the range of each sub-Simon's problem function is a sub-range of the original range of the Simon's problem function to be solved, and each sub-Simon's problem function includes a corresponding substring to be solved; the quantum circuit construction module is configured to construct quantum circuits for solving sub-Simon's problem functions corresponding to each computing node; the operation module is configured to send the quantum circuits for solving sub-Simon's problem functions to the corresponding quantum computing modules respectively, and receive the measurement results returned by the quantum computing modules; the calculation module is configured to calculate the corresponding substrings to be solved of the sub-Simon's problem functions based on the measurement results returned by the quantum computing modules running the quantum circuits for solving sub-Simon's problem functions; the corresponding substrings to be solved are combined in the preset combination order of the domains of the sub-Simon's problem functions in the original domain of the Simon's problem function to be solved to obtain the substring to be solved of the Simon's problem function to be solved.

[0027] Optionally, the computing device further includes one or more quantum computing modules; when there is one quantum computing module, the operation module sends the constructed multiple quantum circuits for solving sub-Simon's problem functions to the quantum computing module in a serial manner, and when there are multiple quantum computing modules, the operation module sends the constructed multiple quantum circuits for solving sub-Simon's problem functions to the multiple quantum computing modules in a serial and / or parallel manner; each quantum computing module runs the quantum circuit for solving the sub-Simon's problem function of the corresponding computing node and sends the measurement result to the operation module.

[0028] According to another aspect of the present invention, the present invention also provides an electronic device, including a processor and a memory, where computer instructions are stored in the memory, and when the processor runs the computer instructions, it executes the aforementioned distributed quantum computing method for Simon's problem.

[0029] According to another aspect of the present invention, the present invention also provides a computer-readable storage medium storing computer instructions, which, when executed by a processor, perform the aforementioned distributed quantum computing method for the Simon problem.

[0030] The present invention combines the concept of distributed computing with quantum algorithms, decomposes the complex and resource-intensive task of solving the Simon problem into a series of smaller and more manageable subtasks. These subtasks can be assigned to one or more quantum computing modules and processed serially or in parallel, achieving efficient solution of the Simon problem. Meanwhile, while reducing the quantum resource requirements and computing costs, due to the reduction in the number of qubits applied, the impact of circuit noise on quantum states is also significantly reduced, thus improving the quantum fidelity and further enhancing the computing accuracy of the solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Next, the preferred embodiments of the present invention will be further described in detail with reference to the drawings, where:

[0032] Figure 1 is a flowchart of a distributed quantum computing method for the Simon problem according to an embodiment of the present invention;

[0033] Figure 2 is a flowchart of a method for constructing a sub-Simon problem function corresponding to a target computing node according to an embodiment of the present invention;

[0034] Figure 3 is a schematic diagram of a quantum circuit for solving a sub-Simon problem function corresponding to a computing node according to an embodiment of the present invention;

[0035] Figure 4 is a flowchart of a method for solving the Simon problem based on multiple computing nodes and their quantum circuits according to an embodiment of the present invention;

[0036] Figure 5 is a schematic diagram of a quantum circuit for solving when multiple computing nodes execute their respective sub-Simon problem functions in parallel according to an embodiment of the present invention;

[0037] Figure 6 is a block diagram of the principle of a distributed quantum computing device for the Simon problem according to an embodiment of the present invention;

[0038] Figure 7 is a block diagram of the principle of a distributed quantum computing device for the Simon problem according to another embodiment of the present invention;

[0039] Figure 8It is a block diagram of the principle of a distributed quantum computing device for the Simon problem according to another embodiment of the present invention;

[0040] Figure 9 It is a block diagram of the structural principle of an electronic device according to an embodiment of the present invention. Detailed implementation manners

[0041] To make the objectives, 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 with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0042] In the following detailed description, reference may be made to the accompanying drawings that form a part hereof and in which are shown, by way of illustration, specific embodiments in which the application may be practiced. In the drawings, like reference numerals describe substantially similar components in different figures. The various specific embodiments of the present application have been described in sufficient detail below to enable those of ordinary skill in the art with relevant knowledge and technology to implement the technical solutions of the present application. It should be understood that other embodiments may be utilized or structural, logical, or electrical changes may be made to the embodiments of the present application.

[0043] In addition, the "first", "second", etc. in the technical feature names of the present invention are not used to represent an order, but to distinguish different technical features with the same name.

[0044] In today's noisy intermediate-scale quantum (NISQ) era, compared with building a large-scale general-purpose quantum computer, the technical path to realizing a small-scale quantum processor appears to be more practical and feasible. The concept of distributed quantum computing (DQC) is an innovative move that ingeniously integrates the essence of distributed systems with quantum information processing technology. The implementation of this architecture relies on a carefully designed distributed quantum algorithm to ensure its effectiveness in practical applications.

[0045] See Figure 1 , Figure 1 is a flowchart of a distributed quantum computing method for the Simon problem according to an embodiment of the present invention. In the present invention, the Boolean function in the Simon problem to be solved is: f: {0, 1} n →{0, 1} m , n is the number of binary bits of the original independent variable, simply referred to as the number of bits in the original domain, {0, 1} n is called the original domain; m is the number of binary bits of the original dependent variable, simply referred to as the number of bits in the original range, m ≥ n - 1, {0, 1}m is called the original value range; and it satisfies that for all independent variable values x, y ∈ {0, 1} n , there is f(x) = f(y) if and only if x = y or s is the string to be solved, s ∈ {0, 1} n , hereinafter, the Boolean function in the aforementioned Simon problem to be solved is simply referred to as the Simon problem function to be solved. The distributed quantum computing method for the Simon problem in this embodiment includes the following steps:

[0046] Step S1: Obtain the Simon problem function to be solved, the number of computing nodes, and the number of domain qubits of each computing node. Among them, the total number of domain qubits of all computing nodes is equal to the number of binary bits of the original domain of the Simon problem function to be solved.

[0047] Step S2: Construct a sub-Simon problem function corresponding to each computing node. Among them, based on the number of domain qubits of each computing node, the original domain and range of the Simon problem function to be solved, construct a sub-Simon problem function corresponding to each computing node. When the domains of all sub-Simon problem functions are combined together in the preset combination order, they form the original domain of the Simon problem function to be solved. The range of each sub-Simon problem function is a sub-range of the original range of the Simon problem function to be solved, and each sub-Simon problem function has a substring to be solved.

[0048] Step S3: Construct a quantum circuit for solving the sub-Simon problem function corresponding to each computing node.

[0049] Step S4: Based on the computing nodes, respectively run the quantum circuits for solving the corresponding sub-Simon problem functions to solve the corresponding sub-Simon problem functions to obtain the corresponding substrings to be solved.

[0050] Step S5: Combine the corresponding substrings to be solved in the preset combination order of the domain of each sub-Simon problem function in the original domain of the Simon problem function to be solved to obtain the string s to be solved of the Simon problem function to be solved.

[0051] The computing nodes in the present invention can also be called computing tasks for completing one Simon problem solution. Multiple computing nodes, that is, multiple computing tasks, can be implemented by a quantum computing module in a serial manner or by multiple quantum computing modules in a parallel manner.

[0052] In step S1, the number of computing nodes is set to t, where the number of computing nodes t satisfies 2 ≤ t ≤ n. Based on the number of qubits of each computing node, the number of qubits n available for its domain is determined. j , where j represents the serial number of any computing node, and j ∈ {0, 1, …, t - 1}. The sum of the number of domain qubits of all computing nodes is equal to the number of bits in the original domain of the Simon problem to be solved, that is, it satisfies Therefore, the total number of qubits of each computing node is n j + m.

[0053] In step S2, when constructing the sub-Simon problem function corresponding to each computing node, refer to Figure 2 , Figure 2 is a flowchart of the method for constructing the sub-Simon problem function corresponding to a computing node according to an embodiment of the present invention, which includes the following steps:

[0054] Step S21, divide the original domain of the Simon problem function to be solved to obtain a composite domain. Specifically, according to the number of domain qubits of the target computing node, the same number of second bits are determined from the bits of the original domain of the Simon problem function to be solved as the domain bits of the sub-Simon problem function, and the remaining bits are used as the first bits of the first domain; the second bit values are sequentially extracted from each original independent variable value of the original domain to form each sub-independent variable value of the sub-Simon problem function, and all the sub-independent variable values form the domain of the sub-Simon problem function of the target computing node; the first bit values are sequentially extracted from each original independent variable value of the original domain to form each first independent variable value, and all the first independent variable values form the first domain; wherein, when determining the domain bits of the sub-Simon problem function from the original domain bits of the Simon problem function to be solved, bits can be extracted from any position in the original domain of the Simon problem function to be solved as the domain bits of the sub-Simon problem function, and all the domain bits of the sub-Simon problem functions corresponding to all computing nodes do not repeat, and the domain of the sub-Simon problem function and the first sub-domain form a composite domain.

[0055] Step S22, obtain the corresponding original dependent variable value as the first dependent variable value from the original range of the Simon problem function to be solved based on the composite domain. Specifically, each sub-independent variable value in the domain of the sub-Simon problem function and each first independent variable value in the first sub-domain are combined together in the order in the original domain to form an original independent variable value in the original domain, and the corresponding original dependent variable value is obtained from the original range of the Simon problem function to be solved as the first dependent variable value.

[0056] Step S23: Determine the value range of the sub-Simon problem function. Specifically, one first dependent variable value is determined from multiple first dependent variable values corresponding to each sub-independent variable value according to the same value-taking function as the sub-dependent variable value corresponding to the sub-independent variable value. Among them, the sub-dependent variable values corresponding to each sub-independent variable value constitute the sub-value range of the sub-Simon problem function of the target calculation node.

[0057] In step S22 of this embodiment, a composite domain is obtained by combining the domain of the target sub-Simon problem function and the first sub-domain. In one embodiment, the first sub-domain is used as the first-layer domain, and the domain of the target sub-Simon problem function is the second-layer domain. In the composite function corresponding to the composite domain, the dependent variable value obtained based on each first independent variable value of the first-layer domain is a sub-function based on the second-layer domain. The number of sub-functions is determined by the number of binary bits of the first independent variable value in the first-layer domain; with one independent variable value in the second-layer domain, that is, one sub-independent variable value in the domain of the sub-Simon problem function, a unique original dependent variable value can be determined from the original value range through the sub-function. In the present invention, it is named the first dependent variable value. The total number of first dependent variable values is determined by combining the number of binary bits of the independent variable in the second-layer domain and the number of sub-functions.

[0058] For example, take the jth calculation node Note j as the target calculation node, and the number of qubits available for its domain is represented as n j . Then the domain of the corresponding target sub-Simon problem function is represented as {0, 1}^n j , that is, the sub-independent variable bits of the target sub-Simon problem function total n j bits. Since the original domain of the Simon problem function to be solved is {0, 1}^n, that is, the original independent variable bits of the Simon problem function to be solved total n bits, the bits of the first independent variable in the first domain total n - n j bits. Therefore, the dependent variable value obtained based on each first independent variable value in the first domain is a sub-function, and its number is The number of first dependent variable values obtained through all sub-functions is One sub-independent variable value of each target sub-Simon problem function corresponds to a number of first dependent variable values.

[0059] In step S23, the value-taking function is the maximum value function or the minimum value function. Correspondingly, when constructing the value range of the sub-Simon problem function, among the values corresponding to one sub-independent variable value When determining one of the first dependent variable values as the sub-dependent variable value of the sub-Simon problem function, the first dependent variable value with the largest or smallest dependent variable value is used as the sub-dependent variable value corresponding to the sub-independent variable value.

[0060] In addition, when the number t of computing nodes is greater than or equal to 2, when constructing sub-Simon problem functions corresponding to the t computing nodes, all the computing nodes can be sorted, and then according to the sorting of the computing nodes, in the bits of the original domain, in the order from high to low or from low to high, the second bits with the same number as the number of domain qubits of each computing node are respectively cut out to obtain the domain bits of the sub-Simon problem function corresponding to each computing node.

[0061] For example, the method of constructing sub-Simon problem functions corresponding to each computing node in the order from high to low is described as follows:

[0062] First, for the Simon problem function to be solved, the number of binary bits in its domain is n, the number of binary bits in its range is m, and there are t computing nodes in total. After sorting them, the computing node number is represented by the letter j, and j ∈ {0, 1,..., t - 1}. Among them, the number of qubits used for the domain of each computing node is n j , satisfying and j ∈ {0, 1,..., t - 1}, that is, the binary bits of the domain of the sub-Simon problem function corresponding to each computing node correspond one-to-one with the qubits used for the domain of the computing node.

[0063] For the 0th computing node, that is, the case where j = 0, the construction process of the sub-Simon problem function is as follows:

[0064] Select the last binary bits from the original domain of the Simon problem function to be solved to divide the Simon problem function to be solved, so as to obtain the following sub-functions, that is:

[0065]

[0066] Among them, k represents the serial number of the sub-function, is an n j -bit binary number, m k represents the independent variable of the kth sub-function and is also the sub-independent variable of the sub-Simon problem function corresponding to the jth computing node; is the remaining binary bits in the original domain except for the domain bits of the sub-Simon problem function of the jth computing node, and there are

[0067] bits, which constitute the first sub-domain bits and are also the binary representation of k.

[0068] As can be seen from the above expressions, corresponding to the domain of the sub-Simon problem function, the same sub-independent variable value corresponds to sub-functions. A specific original independent variable value of the Simon problem function to be solved can be jointly formed by a specific sub-independent variable value and a specific first independent variable value of a sub-function, so that a specific dependent variable value can be determined from the original value range of the Simon problem function to be solved. Therefore, corresponding to a sub-independent variable value of the sub-Simon problem function, dependent variable values can be determined from the original value range of the Simon problem function to be solved. For the sake of factorization, these dependent variable values are called the first dependent variable values.

[0069] Then, based on the maximum value formula:

[0070]

[0071] where a specific independent variable value m of the sub-Simon problem function corresponding to the j-th computing node j , from the first dependent variable values, a maximum value is taken as the corresponding sub-dependent variable value, thus obtaining the sub-Simon problem function of the j-th computing node

[0072] For the j-th node (j ∈ {1, 2,..., t - 2}), the first and the last binary bits are selected from the original domain of the Simon problem function to be solved to divide the Simon problem function to be solved, and the following sub-functions are obtained, that is

[0073]

[0074] where k represents the serial number of the sub-function, is an n j bit binary number, and m k represents the independent variable of the k-th sub-function and is also the sub-independent variable of the sub-Simon problem function corresponding to the j-th computing node;

[0075]

[0076] is the remaining binary bits in the original domain except for the domain bits of the sub-Simon problem function of the j-th computing node, with a total of , which constitutes the first sub-domain bits and is also the binary representation of k.

[0077] As can be seen from the above expressions, corresponding to the domain of the sub-Simon problem function, the same sub-independent variable value corresponds to sub-functions respectively, and first dependent variable values can be obtained from the range of the Simon problem function to be solved.

[0078] Then, based on the maximum value formula:

[0079]

[0080] where corresponds to a specific sub-independent variable value m of the sub-Simon problem function of the j-th computing node j , from first dependent variable values, the maximum value is taken as the corresponding sub-dependent variable value, thus obtaining the sub-Simon problem function of the j-th computing node

[0081] For the last computing node (j = t - 1), the first binary bits are selected from the original domain of the Simon problem function to be solved to divide the Simon problem function to be solved, and the following sub-functions are obtained, that is

[0082]

[0083] where k represents the serial number of the sub-function, is an n j -bit binary number, m k represents the independent variable of the k-th sub-function and is also the sub-independent variable of the sub-Simon problem function corresponding to the j-th computing node; is the remaining binary bits in the original domain except for the domain bits of the sub-Simon problem function of the j-th computing node and is also the binary representation of k.

[0084] As can be seen from the above expressions, corresponding to the domain of the sub-Simon problem function, the same sub-independent variable value corresponds to sub-functions respectively, and first dependent variable values can be obtained from the range of the Simon problem function to be solved.

[0085] Then, based on the maximum value formula:

[0086] Among them an independent variable value m of the sub-Simon problem function corresponding to the j-th computing node j , from the maximum value is taken from the first dependent variable values as the corresponding sub-dependent variable value, thus obtaining the sub-Simon problem function of the j-th computing node

[0087] In addition, although the foregoing solution determines the maximum value from multiple first dependent variable values as the sub-dependent variable value, it is also possible to determine the minimum value from multiple first dependent variable values as the sub-dependent variable value.

[0088] After the processing of the foregoing step S2, a corresponding sub-Simon problem function is constructed for each computing node, reducing the number of qubits required by the computing node. Moreover, the embodiments of the present invention can flexibly construct corresponding sub-Simon problem functions according to the number of qubits provided by the existing quantum computing modules, and can make full use of the resources of the existing devices.

[0089] In step S3, the quantum circuit for solving the sub-Simon problem function corresponding to each computing node is constructed as Figure 3 shown Figure 3 is a schematic diagram of the quantum circuit for solving the sub-Simon problem function corresponding to a computing node according to an embodiment of the present invention.

[0090] The qubits required for a computing node include n j qubits corresponding to the domain of the sub-Simon problem function and m qubits corresponding to the range, where the module B gj is a quantum circuit unit capable of implementing the Oracle (black box function, or query function) corresponding to the sub-Simon problem function. The Oracle can implement x and y are respectively two sub-independent variable values of the sub-Simon problem function, and g j (x) is the dependent variable value of the sub-Simon problem function corresponding to the sub-independent variable value x. is the l-th measurement value. This quantum circuit unit is the same as the quantum circuit unit used when Daniel Simon proposed to solve the Simon problem in a quantum computing manner. The specific quantum circuit depends on the specific function parameters n and m, and those of ordinary skill in the art can obtain it according to common knowledge in the industry or by referring to relevant literature, and will not be elaborated here.

[0091] Figure 4 is a flowchart of the method for solving the Simon problem based on multiple computing nodes and their quantum circuits according to an embodiment of the present invention. CombiningFigure 3 , the method comprises the following steps:

[0092] Step S101, let j = 0.

[0093] Step S102, let l = 1.

[0094] Step S103, initialize n j domain qubits. In one embodiment, initialize n j domain qubits to

[0095] Step S104, initialize m range qubits. In one embodiment, initialize m range qubits to

[0096] Step S105, generate the sub-Simon problem function corresponding to the computing node according to Figure 2 the method

[0097] Step S106, perform a Hadamard gate ( j gate) on the first n qubits.

[0098] Step S107, perform on all qubits where y ∈ {0, 1} m .

[0099] Step S108, perform a Hadamard gate ( j gate) on the first n qubits.

[0100] Step S109, measure the first n j qubits to obtain a first measurement value

[0101] Step S110, determine whether l = n j is satisfied. If it is satisfied, execute Step S112. If it is not satisfied, in Step S111, let l = l + 1 and return to Step S103.

[0102] Step S112, solve the linear equation set 1-1 to obtain the substring S j , where ......

[0104]

[0105] Step S113, determine whether j=t-1 is satisfied. If so, execute step S115. If not, in step S114, set j=j+1 and return to step S102.

[0106] Step S115, sum up t substrings S j Get the string s of the Simon problem to be solved. Where s=S0S1…S t-1 s∈{0,1} n .

[0107] Among them, step S103 to step S109 is an evolution and measurement process, and the measurement result For a universal quantum solution to the Simon problem, the orthogonality between the measurement result ψ and the string s to be solved is satisfied, so an equation ψ·s=0 is obtained based on each measurement result. In order to solve the string s in the Simon problem, it is necessary to execute at least n-1 times to obtain n-1 different measurement results ψ j , and then a system of equations is obtained to solve the string s to be solved. Corresponding to this embodiment, for each sub-Simon problem function, it is necessary to measure n j times, thus obtaining the above equation set 1-1. The query complexity of solving each sub-Simon problem is O(n j ), which obviously further reduces the query complexity compared to the current query complexity O(n) of the Simon problem.

[0108] exist Figure 4 In the processing method shown, each computing node is executed in a serial manner to obtain its own substring. However, it can be known that the computing nodes can also be executed in parallel, such as Figure 5 As shown, Figure 5 According to one embodiment of the present invention, the 0th computing node Note 0 To Note t-1 Schematic diagram of the quantum circuit for solving the sub-Simon problem functions in parallel. First, according to the number of computing nodes, Figure 2 The method shown in the figure calculates the corresponding sub-Simon problem functions g0,…,g t-1 , and construct quantum circuits for each computing node respectively. The quantum circuit units Bg0 to Bg t-1 Execute the corresponding Oracle function calculations respectively to solve the corresponding sub-Simon problem functions.

[0109] The technical solution of the present invention is exemplarily described below through a specific embodiment.

[0110] In the Simon's problem of this embodiment, n = 4 and m = 3. Assume that the string to be solved is s = 1001. The truth table of the Boolean function f corresponding to the Simon's problem in this embodiment is shown in Table 1 below.

[0111] Table 1: Truth table of the function of the Simon's problem to be solved

[0112] x f(x) x f(x) x f(x) x f(x) 0000 000 0100 100 1000 001 1100 101 0001 001 0101 101 1001 000 1101 100 0010 010 0110 110 1010 011 1110 111 0011 011 0111 111 1011 010 1111 110

[0113] In Table 1, x is the original independent variable and f(x) is the original dependent variable. Among them, the number of binary bits in the original domain is 4 bits, and the number of binary bits in the original range is 3 bits. In this embodiment, two quantum computing modules supporting 5 qubits are used for calculation, so there are two calculation nodes accordingly, and thus the domain qubits of each calculation node are 2.

[0114] According to the method of constructing the sub-Simon's problem function described above, first divide the original domain to obtain the domain of the target sub-Simon's problem function, and then obtain the corresponding range. In this embodiment, the calculation node numbers are 0 and 1. Corresponding to the 0th calculation node, select the two high-order bits on the left as the domain bits of the sub-Simon's problem function, and the 2 low-order bits on the right as the first domain bits. Thus, 2 2 A total of 4 sub-functions are obtained, which are respectively represented as f 0 00 、f 0 01 、f 0 10 and f 0 11 , where the superscript 0 represents the 0th calculation node, and the subscripts 00, 01, 10, and 11 represent a specific independent variable value in the first domain, which can also be regarded as the binary representation of the sub-function number. Corresponding to the sub-independent variables of the domain of the sub-Simon's problem function, the corresponding sub-dependent variable values are obtained from the original range respectively, and the truth values obtained corresponding to the 4 sub-functions are as follows.

[0115] Table 2: Truth table of the first sub-function f 0 00

[0116] <![CDATA[x 子 > <![CDATA[f 0 00 > 00 000 01 100 10 001 11 101

[0117] Table 3: Truth table of the second sub-function f 0 01

[0118] <![CDATA[x 子 > <![CDATA[f 0 01 <!-- 11 -->]]> 00 001 01 101 10 000 11 100

[0119] Table 4: Truth table of the third sub-function f 0 10Truth table of

[0120] <![CDATA[x 子 > <![CDATA[f 0 10 > 00 010 01 110 10 011 11 111

[0121] Table 5: The fourth sub - function f 0 11 Truth table of

[0122] <![CDATA[x 子 > <![CDATA[f 0 11 > 00 011 01 111 10 010 11 110

[0123] The x in the above 4 tables 子 is the sub - independent variable of the sub - Simon problem function.

[0124] Based on the above 4 truth tables, for each value of the sub - independent variable x of the sub - Simon problem function 子 , take the maximum value among every 4 values as a corresponding value in the range of the dependent variable of the sub - Simon problem. Thus, the sub - Simon problem function g0 of the 0th node is generated, and its truth table is as follows.

[0125] Table 6: Truth table of the sub - Simon problem function g0 of the 0th node

[0126] <![CDATA[x 子 > <![CDATA[g0]]> 00 011 01 111 10 011 11 111

[0127] From the quantum circuit that executes the sub - Simon problem function g0, the quantum circuit diagram can be referred to Figure 3 , corresponding to this embodiment, n j = 2, m = 3. Run and measure twice according to the steps in Figure 4 to obtain a system of equations, and after solving, the corresponding substring S0 = 10 is obtained.

[0128] Similarly, for the 1st computing node, determine that the lower two bits are its domain of definition, and the higher two bits are the first domain of definition. Referring to the foregoing method, 4 sub - functions can be obtained: f 1 00 , f 1 01 , f 1 10 , f 1 11 , and thus the sub - Simon problem function g1 is obtained, and its truth table is as follows.

[0129] Table 7: Truth table of the sub - Simon problem function g1 of the 1st node

[0130] <![CDATA[x 子 > <![CDATA[g1]]> 00 101 01 101 10 111 11 111

[0131] Execute the quantum circuit of the sub - Simon problem function g1 and solve to obtain the substring S1 = 01.

[0132] Finally, the two strings are sorted and combined according to the order of the domains of the two sub-Simon problem functions in the original definition. That is, if the domain of the sub-Simon problem function is in the higher position in the original definition, the substring is arranged in the higher position; if the domain of the sub-Simon problem function is in the lower position in the original definition, the substring is arranged in the lower position. The string s to be obtained finally is s = S0S1 = 1001.

[0133] As can be seen from this embodiment, even with only a 5-qubit quantum computing module, the original Simon problem can still be solved. In contrast, the existing quantum solution methods in the current art require 7 qubits to solve the problem. As the parameters n and m in the Simon problem function increase, the effect achieved by the method provided by the present invention will be more significant.

[0134] On the other hand, the invention provides a distributed quantum computing device for the Simon problem. Refer to Figure 6 , Figure 6 is a schematic block diagram of a distributed quantum computing device for the Simon problem according to an embodiment of the present invention. In this embodiment, the distributed quantum computing device (hereinafter referred to as the solving device) 10 for the Simon problem includes a parameter acquisition module 1, a sub-Simon problem function construction module 2, a quantum circuit construction module 3, an operation module 4, and a calculation module 5. Among them, the parameter acquisition module 1 is configured to acquire the Simon problem function to be solved, the number of computing nodes, and the number of domain qubits of each computing node. The Simon problem function to be solved is: f: {0, 1} n →{0, 1} m , where n is the number of binary bits in the original domain, m is the number of binary bits in the original range, m ≥ n - 1, and it satisfies that for all independent variable values x, y ∈ {0, 1} n , f(x) = f(y) if and only if x = y or s is the string to be obtained, s ∈ {0, 1} n, the sum of the number of domain qubits of all computing nodes is equal to the number of binary bits in the original domain of the Simon problem function to be solved. The sub-Simon problem function construction module 2 is connected to the parameter acquisition module 1 and is configured to construct a sub-Simon problem function corresponding to each computing node based on the number of domain qubits of each computing node and the original domain and range of the Simon problem function to be solved. Among them, when the domains of all sub-Simon problem functions are combined together in a preset combination order, they constitute the original domain of the Simon problem function to be solved. The range of each sub-Simon problem function is a sub-range of the original range of the Simon problem function to be solved, and each sub-Simon problem function has a substring to be solved. The quantum circuit construction module 3 is connected to the sub-Simon problem function construction module 2 and is configured to construct a quantum circuit for solving the sub-Simon problem function corresponding to each computing node. The operation module 4 is configured to send the quantum circuits for solving the sub-Simon problem functions to the corresponding quantum computing modules respectively and receive the measurement results returned by the quantum computing modules. The computing module 5 is connected to the operation module 4 and is configured to calculate the substring to be solved of the corresponding sub-Simon problem function based on the measurement results returned by the quantum computing module running the quantum circuit for solving the sub-Simon problem function; according to the preset combination order of the domain of the sub-Simon problem function in the original domain of the Simon problem function to be solved, combine the corresponding substrings to be solved to obtain the string s to be solved of the Simon problem function to be solved.

[0135] See Figure 7 , Figure 7 FIG. is a schematic block diagram of a distributed quantum computing device for the Simon problem according to another embodiment of the present invention. The solving device 10 in this embodiment further includes a quantum computing module 6. In this embodiment, the parameter acquisition module 1 in the solving device 10 configures the computing nodes and the number of domain qubits of each computing node according to the number of qubits supported by the quantum computing module 6. The operation module 4 sends the quantum circuits for solving in a serial manner to the quantum computing module 6 in sequence. The quantum computing module 6 runs the quantum circuits for solving in sequence and sends the measurement results to the operation module 4. The operation module 4 sends the received measurement results to the computing module 5. The computing module 5 constructs an equation set based on the received measurement results, solves the equation set to obtain the corresponding substring, and then combines the substrings corresponding to all sub-Simon problem functions to obtain the string of the Simon problem function to be solved. According to this embodiment, a Simon problem that previously required a large number of qubits can be solved by a quantum computing module 6 with a relatively small number of qubits.

[0136] See Figure 8 , Figure 8It is a block diagram of the principle of a distributed quantum computing device for Simon's problem according to another embodiment of the present invention. The solving device 10 in this embodiment further includes a plurality of quantum computing modules, such as the first quantum computing module 71, the second quantum computing module 72, up to the t-th quantum computing module 7t in the figure. The operation module 4 is respectively connected to each quantum computing module. In one embodiment, the parameter acquisition module 1 in the solving device 10 configures the computing nodes and the number of domain qubits of each computing node according to the number of qubits supported by each quantum computing module. The operation module 4 sequentially sends the solving quantum circuit in parallel to the corresponding quantum computing module. Each quantum computing module runs the corresponding solving quantum circuit and sends the measured result to the operation module 4. The operation module 4 sends the received measured result to the computing module 5. The computing module 5 calculates to obtain the string of the function of the Simon's problem to be solved. In this embodiment, multiple quantum computing modules run their respective solving quantum circuits in parallel, effectively improving the solving efficiency. Of course, if it is impossible to complete the solution at one time based on the resources of the current multiple quantum computing modules, one or more of the quantum computing modules can also be used to run the solving quantum circuits of multiple sub-Simon's problem functions in a serial manner to complete the solution in Simon's problem.

[0137] Among them, Figure 7 and Figure 8 the solving device 10 in can be implemented by a classical computing device, and the quantum computing module can be a quantum simulator implemented by a classical computing device or a real quantum machine.

[0138] On the other hand, the embodiment of the present invention further provides an electronic device. Refer to Figure 9 , Figure 9 which is a block diagram of the structural principle of an electronic device according to an embodiment of the present invention. As shown in Figure 9 , the electronic device includes a processor and a memory. Computer instructions are stored in the memory. When the processor runs the computer instructions, it executes the distributed quantum computing method for Simon's problem provided by the present invention.

[0139] Specifically, the processor 601 may include a central processing unit (CPU) or a graphics processing unit (GPU), or an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present invention. The memory 602 may include a memory for data or instructions. For example, the memory 602 may be at least one of the following: a hard disk drive (HDD), a read only memory (ROM), a random access memory (RAM), a floppy disk drive, a flash memory, an optical disk, a magneto-optical disk, a magnetic tape, a universal serial bus (USB) drive, or other physical / tangible memory storage devices. Also, the memory 602 includes removable or non-removable (or fixed) media. Further, the memory 602 may be inside or outside the integrated gateway disaster recovery device. The memory 602 may be a non-volatile solid state memory. In other words, generally, the memory 602 includes a tangible (non-transitory) computer-readable storage medium (such as a memory device) encoded with executable instructions, and when the executable instructions stored therein are executed by the processor 601 (such as by one or more processors), the distributed quantum computing method for Simon's problem in the embodiments of the present invention can be implemented.

[0140] In one example, Figure 9 The illustrated electronic device may further include a communication interface 603 and a bus 610. Among them, the processor 601, the memory 602, and the communication interface 603 are connected through the bus 610 to complete the communication with each other. The communication interface 603 is mainly used to implement the communication between the various modules, devices, units, and / or devices in the electronic device.

[0141] The bus 610 includes hardware, software, or both, and can couple the components of the online data flow charging device to each other. For example, the bus may include at least one of the following: an accelerated graphics port (AGP) or other graphics buses, an enhanced industry standard architecture (EISA) bus, a front side bus (FSB), a hypertransport (HT) interconnect, an industry standard architecture (ISA) bus, an infinite bandwidth interconnect, a low pin count (LPC) bus, a memory bus, a microchannel architecture (MCA) bus, a peripheral component interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a serial advanced technology attachment (SATA) bus, a video electronics standards association local (VLB) bus, or other suitable buses. The bus 610 may include one or more buses. Although the embodiments of the present invention describe or illustrate specific buses, the embodiments of the present invention may contemplate any suitable bus or interconnect method.

[0142] On the other hand, an embodiment of the present invention further provides a computer-readable storage medium, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the foregoing distributed quantum computing method for the Simon problem is implemented. The computer-readable storage medium is, for example, a classical computer-readable storage medium, such as a read-only memory (ROM), a random access memory (RAM), a disk storage medium device, an optical storage medium device, a flash memory device, an electrical, optical, or other physical / tangible memory storage device. It can also be a storage medium for storing quantum information and readable by a quantum computer, such as a quantum random access memory (QRAM). QRAM can be regarded as the quantum version of RAM in a classical computer. Through QRAM, a quantum superposition state of information can be created. Compared with RAM that needs to read one by one, data in superposition can be read at superposed addresses. QRAM can be implemented in physical ways such as optics, semiconductor quantum dots, superconducting circuits, ion traps, etc.

[0143] The flowcharts and / or block diagrams of the methods and systems of the embodiments of the present invention are described above by way of example, and the relevant aspects are also described. It should be understood that each block in the flowchart and / or block diagram, or a combination thereof, can be implemented by computer program instructions, or by dedicated hardware that performs a specified function or action, or by a combination of dedicated hardware and computer instructions. When implemented in hardware, it can be, for example, an electronic circuit, an application-specific integrated circuit (ASIC), appropriate firmware, a plug-in, a functional card, etc.; when implemented in software, it is a program or a code segment used to perform the required task. The program or code segment can be stored in a memory, or transmitted through a data signal carried in a carrier wave on a transmission medium or a communication link. The code segment can be downloaded via a computer network such as the Internet, an intranet, etc.

[0144] The above embodiments are only for illustrating the present invention and are not intended to limit the present invention. Those of ordinary skill in the relevant art can make various changes and modifications without departing from the scope of the present invention. Therefore, all equivalent technical solutions should also fall within the scope of the disclosure of the present invention.

Claims

1. A distributed quantum computing method for Simon's problem, characterized in that, The method includes: Obtaining the Simon problem function to be solved, the number of computing nodes, and the number of domain qubits of each computing node, where the sum of the number of domain qubits of all computing nodes is equal to the number of binary bits of the original domain of the Simon problem function to be solved; Based on the number of domain qubits of each computing node, the original domain and the original range of the Simon problem function to be solved, constructing a sub-Simon problem function corresponding to each computing node, where the original domain of the Simon problem function to be solved includes the domains of all sub-Simon problem functions combined in a preset combination order, the range of each sub-Simon problem function is a sub-range of the original range of the Simon problem function to be solved, and each sub-Simon problem function includes a corresponding substring to be obtained; Constructing a quantum circuit for solving the sub-Simon problem function corresponding to each computing node; Respectively running the quantum circuits for solving the sub-Simon problem functions to obtain the corresponding substrings to be obtained; Combining the corresponding substrings in the preset combination order of the domains of the sub-Simon problem functions in the original domain of the Simon problem function to be solved to obtain the string to be obtained of the Simon problem function to be solved.

2. The distributed quantum computing method for Simon's problem according to claim 1, wherein, The steps of constructing a sub-Simon problem function corresponding to each computing node include: According to the number of domain qubits of the computing node, determining the same number of second bits from the bits of the original domain of the Simon problem function to be solved as the domain bits of the sub-Simon problem function, and the remaining bits as the first bits of the first domain; Sequentially extracting the second bit values from each original independent variable value of the original domain to form each sub-independent variable value of the sub-Simon problem function, and all the sub-independent variable values form the domain of the sub-Simon problem function of the computing node; Sequentially extracting the first bit values from each original independent variable value of the original domain to form each first independent variable value, and all the first independent variable values form the first domain; Combining each sub-independent variable value of the sub-Simon problem function with each first independent variable value in the order of their bits in the original domain to form an original independent variable value in the original domain; Obtaining the original dependent variable value corresponding to the original independent variable value from the original range of the Simon problem function to be solved as the first dependent variable value; Determining one first dependent variable value as the sub-dependent variable value corresponding to the sub-independent variable value according to the same value-taking function from the multiple first dependent variable values corresponding to each sub-independent variable value, where the sub-dependent variable values corresponding to each sub-independent variable value form the range of the sub-Simon problem function of the computing node.

3. The distributed quantum computing method for Simon's problem according to claim 2, wherein The value-taking function is the maximum value function or the minimum value function; correspondingly, determining the numerically largest or smallest first dependent variable value from the multiple first dependent variable values corresponding to each sub-independent variable value as the sub-dependent variable value corresponding to the sub-independent variable value.

4. The distributed quantum computing method for Simon's problem according to claim 2, characterized in that, The steps of constructing a sub-Simon problem function corresponding to each computing node further include: Sort all computing nodes; When determining the same number of second bits as the domain qubits of each computing node from the bits of the original domain of the Simon problem function to be solved as the domain bits of the sub-Simon problem function, according to the sorting of the computing nodes, cut out the second bits with the same number as the domain qubits of each computing node from the bits of the original domain in the order from high to low or from low to high in the bits of the original domain to obtain the domain bits of the sub-Simon problem function corresponding to each computing node.

5. The distributed quantum computing method for Simon's problem according to claim 1, wherein When separately running the quantum circuit for solving the sub-Simon problem function to obtain the corresponding substring to be solved, run the quantum circuit for solving the sub-Simon problem function in a serial and / or parallel manner to solve the corresponding sub-Simon problem function.

6. A distributed quantum computing device for Simon's problem, characterized in that, The device includes: A parameter acquisition module configured to acquire the Simon problem function to be solved, the number of computing nodes, and the number of domain qubits of each computing node, wherein the total number of domain qubits of all computing nodes is equal to the number of binary bits of the original domain of the Simon problem function to be solved; A sub-Simon problem function construction module configured to construct a sub-Simon problem function corresponding to each computing node based on the number of domain qubits of each computing node and the original domain and range of the Simon problem function to be solved, wherein when the domains of all sub-Simon problem functions are combined together in a preset combination order, they form the original domain of the Simon problem function to be solved, the range of each sub-Simon problem function is a sub-range of the original range of the Simon problem function to be solved, and each sub-Simon problem function includes a corresponding substring to be solved; A quantum circuit construction module configured to construct a quantum circuit for solving the sub-Simon problem function corresponding to each computing node; An operation module configured to separately send the quantum circuit for solving the sub-Simon problem function to the corresponding quantum computing module and receive the measurement result returned by the quantum computing module; A calculation module configured to calculate the corresponding substring to be solved of the sub-Simon problem function based on the measurement result returned by the quantum computing module running the quantum circuit for solving the sub-Simon problem function; combine the substrings to be solved according to the preset combination order of the domain of the sub-Simon problem function in the original domain of the Simon problem function to be solved to obtain the string to be solved of the Simon problem function to be solved.

7. The distributed quantum computing device for Simon's problem according to claim 6, wherein, The computing device further includes one or more quantum computing modules; when there is one quantum computing module, the operation module sends multiple quantum circuits for solving the sub-Simon problem function to the quantum computing module in a serial manner, and when there are multiple quantum computing modules, the operation module sends multiple quantum circuits for solving the sub-Simon problem function to the multiple quantum computing modules in a serial and / or parallel manner; Each quantum computing module runs a quantum circuit for solving the sub-Simon problem function corresponding to the computing node, and sends the measurement result to the running module.

8. An electronic device, comprising a processor and a memory, characterized in that, The memory stores computer instructions, and when the processor runs the computer instructions, it executes the distributed quantum computing method for the Simon problem as described in any one of claims 1-5.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions, and when the computer instructions are run by the processor, it executes the distributed quantum computing method for the Simon problem as described in any one of claims 1-5.

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