A method for implementing distributed quantum amplitude amplification and related devices

Abstract

The application discloses a kind of method for realizing distributed quantum amplitude amplification and related equipment, method includes: the initial success probability of quantum state is quantified based on target unitary operator, and configuration unitary operator is obtained from target unitary operator based on division parameter;Based on division parameter, Boolean function is split into the subfunction of preset quantity and sequentially distributed to each quantum node;Based on configuration unitary operator, the probability upper limit value of each quantum node is quantified using amplitude estimation;According to probability upper limit value, iteration number is obtained, and according to initial success probability, iteration upper limit is obtained;Based on iteration number, the measurement string corresponding to quantum node is iteratively output by quantum amplitude amplification algorithm, and then target string is verified and determined;Quantum operation result is obtained by summarizing the target string corresponding to all quantum nodes.The application can effectively avoid the dependence of existing distributed quantum computation on quantum communication means such as quantum teleportation, and can be widely applied in the field of data processing.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method and related equipment for realizing distributed quantum amplitude amplification. Background Technology

[0002] Quantum amplitude scaling (QAS) is a generalization of Grover's algorithm and is widely used in quantum algorithms such as quantum search and quantum optimization. Classical QAS methods require preparing a superposition state containing the target state on a single quantum node and amplifying the probability amplitude of the target state through multiple iterations. However, the number of qubits required by this method is positively correlated with the problem size; when dealing with large-scale Boolean functions, the number of qubits required by a single node increases dramatically.

[0003] Currently, quantum computing is in the era of Noisy Medium-Scale Quantum (NISQ). Quantum devices have a limited number of qubits and are constrained by factors such as environmental noise, gate fidelity limitations, and finite coherence time, making it difficult to achieve deep circuits and comprehensive quantum error correction on a single node. Therefore, achieving large-scale quantum amplitude amplification on a single node faces enormous technical challenges.

[0004] Furthermore, distributed quantum computing can solve large-scale problems by combining multiple quantum devices or nodes. However, existing distributed quantum computing methods generally rely on quantum communication methods such as quantum teleportation and nonlocal quantum gates. These methods require establishing quantum entanglement or transmitting quantum states between nodes, which is difficult to implement on practical NISQ devices and incurs high resource costs, thus limiting the scalability and practicality of distributed quantum computing. Summary of the Invention

[0005] The main objective of this invention is to provide a method, apparatus, electronic device, storage medium, and program product for realizing distributed quantum amplitude amplification, aiming to solve at least one problem in the prior art.

[0006] To achieve the above objectives, one aspect of the present invention proposes a method for realizing distributed quantum amplitude amplification, the method comprising: Acquire target data; wherein, the target data includes partitioning parameters, target unitary operators and Boolean functions, the target unitary operators include tensor products of multiple unitary operators, and the Boolean functions are defined on qubits of a preset number of bits; The initial success probability of the quantum state is obtained based on the quantization of the target unitary operator, and the configuration unitary operator is obtained by partitioning the target unitary operator based on the partitioning parameters; Based on the partitioning parameters, the Boolean function is split into a preset number of sub-functions and sequentially assigned to each quantum node; wherein, the sub-functions correspond to the Boolean function by combining the binary representation of the quantum node's index; Based on the configuration unitary operator, the upper probability limit of each quantum node is obtained by amplitude estimation quantization; The number of iterations is obtained by converting the upper probability value, and the upper limit of iterations is obtained by converting the initial success probability. Based on the number of iterations, the measurement string corresponding to the quantum node is output through the quantum amplitude amplification algorithm. The function condition of the measurement string is verified to obtain the verification result. If the verification result is successful, the target string is determined based on the measurement string; otherwise, the iteration count is incremented by 1, and the process is returned to execute the step of outputting the measurement string corresponding to the quantum node based on the iteration count using the quantum amplitude amplification algorithm, until the iteration count is greater than the iteration limit corresponding to the same quantum node. The target strings corresponding to all quantum nodes are summarized to obtain the quantum operation results.

[0007] In some embodiments, obtaining the initial success probability of the quantum state based on the target unitary operator quantization includes the following steps: The target unitary operator is applied to the initial state of a bit with a preset number of bits to obtain the initial success probability of the quantum state; The initial success probability is represented by the probability of satisfying the function condition verification obtained by direct measurement.

[0008] In some embodiments, the configuration unitary operator is obtained from the target unitary operator based on the partitioning parameters, including the following steps: Select the unitary operators in the target unitary operators whose dimension is equal to the partitioning parameter as candidate unitary operators; The configured unitary operator is obtained by the tensor product of all unitary operators after the candidate unitary operator in the target unitary operator; If the candidate unit operator in the target unit operator is followed by only one unit operator, then that unit operator is used as the configuration unit operator.

[0009] In some embodiments, based on partitioning parameters, the Boolean function is split into a preset number of sub-functions and sequentially assigned to each quantum node, including the following steps: The division parameter is used as an exponent, and the preset quantity is obtained by exponentiation of 2; A mapping relationship is constructed based on the qubits of the first partition parameter bits in the Boolean function and the binary representation of the sequence number of each quantum node; Based on the mapping relationship, the Boolean function is split into a preset number of sub-functions, and then each sub-function is assigned to a quantum node with a corresponding index.

[0010] In some embodiments, based on the configuration unitary operator, the upper probability limit of each quantum node is obtained by amplitude estimation quantization, including the following steps: The configured bit depth is determined based on the difference between the preset bit depth and the partitioning parameters; The initial state of configuration is prepared based on the initial state of the bit with the configuration unitary operator and the configuration bit length; Based on the initial configuration state, the probability estimate of each quantum node is obtained through amplitude estimation operation; Using the number of qubits used in amplitude estimation as an exponent, the first value is obtained by exponentiation by 2, and the second value is obtained by exponentiation by 2. The third value is obtained by comparing the ratio of pi to the first value, and the fourth value is obtained by comparing the square of pi to the second value. The upper limit of probability is obtained by summing the probability estimate, the third value, and the fourth value.

[0011] In some embodiments, the number of iterations is obtained by converting the upper limit of probability, and the upper limit of iterations is obtained by converting the initial success probability, including the following steps: Using pi as the numerator, the square root of the upper probability limit combined with the arcsine function as the denominator, the number of iterations is obtained by rounding down. Using pi as the numerator and the square root of the initial success probability combined with the arcsine function as the denominator, the upper limit of the iteration is obtained by rounding down.

[0012] In some embodiments, the measurement string is subjected to function condition verification to obtain the verification result, including the following steps: The candidate string is obtained by combining the binary representation of the quantum node number corresponding to the measurement string with the measurement string; The candidate string is used as the input to a Boolean function. If the output of the Boolean function is 1, the verification result is determined to be successful; otherwise, the verification result is determined to be unsuccessful. The target string represents the candidate string that passed the verification.

[0013] To achieve the above objectives, another aspect of the present invention provides an apparatus for realizing distributed quantum amplitude amplification, the apparatus comprising: The first module is used to acquire target data; the target data includes partitioning parameters, target unitary operators, and Boolean functions. The target unitary operators include the tensor product of multiple unitary operators, and the Boolean functions are defined on qubits of a preset number of bits. The second module is used to obtain the initial success probability of the quantum state based on the quantization of the target unitary operator, and to obtain the configuration unitary operator from the target unitary operator based on the partitioning parameters; The third module is used to split the Boolean function into a preset number of sub-functions based on the partitioning parameters and distribute them sequentially to each quantum node; wherein, the sub-functions correspond to the Boolean function by combining the binary representation of the quantum node's index; The fourth module is used to obtain the upper probability limit of each quantum node based on the configuration unitary operator and the amplitude estimation quantization. The fifth module is used to convert the upper limit of probability into the number of iterations, and to convert the upper limit of iterations into the initial success probability. The sixth module is used to output the measurement string corresponding to the quantum node based on the number of iterations using the quantum amplitude amplification algorithm, to verify the function condition of the measurement string, and to obtain the verification result. The seventh module is used to determine the target string based on the measurement string if the verification result is successful; otherwise, the iteration count is incremented by 1, and the operation of the sixth module is returned until the iteration count is greater than the iteration limit corresponding to the same quantum node. The eighth module is used to summarize the target strings corresponding to all quantum nodes and obtain the quantum operation results.

[0014] To achieve the above objectives, another aspect of the present invention provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the aforementioned method.

[0015] To achieve the above objectives, another aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned method.

[0016] To achieve the above objectives, another aspect of the present invention provides a computer program product, including a computer program that, when executed by a processor, implements the aforementioned method.

[0017] The embodiments of the present invention include at least the following beneficial effects: The present invention provides a method, apparatus, electronic device, storage medium, and program product for realizing distributed quantum amplitude amplification. This solution acquires target data; wherein the target data includes partitioning parameters, a target unitary operator, and a Boolean function. The target unitary operator includes a tensor product of multiple unitary operators, and the Boolean function is defined on a preset number of qubits. The initial success probability of the quantum state is obtained based on quantization of the target unitary operator; a configuration unitary operator is obtained by partitioning the target unitary operator based on the partitioning parameters; based on the partitioning parameters, the Boolean function is split into a preset number of sub-functions and sequentially allocated to each quantum node; wherein the sub-functions are obtained by combining the binary representation of the quantum node's index with the Boolean function. The algorithm involves several steps: First, based on the configuration unitary operator, the upper probability limit of each quantum node is obtained using amplitude estimation quantization. The upper probability limit is then used to calculate the number of iterations, and the initial success probability is used to calculate the upper limit of iterations. Based on the number of iterations, the measurement string corresponding to the quantum node is output using the quantum amplitude amplification algorithm. The measurement string is then subjected to function condition verification to obtain the verification result. If the verification result is successful, the target string is determined based on the measurement string. Otherwise, the iteration count is incremented by 1, and the algorithm returns to execute the step of outputting the measurement string corresponding to the quantum node based on the number of iterations using the quantum amplitude amplification algorithm, until the number of iterations exceeds the upper limit of iterations for the same quantum node. Finally, the target strings corresponding to all quantum nodes are summarized to obtain the quantum operation result. This invention, through the decomposition of unitary operators with tensor product structures and the division of Boolean functions into multiple sub-functions distributed to various quantum nodes, enables distributed quantum amplitude amplification without quantum communication. This effectively avoids the dependence of existing distributed quantum computing on quantum communication methods such as quantum teleportation. Specifically, by decomposing the large-scale quantum amplitude amplification problem into multiple smaller sub-problems processed in parallel by each node, this invention effectively reduces the number of qubits required per node, thereby enabling larger-scale quantum amplitude amplification. Furthermore, this invention utilizes quantum amplitude estimation techniques to address the issue of unknown initial success probabilities at each node after sub-function division, ensuring the correct operation of the amplitude amplification algorithm on each node. Simultaneously, by having each node independently output solutions that meet the conditions, this method has the potential to output multiple target strings compared to centralized methods, effectively improving the algorithm's computational power. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of an implementation environment for a method of realizing distributed quantum amplitude amplification provided in an embodiment of the present invention; Figure 2 This is a flowchart illustrating the method for achieving distributed quantum amplitude amplification provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the overall architecture of the method for realizing distributed quantum amplitude amplification provided in the embodiments of the present invention; Figure 4 This is a schematic diagram illustrating the process architecture of the method for achieving distributed quantum amplitude amplification provided in this embodiment of the invention. Figure 5 This is a schematic diagram of the structure of the device for realizing distributed quantum amplitude amplification provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the embodiments of this invention; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this invention as detailed in the appended claims.

[0020] It is understood that the terms "first," "second," etc., used in this invention may be used to describe various concepts, but unless specifically stated otherwise, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, without departing from the scope of embodiments of this invention, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the words "if" or "when" as used herein may be interpreted as "when," "in response to determination," or "in the event of a determination."

[0021] The terms “at least one,” “multiple,” “each,” “any,” etc., used in this invention, “at least one” includes one, two, or more than two; “multiple” includes two or more than two; “each” refers to each of the corresponding multiple; and “any” refers to any one of the multiple.

[0022] Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used in this invention is for descriptive purposes only and is not intended to limit the invention.

[0023] To facilitate understanding of the technical content of the present invention, the meanings of the terms related to the technical features that may be involved in the present invention will be explained first: Distributed quantum computing: Distributed quantum computing can solve a large-scale problem by combining multiple quantum devices or nodes.

[0024] Quantum amplitude amplification: This is a generalization of Grover's algorithm, used to increase the probability of obtaining a certain ground state from a given quantum state. Therefore, it is an important component of many quantum algorithms.

[0025] Quantum amplitude estimation: used to estimate the probability amplitude of a portion of the ground states in a given quantum state.

[0026] NISQ (Noisy Intermediate-scale Quantum): The number of qubits reaches tens to hundreds (or even more), but noise, gate fidelity limitations, and finite coherence time make it difficult to perform deep circuits and full quantum error correction. Therefore, in the NISQ era, it was impossible to implement large-scale deep circuit quantum algorithms on a single node.

[0027] Boolean function: A function whose domain is a set of Boolean variables and whose range is Boolean values. The most common form is... The input is an n-bit binary string, and the output is 0 or 1.

[0028] Quantum circuits are a type of gate model used to describe quantum computing processes. They represent quantum algorithms as an ordered combination of several qubits (a series of quantum gates (unitary operators) applied to them), and project the quantum state into classical bit outputs through measurement at the end (or in the middle).

[0029] In related technologies, how to achieve large-scale quantum amplitude amplification using a distributed architecture without relying on quantum communication, and reduce the number of qubits required for a single node, is a technical problem that urgently needs to be solved in this field.

[0030] In view of this, this invention provides a method and related device for realizing distributed quantum amplitude amplification. This method involves acquiring target data, which includes partitioning parameters, a target unitary operator, and a Boolean function. The target unitary operator comprises a tensor product of multiple unitary operators, and the Boolean function is defined on a qubit of a predetermined number of bits. The initial success probability of the quantum state is obtained by quantization based on the target unitary operator. A configuration unitary operator is obtained by partitioning the target unitary operator based on the partitioning parameters. Based on the partitioning parameters, the Boolean function is split into a predetermined number of sub-functions and sequentially allocated to each quantum node. The sub-functions correspond to the Boolean function by combining the binary representation of the quantum node's index. Based on the configuration unitary operator... The algorithm first uses amplitude estimation to quantize and obtain the upper probability limit for each quantum node. It then converts this upper probability limit into the number of iterations and the initial success probability into the upper limit of iterations. Based on the number of iterations, it outputs the measurement string corresponding to the quantum node using a quantum amplitude amplification algorithm. The measurement string is then subjected to function condition verification to obtain the verification result. If the verification result is successful, the target string is determined based on the measurement string; otherwise, the iteration count is incremented by 1, and the algorithm returns to execute the step of outputting the measurement string corresponding to the quantum node based on the number of iterations using the quantum amplitude amplification algorithm, until the number of iterations exceeds the upper limit of iterations for the same quantum node. Finally, the target strings corresponding to all quantum nodes are summarized to obtain the quantum operation result. This invention, through the decomposition of unitary operators with tensor product structures and the division of Boolean functions into multiple sub-functions distributed to various quantum nodes, enables distributed quantum amplitude amplification without quantum communication. This effectively avoids the dependence of existing distributed quantum computing on quantum communication methods such as quantum teleportation. Specifically, by decomposing the large-scale quantum amplitude amplification problem into multiple smaller sub-problems processed in parallel by each node, this invention effectively reduces the number of qubits required per node, thereby enabling larger-scale quantum amplitude amplification. Furthermore, this invention utilizes quantum amplitude estimation techniques to address the issue of unknown initial success probabilities at each node after sub-function division, ensuring the correct operation of the amplitude amplification algorithm on each node. Simultaneously, by having each node independently output solutions that meet the conditions, this method has the potential to output multiple target strings compared to centralized methods, effectively improving the algorithm's computational power.

[0031] It is understood that the method for achieving distributed quantum amplitude amplification provided by this invention can be applied to any computer device with data processing and computing capabilities, and this computer device can be various terminals or servers. When the computer device in the embodiment is a server, the server is an independent physical server, or a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN (Content Delivery Network), and big data and artificial intelligence platforms. Optionally, the terminal can be a smartphone, tablet, laptop, or desktop computer, but it is not limited to these.

[0032] like Figure 1 The diagram shown is a schematic representation of an implementation environment provided by an embodiment of the present invention. (Refer to...) Figure 1 The implementation environment includes at least one terminal 102 and a server 101. The terminal 102 and the server 101 can be connected via a network, either wirelessly or via a wired connection, to complete data transmission and exchange.

[0033] Server 101 can be a standalone physical server, a server cluster or distributed system consisting of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN (Content Delivery Network), and big data and artificial intelligence platforms.

[0034] Additionally, server 101 can also be a node server in a blockchain network. Blockchain is a novel application model of computer technologies such as distributed data storage, peer-to-peer transmission, consensus mechanisms, and encryption algorithms.

[0035] Terminal 102 can be a smartphone, tablet computer, laptop computer, desktop computer, smart speaker, smartwatch, etc., but is not limited to these. Terminal 102 and server 101 can be directly or indirectly connected via wired or wireless communication, and this embodiment of the invention does not impose any limitations.

[0036] For example, based on Figure 1 The implementation environment shown in this embodiment of the invention provides a method for realizing distributed quantum amplitude amplification. The following description uses the application of this method for realizing distributed quantum amplitude amplification in server 101 as an example. It can be understood that this method for realizing distributed quantum amplitude amplification can also be applied in terminal 102.

[0037] Reference Figure 2 , Figure 2 This is an optional flowchart of a method for realizing distributed quantum amplitude amplification provided by an embodiment of the present invention. The execution subject of this method for realizing distributed quantum amplitude amplification can be any of the aforementioned computer devices (including servers or terminals). Figure 2 The method may include, but is not limited to, steps S100 to S800.

[0038] Step S100: Obtain target data; The target data includes partitioning parameters, target unitary operators, and Boolean functions. The target unitary operators include the tensor product of multiple unitary operators, and the Boolean functions are defined on qubits of a predetermined number of bits. For example, in some specific embodiments, the input of the present invention includes a given Boolean function. , This indicates the number of input variables for the function. Represents all lengths Given a set of binary strings (each component is either 0 or 1), and a measurement-free algorithm... (This can be considered a You operator), regarding the You operator It is required that it can be composed of two or more unitary operator tensors, i.e. Furthermore, the partitioning parameters can be configured according to actual needs.

[0039] Step S200: Obtain the initial success probability of the quantum state based on the target unitary operator quantization, and obtain the configuration unitary operator from the target unitary operator based on the partitioning parameters; It should be noted that, in some embodiments, obtaining the initial success probability of a quantum state based on the quantization of the target unitary operator may include the following steps: applying the target unitary operator to the initial state of a bit with a preset number of bits to obtain the initial success probability of the quantum state; wherein, the initial success probability represents the probability of satisfying the function condition verification obtained by direct measurement.

[0040] For example, in some specific embodiments, since given Therefore, it can be used to (Bit initial state, The initial success probability of obtaining a quantum state after (referring to the number of qubits) (i.e., the probability that direct measurement can satisfy the condition) The probability of the target string).

[0041] It should be noted that, in some embodiments, obtaining the configuration unitary operator from the target unitary operator based on the partitioning parameters may include the following steps: taking the unitary operators in the target unitary operator whose dimension is equal to the partitioning parameters as candidate unitary operators; obtaining the configuration unitary operator based on the tensor product of all unitary operators after the candidate unitary operators in the target unitary operator; wherein, if there is only one unitary operator after the candidate unitary operator in the target unitary operator, that unitary operator is taken as the configuration unitary operator.

[0042] For example, in some specific implementations, for , This represents the number of unitary operators in the tensor integral solution (the number of blocks into which the total subbit system is divided). Tensor-sense The Let the dimension of a unitary operator be denoted as . (That is, the operation of the unit of the west) On each quantum bit, That is, the partitioning parameters), with , For example, the unitary operator is configured using... .

[0043] Step S300: Based on the partitioning parameters, the Boolean function is split into a preset number of sub-functions and sequentially assigned to each quantum node; Among them, the sub-function corresponds to the Boolean function by combining the binary representation of the quantum node's index; It should be noted that in some embodiments, step S300 may include the following steps: using the partitioning parameter as an exponent, obtaining a preset number through exponentiation of 2; constructing a mapping relationship between the qubits of the first partitioning parameter bits in the Boolean function and the binary representation of the sequence number of each quantum node; splitting the Boolean function into a preset number of sub-functions based on the mapping relationship, and then assigning each sub-function to the quantum node with the corresponding sequence number.

[0044] For example, in some specific embodiments, the present invention will enter a sub-function partitioning module for a given Boolean function, which is a classic calculation (processing) process, and divide the given Boolean function into m sub-functions in the following way. ,in ( That is, the partitioning parameters):

[0045] in , representing the One quantum node, yes The binary representation of It is handed over to the first Sub-functions of quantum node operations. In other words, each sub-function Corresponding to the original function For example, given a Boolean function ,pass The function calculated by each node is then, for the centralized approach, the calculated function... ( (0 or 1), corresponding to the sub-function calculated at the 0th node. Given a Boolean function, and processing these m sub-functions in parallel using m quantum devices (m quantum nodes), the state of each node can be directly measured to obtain the desired result. The probability of the string (i.e., the initial success probability of each node). It is an unknown value, where the subscript is... Indicates the position of the first Each node.

[0046] Step S400: Based on the configuration unitary operator, the upper probability limit of each quantum node is obtained by amplitude estimation quantization. It should be noted that in some embodiments, step S400 may include the following steps: determining the number of configured bits based on the difference between the preset number of bits and the partitioning parameter; preparing an initial configuration state based on the initial state of the bits with the configured unitary operator and the number of configured bits; obtaining a probability estimate of each quantum node based on the initial configuration state through amplitude estimation operation; using the number of quantum bits to which amplitude estimation is applied as an exponent, obtaining a first value through a 1x exponentiation operation, and obtaining a second value through a 2x exponentiation operation; obtaining a third value based on the ratio of pi to the first value, and obtaining a fourth value based on the ratio of the square of pi to the second value; and obtaining an upper probability limit value based on the sum of the probability estimate, the third value, and the fourth value.

[0047] For example, in some specific implementations, each node prepares an initial state for amplitude estimation. By applying the quantum amplitude estimation algorithm, using The initial success probability of preparing the initial state for each qubit pair By making an estimate, we can obtain the first... The estimated value of each node Furthermore, according to the quantum amplitude estimation algorithm, it is possible to achieve amplitudes greater than... The probability guarantees the difference between the estimated value and the actual value:

[0048] That is ,in It is the number of qubits used for quantum amplitude estimation.

[0049] Step S500: The number of iterations is obtained by converting the upper limit of probability, and the upper limit of iterations is obtained by converting the initial success probability. It should be noted that in some embodiments, step S500 may include the following steps: using pi as the numerator, combining the square root of the upper probability limit with the arcsine function as the denominator, and obtaining the number of iterations by rounding down; using pi as the numerator, combining the square root of the initial success probability with the arcsine function as the denominator, and obtaining the upper limit of iterations by rounding down.

[0050] For example, in some specific implementations, due to the m nodes and the initial success probability There must be a node whose success probability satisfies Therefore, there is Furthermore, based on the principle of the quantum amplitude amplification algorithm, its iteration count... Compared with the initial success probability The following relationship exists:

[0051] In the formula, Represents the arcsine function. This indicates rounding down to the nearest integer.

[0052] Therefore, based on the above The range can be used to obtain the number of iterations in subsequent quantum amplitude expansion. The range, that is:

[0053] Each node will As The initial value (i.e., the number of initial iterations), and then... As the upper limit of iteration.

[0054] Step S600: Based on the number of iterations, the measurement string corresponding to the quantum node is output through the quantum amplitude amplification algorithm, and the function condition verification is performed on the measurement string to obtain the verification result; It should be noted that in some embodiments, the verification of the measurement string by function conditions to obtain the verification result may include the following steps: combining the binary representation of the quantum node number corresponding to the measurement string with the measurement string to obtain a candidate string; using the candidate string as the input of a Boolean function, if the output result of the Boolean function is 1, the verification result is determined to be passed; otherwise, the verification result is determined to be failed; wherein, the target string represents the candidate string whose verification result is passed.

[0055] For example, in some specific embodiments, an initial state is first prepared. According to the iterative operator of the quantum amplitude amplification algorithm , Characterizing reflection with respect to the all-zero state, Characterization of Boolean functions The physical meaning of the iterative operator for reflecting the marked state (target state) is: First, mark the target state (according to the Boolean function). ), Based on the initial state The reflection (equivalent to the reflection about the initial uniformity in Grover's algorithm) is repeatedly applied. The target state can be gradually amplified (satisfying) The amplitude of ) is used to obtain the solution with high probability; where:

[0056] Then based on the number of iterations After repeatedly applying the iterative operator to the initial state, the final state of the i-th node is... The measurement string is measured and output, and then matched with the index of the quantum node. Combine and verify n-digit strings Does it meet the requirements? If satisfied, then the first Each node will string Output as the target string.

[0057] Step S700: If the verification result is successful, determine the target string based on the measurement string; otherwise, increment the iteration count by 1 and return to execute the step of outputting the measurement string corresponding to the quantum node based on the iteration count using the quantum amplitude amplification algorithm, until the iteration count is greater than the iteration limit corresponding to the same quantum node. For example, in some specific implementations, if the following conditions are met, then the first... Each node will string If the target string is output, otherwise the iteration count is incremented by 1, and the measurement string corresponding to the quantum node is output through the quantum amplitude amplification algorithm in a loop. Then the first... The calculation of each node.

[0058] Step S800: Summarize the target strings corresponding to all quantum nodes to obtain the quantum operation results; For example, in some specific implementations, the target string obtained from all nodes is output to obtain the quantum operation result of the Boolean function.

[0059] To explain in detail the principle of the technical solution of the present invention, the overall process of the present invention will be described below with reference to some specific embodiments. It is easy to understand that the following is an explanation of the technical principle of the present invention and should not be regarded as a limitation of the present invention.

[0060] In view of the related drawbacks of the prior art, the present invention introduces a method for implementing distributed quantum amplitude amplification, which mainly includes four parts: sub-function division, quantum amplitude estimation, quantum amplitude amplification, verification and output. The main inventive point is to achieve a distributed structure through sub-function division and solve the situation where the initial success probability in the process of quantum amplitude amplification after sub-function division is unknown through quantum amplitude estimation. Compared with the existing methods, the present invention can solve the problem of quantum amplitude amplification on a larger scale, and compared with other distributed quantum computing methods, the present invention does not involve quantum communication.

[0061] The present invention is applied to the situation of quantum amplitude amplification with a specific structure. Specifically, it refers to the unitary operator acting on the n-bit initial state which is composed of two or more unitary operators in tensor form, that is, . In addition, the present invention is applied to the process of quantum amplitude amplification where a single node requires n qubits and is implemented through m nodes of n-j qubits, where , generally the value of j is small, so the value of m is also small. In addition, the present invention is also applied to the situation where distributed quantum computing is required between multiple nodes but quantum communication cannot be established. In some specific application scenarios, the technical solution of the present invention can be realized through the following process steps: 1) The input of the present invention includes a given Boolean function , a given non-measurement algorithm (which can be regarded as a unitary operator). For the unitary operator , it is required that it can be composed of two or more unitary operators in tensor form, that is, . For , represents the th unitary operator in the tensor form of , and its dimension is denoted as (that is, this unitary operator acts on qubits). In addition, since is given, the initial success probability of the quantum state obtained after it acts on (the bit initial state), that is, the probability of directly measuring a target string that satisfies is also known; 2) For the sake of simplicity of narration, hereinafter , is taken as an example, which does not affect the coverage of the present invention; 3) The output of the present invention is an n-bit target string, and multiple results may be output; 4) As Figure 3 and Figure 4As shown, this invention, for a given Boolean function, enters the sub-function partitioning module, which is a classic calculation (processing) procedure. The given Boolean function is divided into m sub-functions in the following way. ,in :

[0062] in , representing the One quantum node, yes The binary representation of It is handed over to the first Sub-functions of quantum node operations. In other words, each sub-function Corresponding to the original function For example, given a Boolean function ,pass The function calculated by each node is then, for the centralized approach, the calculated function... This corresponds to the sub-function calculated at node 0. Given a Boolean function, and processing these m sub-functions in parallel using m quantum devices (m quantum nodes), the state of each node can be directly measured to obtain the desired result. The probability of the string (i.e., the initial success probability of each node). It is an unknown value, where the subscript is... Indicates the position of the first One node; 5) Each node prepares an initial state for amplitude estimation. The estimated value of the k-th node can be obtained through amplitude estimation. Furthermore, there will be ,in It is the number of qubits used for quantum amplitude estimation; 6) Furthermore, given the number of m nodes and the initial success probability... There must be a node whose success probability satisfies Therefore, there is Furthermore, based on the principle of the quantum amplitude amplification algorithm, its iteration count... Compared with the initial success probability The following relationship exists:

[0063] Therefore, based on the above The range can be used to obtain the number of iterations in subsequent quantum amplitude expansion. The range, that is:

[0064] 7) Take each node

[0065] 8) Preparation of initial state According to the number of iterations Run the quantum amplitude amplification algorithm to measure and output the string. ; 9) Verify the n-digit string Does it meet the requirements? If satisfied, then the first Each node will string Output the target string as the output; otherwise, increment the iteration count by 1. Then the first... Calculate the number of nodes, otherwise return 8); 10) Output the target string obtained from all nodes; In some alternative implementations, 5)-9) can be replaced by running the following unknown initial success probability quantum amplitude amplification algorithm at each node, which can be implemented as follows: 11-1) Order Take any constant c to satisfy ; 11-2) ,set up ; 11-3) Choose any integer between 1 and M as the iteration number. Preparation of initial state According to the number of iterations Run the quantum amplitude amplification algorithm to measure and output the string. ; 11-4) Verify the n-digit string Does it meet the requirements? If satisfied, then the first Each node will string Output the target string as the output string; otherwise, return to step 11-2. Among these alternative methods, there is a possibility that the original method will keep entering a loop, so an upper limit needs to be set, and the success rate of the method is significantly lower than that of the original method.

[0066] In summary, the method of this invention effectively reduces the number of qubits required for a single node by achieving distributed quantum amplitude amplification. Furthermore, by using sub-function partitioning, the method of this invention circumvents quantum communication while simultaneously achieving distributed quantum computing. Compared to existing technologies, the embodiments of this invention offer at least the following beneficial effects: 1) The partitioning of subfunctions enables distributed quantum computing without quantum communication; 2) Since the m sub-functions are processed by m devices, each device may output the target string. Compared with the centralized amplitude amplification, the method of the present invention has the potential to output multiple target strings. 3) The technical solution of this invention effectively reduces the number of qubits required for a single node by realizing distributed quantum computing; 4) By quantizing the number of iterations, the cyclic iteration of amplitude expansion can be realized, which can effectively solve the problem that the initial success probability of each node after the sub-function is unknown and the amplitude expansion algorithm cannot be directly applied.

[0067] like Figure 5 As shown, this embodiment of the invention also provides a device 900 for realizing distributed quantum amplitude amplification, which can implement the above-described method. This device may include: The first module 901 is used to acquire target data; wherein, the target data includes partitioning parameters, target unitary operators and Boolean functions, the target unitary operators include tensor products of multiple unitary operators, and the Boolean functions are defined on qubits of a preset number of bits; The second module 902 is used to obtain the initial success probability of the quantum state based on the quantization of the target unitary operator, and to obtain the configuration unitary operator from the target unitary operator based on the partitioning parameters; The third module 903 is used to split a Boolean function into a preset number of sub-functions based on partitioning parameters and sequentially distribute them to various quantum nodes; wherein, the sub-functions correspond to the Boolean function by combining the binary representation of the quantum node's index; The fourth module 904 is used to obtain the upper probability limit of each quantum node based on the configuration unitary operator and the amplitude estimation quantization. The fifth module, 905, is used to convert the upper limit of probability into the number of iterations and the upper limit of iterations into the initial success probability. The sixth module, 906, is used to output the measurement string corresponding to the quantum node based on the number of iterations using the quantum amplitude amplification algorithm, perform function condition verification on the measurement string, and obtain the verification result. Module 7, 907, is used to determine the target string based on the measurement string if the verification result is successful; otherwise, the iteration count is incremented by 1, and the operation of Module 6 is returned until the iteration count is greater than the iteration limit corresponding to the same quantum node. Module 8, 908, is used to summarize the target strings corresponding to all quantum nodes and obtain the quantum operation results.

[0068] It is understood that the content of the above method embodiments is applicable to the present device embodiments. The specific functions implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0069] This invention also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method described above. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0070] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0071] like Figure 6 As shown, Figure 6 The hardware structure of an electronic device 1000 according to another embodiment is illustrated. The electronic device 1000 includes: The processor 1001 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (aSIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present invention. The memory 1002 can be implemented as a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RaM). The memory 1002 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 1002 and is called and executed by the processor 1001. Input / output interface 1003 is used to implement information input and output; The communication interface 1004 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.). Bus 1005 transmits information between various components of the device (e.g., processor 1001, memory 1002, input / output interface 1003, and communication interface 1004); The processor 1001, memory 1002, input / output interface 1003 and communication interface 1004 are connected to each other within the device via bus 1005.

[0072] The electronic device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0073] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0074] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0075] This invention also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0076] It is understood that the content of the above method embodiments is applicable to the embodiments of this program product. The specific functions implemented by the embodiments of this program product are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0077] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0078] This invention provides a method, apparatus, electronic device, storage medium, and program product for distributed quantum amplitude amplification. The method involves acquiring target data, which includes partitioning parameters, a target unitary operator, and a Boolean function. The target unitary operator comprises a tensor product of multiple unitary operators, and the Boolean function is defined on a predetermined number of qubits. The method quantizes the target unitary operator to obtain the initial success probability of the quantum state. Based on the partitioning parameters, it partitions the target unitary operator to obtain a configuration unitary operator. Based on the partitioning parameters, it decomposes the Boolean function into a predetermined number of sub-functions and sequentially distributes them to various quantum nodes. The sub-functions correspond to the Boolean function by combining the binary representation of the quantum node's index. Based on the configuration... The unitary operator is used to quantize the probability upper limit of each quantum node using amplitude estimation. The number of iterations is derived from the probability upper limit, and the iteration upper limit is derived from the initial success probability. Based on the number of iterations, the measurement string corresponding to the quantum node is output through the quantum amplitude amplification algorithm. The measurement string is then subjected to function condition verification to obtain the verification result. If the verification result is successful, the target string is determined based on the measurement string. Otherwise, the iteration count is incremented by 1, and the process returns to the step of outputting the measurement string corresponding to the quantum node through the quantum amplitude amplification algorithm based on the number of iterations, until the number of iterations exceeds the iteration upper limit corresponding to the same quantum node. The target strings corresponding to all quantum nodes are then summarized to obtain the quantum operation result. This invention, through the decomposition of unitary operators with tensor product structures and the division of Boolean functions into multiple sub-functions distributed to various quantum nodes, enables distributed quantum amplitude amplification without quantum communication. This effectively avoids the dependence of existing distributed quantum computing on quantum communication methods such as quantum teleportation. Specifically, by decomposing the large-scale quantum amplitude amplification problem into multiple smaller sub-problems processed in parallel by each node, this invention effectively reduces the number of qubits required per node, thereby enabling larger-scale quantum amplitude amplification. Furthermore, this invention utilizes quantum amplitude estimation techniques to address the issue of unknown initial success probabilities at each node after sub-function division, ensuring the correct operation of the amplitude amplification algorithm on each node. Simultaneously, by having each node independently output solutions that meet the conditions, this method has the potential to output multiple target strings compared to centralized methods, effectively improving the algorithm's computational power.

[0079] The embodiments described in this invention are for the purpose of more clearly illustrating the technical solutions of the embodiments of this invention, and do not constitute a limitation on the technical solutions provided by the embodiments of this invention. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this invention are also applicable to similar technical problems.

[0080] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of the present invention, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0081] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0082] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0083] The preferred embodiments of the present invention have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present invention. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and spirit of the present invention should be within the scope of the claims of the present invention.

Claims

1. A method for realizing distributed quantum amplitude amplification, characterized in that, The method includes the following steps: Acquire target data; wherein the target data includes partitioning parameters, a target unitary operator, and a Boolean function, the target unitary operator includes a tensor product of multiple unitary operators, and the Boolean function is defined on a qubit of a preset number of bits; The initial success probability of the quantum state is obtained based on the quantization of the target unitary operator, and the configuration unitary operator is obtained from the target unitary operator based on the partitioning parameters; Based on the partitioning parameters, the Boolean function is split into a preset number of sub-functions and sequentially assigned to each quantum node; wherein, the sub-functions correspond to the Boolean function by combining the binary representation of the quantum node's index; Based on the configured unitary operator, the upper probability limit of each quantum node is obtained by amplitude estimation quantization; The number of iterations is obtained by converting the upper limit of the probability value, and the upper limit of the iterations is obtained by converting the initial success probability. Based on the number of iterations, the measurement string corresponding to the quantum node is output through the quantum amplitude amplification algorithm, and the function condition verification is performed on the measurement string to obtain the verification result. If the verification result is successful, the target string is determined based on the measurement string; otherwise, the iteration count is incremented by 1, and the process returns to the step of outputting the measurement string corresponding to the quantum node based on the iteration count using the quantum amplitude amplification algorithm, until the iteration count is greater than the iteration limit corresponding to the same quantum node. The target strings corresponding to all the quantum nodes are summarized to obtain the quantum operation results.

2. The method according to claim 1, characterized in that, The initial success probability of obtaining the quantum state based on the target unitary operator quantization includes the following steps: The target unitary operator is applied to the initial state of the preset number of bits to obtain the initial success probability of the quantum state; The initial success probability is represented by the probability of satisfying the function condition verification obtained by direct measurement.

3. The method according to claim 1, characterized in that, The process of obtaining the configuration unitary operator from the target unitary operator based on the partitioning parameters includes the following steps: Select the unitary operators in the target unitary operators whose dimension is equal to the partitioning parameter as candidate unitary operators; The configured unitary operator is obtained by the tensor product of all unitary operators following the candidate unitary operator in the target unitary operator; If the candidate unitary operator in the target unitary operator is followed by only one unitary operator, then that unitary operator is used as the configured unitary operator.

4. The method according to claim 1, characterized in that, The step of splitting the Boolean function into a preset number of sub-functions based on the partitioning parameters and sequentially assigning them to each quantum node includes the following steps: The preset quantity is obtained by using the division parameter as an exponent and performing an exponentiation of 2. A mapping relationship is constructed based on the qubits of the partitioning parameter bits in the Boolean function and the binary representation of the sequence number of each quantum node; Based on the mapping relationship, the Boolean function is split into the preset number of sub-functions, and then each sub-function is assigned to the quantum node with the corresponding index.

5. The method according to claim 1, characterized in that, The step of obtaining the upper probability limit of each quantum node based on the configured unitary operator and using amplitude estimation quantization includes the following steps: The configuration bit length is determined based on the difference between the preset bit length and the partitioning parameter; The initial state of configuration is prepared based on the configuration unitary operator and the initial state of the configuration bit size; Based on the initial configuration, the probability estimate of each quantum node is obtained through amplitude estimation calculation; Using the number of qubits used in the amplitude estimation as an exponent, the first value is obtained by exponentiation by 2, and the second value is obtained by exponentiation by 2. The third value is obtained by the ratio of pi to the first value, and the fourth value is obtained by the ratio of the square of pi to the second value. The upper limit of probability is obtained by summing the probability estimate, the third value, and the fourth value.

6. The method according to claim 1, characterized in that, The process of obtaining the number of iterations based on the upper limit of probability and obtaining the upper limit of iterations based on the initial success probability includes the following steps: Using pi as the numerator and the square root of the upper probability limit combined with the arcsine function as the denominator, the number of iterations is obtained by rounding down. Using pi as the numerator and the square root of the initial success probability combined with the arcsine function as the denominator, the upper limit of the iteration is obtained by rounding down.

7. The method according to claim 1, characterized in that, The process of performing function condition verification on the measurement string to obtain the verification result includes the following steps: The binary representation of the sequence number of the quantum node corresponding to the measurement string is combined with the measurement string to obtain a candidate string; The candidate string is used as the input to the Boolean function. If the output of the Boolean function is 1, the verification result is determined to be passed; otherwise, the verification result is determined to be failed. The target string represents the candidate string whose verification result is passed.

8. A device for realizing distributed quantum amplitude amplification, characterized in that, The device includes: The first module is used to acquire target data; wherein, the target data includes partitioning parameters, a target unitary operator, and a Boolean function, the target unitary operator includes a tensor product of multiple unitary operators, and the Boolean function is defined on a qubit of a preset number of bits; The second module is used to obtain the initial success probability of the quantum state based on the target unitary operator quantization, and to obtain the configuration unitary operator from the target unitary operator based on the partitioning parameters; The third module is used to split the Boolean function into a preset number of sub-functions based on the partitioning parameters and sequentially assign them to each quantum node; wherein, the sub-functions correspond to the Boolean function by combining the binary representation of the quantum node's index; The fourth module is used to obtain the upper probability limit of each quantum node based on the configured unitary operator and using amplitude estimation quantization. The fifth module is used to convert the probability upper limit value into the number of iterations and the initial success probability into the upper limit of iterations. The sixth module is used to output the measurement string corresponding to the quantum node based on the number of iterations using the quantum amplitude amplification algorithm, perform function condition verification on the measurement string, and obtain the verification result; The seventh module is used to determine the target string based on the measurement string if the verification result is passed; otherwise, it increments the iteration count by 1 and returns to execute the operation of the sixth module until the iteration count is greater than the iteration limit corresponding to the same quantum node. The eighth module is used to summarize the target strings corresponding to all the quantum nodes to obtain the quantum operation results.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method according to any one of claims 1 to 7.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the method according to any one of claims 1 to 7.

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