Quantum system data processing method based on light quantum and light quantum computer
By constructing and adjusting optical quantum circuits, the efficiency and energy consumption limitations of solving ordinary differential equations in existing technologies have been overcome, realizing high-precision optical quantum computing, which is suitable for tasks such as financial forecasting and speech recognition, as well as high-performance computing clusters.
Patent Information
- Application Number
- CN202511700147.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-10
- Publication Date
- 2026-02-13
AI Technical Summary
In existing technologies, numerical methods based on classical computers and traditional quantum computing schemes are difficult to solve ordinary differential equations efficiently and accurately, especially in high-dimensional and large-scale problems, where computational complexity and energy consumption are limited.
By acquiring ordinary differential equations and their property information, an initial optical quantum circuit is constructed, and the target optical quantum circuit is determined through measurement and iterative adjustment for data processing of quantum systems, achieving high-precision solutions.
It enhances the expressive power of optical quantum circuits, reduces the energy consumption of quantum system operations, and enables high-precision solutions to ordinary differential equations in the optical domain, making it suitable for high-speed real-time decision-making tasks and high-performance computing clusters.
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Figure CN121525890A_ABST
Abstract
Description
[0001] This application is a divisional application of the parent application with the filing date of October 10, 2025, the parent application number of 202511439677X, and the invention name of "Quantum system data processing method based on optical quanta and optical quantum computer". TECHNICAL FIELD
[0002] The present application relates to the technical field of quantum computing, in particular to a quantum system data processing method based on optical quanta and an optical quantum computer. BACKGROUND
[0003] Ordinary Differential Equations (ODEs) are a fundamental mathematical tool for describing the dynamic evolution of physical systems, chemical reactions, biological processes, financial models, etc. Efficient and accurate solution of ordinary differential equations is of great significance in scientific research and engineering applications.
[0004] Currently, the existing technology mainly solves ordinary differential equations through numerical methods based on classical computers and schemes based on traditional quantum computing.
[0005] However, both of these processing schemes have fundamental and irreconcilable limitations. SUMMARY
[0006] The purpose of the present application is to provide a quantum system data processing method based on optical quanta and an optical quantum computer to solve the limitations in the prior art.
[0007] To achieve the above purpose, the technical solutions adopted by the embodiments of the present application are as follows: In a first aspect, an embodiment of the present application provides a quantum system data processing method based on optical quanta, comprising: obtaining an ordinary differential equation and attribute information of the ordinary differential equation, the attribute information at least including domain information and boundary conditions; constructing an initial optical quantum circuit corresponding to the ordinary differential equation according to the number of frequency spectra of the ordinary differential equation and the attribute information of the ordinary differential equation, the initial optical quantum circuit at least including a unitary matrix and a phase shifter; measuring the initial optical quantum circuit, and determining a target function corresponding to the initial optical quantum circuit according to the measurement result; determining loss information of the target function, determining whether to apply the initial optical quantum circuit according to the loss information, if yes, taking the initial optical quantum circuit as a target optical quantum circuit, and if no, iteratively adjusting the initial optical quantum circuit according to the loss information, and taking the initial optical quantum circuit at the end of iteration as the target optical quantum circuit; performing operation on input data of a quantum system based on the target optical quantum circuit.
[0008] Optionally, the constructing the initial optical quantum circuit corresponding to the ordinary differential equation according to the spectral quantity of the ordinary differential equation and the attribute information of the ordinary differential equation comprises: determining optical quantum parameters according to the spectral quantity of the ordinary differential equation, the optical quantum parameters at least comprising: waveguide number, phase shifter number and photon number; constructing the optical quantum circuit according to the optical quantum parameters, the attribute information of the ordinary differential equation and a preset optical quantum circuit architecture.
[0009] Optionally, the determining the optical quantum parameters according to the spectral quantity of the ordinary differential equation comprises: obtaining preset photon number preference information; determining the optical quantum parameters according to the spectral quantity of the ordinary differential equation and the photon number preference information.
[0010] Optionally, the constructing the optical quantum circuit according to the optical quantum parameters, the attribute information of the ordinary differential equation and a preset optical quantum circuit architecture comprises: configuring an intermediate optical quantum circuit according to the optical quantum parameters and the preset optical quantum circuit architecture; secondarily configuring the intermediate optical quantum circuit according to the attribute information of the ordinary differential equation to obtain the initial optical quantum circuit.
[0011] Optionally, the secondarily configuring the intermediate optical quantum circuit according to the attribute information of the ordinary differential equation to obtain the initial optical quantum circuit comprises: determining input variables of the intermediate optical quantum circuit according to the definition domain information; determining phases of phase shifters in the intermediate optical quantum circuit according to the input variables, and configuring the intermediate optical quantum circuit according to the phases of the phase shifters to obtain the initial optical quantum circuit.
[0012] Optionally, the determining the phases of the phase shifters in the intermediate optical quantum circuit according to the input variables comprises: determining the phases of the phase shifters in the intermediate optical quantum circuit according to the input variables and index information corresponding to the phase shifters in the intermediate optical quantum circuit.
[0013] Optionally, the measuring the initial optical quantum circuit, determining a target function corresponding to the initial optical quantum circuit according to a measurement result, comprises: performing a photon number resolving measurement on the initial optical quantum circuit to obtain a measurement result, the measurement result being used to indicate a multi-photon event probability distribution; performing a weighted summation on the measurement result to obtain the target function corresponding to the initial optical quantum circuit.
[0014] Optionally, the determining loss information of the target function comprises: determining a current solution of the ordinary differential equation according to the target function; determining loss information of the target function according to the current solution.
[0015] Optionally, the determining whether to apply the initial optical quantum circuit according to the loss information comprises: if the loss information is less than a preset loss threshold, determining to apply the initial optical quantum circuit; if the loss information is greater than the preset loss threshold, adjusting a unitary matrix in the initial optical quantum circuit according to the loss information.
[0016] In a second aspect, another embodiment of the present application provides a quantum system data processing apparatus based on optical quantum, the apparatus comprising: an acquisition module configured to acquire an ordinary differential equation and attribute information of the ordinary differential equation, the attribute information at least comprising domain information and boundary conditions; a construction module configured to construct an initial optical quantum circuit corresponding to the ordinary differential equation according to a frequency spectrum number of the ordinary differential equation and the attribute information of the ordinary differential equation, the initial optical quantum circuit at least comprising a unitary matrix and a phase shifter; a determination module configured to measure the initial optical quantum circuit, and determine a target function corresponding to the initial optical quantum circuit according to a measurement result; the determination module is further configured to determine loss information of the target function, determine whether to apply the initial optical quantum circuit according to the loss information, if yes, use the initial optical quantum circuit as a target optical quantum circuit, and if no, iteratively adjust the initial optical quantum circuit according to the loss information, and use the initial optical quantum circuit at the end of iteration as the target optical quantum circuit; an operation module configured to perform operation on input data of a quantum system based on the target optical quantum circuit.
[0017] Optionally, the construction module is specifically configured to: determine a photonic parameter according to the spectrum number of the ordinary differential equation, the photonic parameter at least comprising a waveguide number, a phase shifter number and a photon number; construct the photonic quantum circuit according to the photonic quantum parameter, attribute information of the ordinary differential equation and a preset photonic quantum circuit architecture.
[0018] Optionally, the constructing module is specifically used for: obtaining preset photon number preference information; determining a photonic quantum parameter according to the spectrum number of the ordinary differential equation and the photon number preference information.
[0019] Optionally, the constructing module is specifically used for: configuring an intermediate photonic quantum circuit according to the photonic quantum parameter and a preset photonic quantum circuit architecture; secondarily configuring the intermediate photonic quantum circuit according to attribute information of the ordinary differential equation to obtain the initial photonic quantum circuit.
[0020] Optionally, the constructing module is specifically used for: determining an input variable of the intermediate photonic quantum circuit according to the definition domain information; determining a phase of a phase shifter in the intermediate photonic quantum circuit according to the input variable, and configuring the intermediate photonic quantum circuit according to the phase of the phase shifter to obtain the initial photonic quantum circuit.
[0021] Optionally, the constructing module is specifically used for: determining a phase of a phase shifter in the intermediate photonic quantum circuit according to the input variable and index information corresponding to the phase shifter in the intermediate photonic quantum circuit.
[0022] Optionally, the determining module is specifically used for: performing photon number resolution measurement on the initial photonic quantum circuit to obtain a measurement result, the measurement result being used to indicate a multi-photon event probability distribution; performing weighted summation on the measurement result to calculate a target function corresponding to the initial photonic quantum circuit.
[0023] Optionally, the determining module is specifically used for: determining a current solution of the ordinary differential equation according to the target function; determining loss information of the target function according to the current solution.
[0024] Optionally, the determining module is specifically used for: if the loss information is less than a preset loss threshold, determining to apply the initial photonic quantum circuit; If the loss information is greater than a preset loss threshold, a unitary matrix in the initial optical quantum circuit is adjusted according to the loss information.
[0025] In a third aspect, another embodiment of the present application provides an optical quantum computer, comprising the target optical quantum circuit of any one of the first aspect.
[0026] In a fourth aspect, another embodiment of the present application provides an electronic device, comprising a processor, a storage medium and a bus, the storage medium storing machine readable instructions executable by the processor, when the electronic device is running, the processor and the storage medium communicate through the bus, and the processor executes the machine readable instructions to perform the steps of the method of any one of the first aspect.
[0027] In a fifth aspect, another embodiment of the present application provides a computer readable storage medium, the computer readable storage medium storing a computer program, when the computer program is run by a processor, performing the steps of the method of any one of the first aspect.
[0028] The beneficial effects of the present application are: by obtaining the ordinary differential equation of the quantum system and the attribute information, and constructing the initial optical quantum circuit according to the number of frequency spectrum of the ordinary differential equation and the attribute information, and measuring the initial optical quantum circuit, the target function can be determined according to the measurement result, and the target optical quantum circuit is obtained according to the loss information of the target function, so that the input data of the quantum system can be operated based on the target optical quantum circuit, not only the target optical quantum circuit corresponding to the ordinary differential equation of any complexity can be obtained equivalently and deterministically, the expression ability of the optical quantum circuit is improved, but also the operation of the input data of the quantum system in the optical domain is completed, the energy consumption in the operation process of the quantum system is reduced, that is, the expression ability of the optical quantum circuit is greatly improved, and high-precision solution of the ordinary differential equation is realized.
[0029] And in the case of a photon number resolving detector, the more the number of photons, the more the Fourier coefficients that can be fitted, the more the frequency spectrum, so that the present application can maximize the use of the original Fourier series expression ability of the optical quantum, and accurately express the solution of the ordinary differential equation through the combination of high, medium and low frequency terms.
[0030] In addition, the target optical quantum circuit obtained by the present application also has the advantages of smaller required quantum circuit complexity and no need for the participation of nonlinear optical devices, which can significantly improve the usability, practicality and value of quantum hardware in practical applications in the current development stage of noisy and medium-scale quantum computing.
[0031] Meanwhile, due to the photon property of the target optical quantum circuit, the obtained target optical quantum circuit can also be applied to any time series task requiring high-speed real-time decision, such as speech recognition, financial prediction, etc. In addition, the present application can also be applied to a high-performance optical quantum computing cluster in parallel or distributed, and deployed to the fields of financial processing, logistics manufacturing, and artificial intelligence through super-fusion and other ways. BRIEF DESCRIPTION OF DRAWINGS
[0032] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.
[0033] Figure 1 A flowchart of a quantum system data processing method based on light quantum provided by an embodiment of the present application; Figure 2 A flowchart of constructing an initial optical quantum circuit corresponding to an ordinary differential equation in a quantum system data processing method based on light quantum provided by an embodiment of the present application; Figure 3 A flowchart of determining an optical quantum parameter in a quantum system data processing method based on light quantum provided by an embodiment of the present application; Figure 4 A flowchart of constructing an optical quantum circuit in a quantum system data processing method based on light quantum provided by an embodiment of the present application; Figure 5 A flowchart of obtaining an initial optical quantum circuit in a quantum system data processing method based on light quantum provided by an embodiment of the present application; Figure 6 A flowchart of determining a target function corresponding to an initial optical quantum circuit in a quantum system data processing method based on light quantum provided by an embodiment of the present application; Figure 7 A flowchart of determining loss information of a target function in a quantum system data processing method based on light quantum provided by an embodiment of the present application; Figure 8 A flowchart of determining whether to apply an initial optical quantum circuit in a quantum system data processing method based on light quantum provided by an embodiment of the present application; Figure 9 A schematic diagram of a quantum system data processing device based on light quantum provided by an embodiment of the present application; Figure 10 An electronic device structure schematic diagram provided by an embodiment of the present application. DETAILED DESCRIPTION
[0034] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. It should be understood that the drawings in the present application only serve the purpose of description and illustration, and are not used to limit the scope of protection of the present application. In addition, it should be understood that the schematic drawings are not drawn according to the actual proportions. The flowcharts used in the present application show the operations implemented according to some embodiments of the present application. It should be understood that the operations of the flowcharts can not be implemented in sequence, and the steps without logical context relationship can be reversed in sequence or implemented simultaneously. In addition, one or more other operations can be added to the flowcharts or one or more operations can be removed from the flowcharts by those skilled in the art under the guidance of the content of the present application.
[0035] In addition, the described embodiments are only some of the embodiments of the present application, not all the embodiments. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.
[0036] It should be noted that the term "comprising" will be used in the embodiments of the present application to indicate the presence of the features declared thereafter, but does not exclude the addition of other features.
[0037] At present, the existing technology mainly solves ordinary differential equations through numerical methods based on classical computers and schemes based on traditional quantum computing.
[0038] However, the numerical methods based on classical computers are limited by computational complexity and energy consumption, and it is difficult to efficiently process high-dimensional, rigid and large-scale problems; and the schemes based on traditional digital quantum computing are limited by problem mapping, data I / O bottlenecks and harsh requirements for future hardware, and are difficult to be practically used in the short term. Therefore, both of the two processing schemes have fundamental and difficult to reconcile limitations.
[0039] The embodiment of the present application is based on the above problems, and proposes a quantum system data processing method based on optical quantum. The initial optical quantum circuit is constructed according to the frequency spectrum quantity of the ordinary differential equation and the attribute information, and the initial optical quantum circuit is measured, so that the objective function can be determined according to the measurement result, and the target optical quantum circuit is obtained according to the loss information of the objective function, so that the input data of the quantum system can be operated based on the target optical quantum circuit, the expression ability of the optical quantum circuit can be greatly improved, and the high-precision solution of the ordinary differential equation can be realized.
[0040] It can be understood that by performing the steps of the quantum system data processing method based on optical quantum provided by the embodiment of the present application, the expression mechanism of the ordinary differential equation can be realized at the physical level, so that the low energy consumption characteristics of photonic computing and the general programmable ability of electronic computing can be combined, and high energy efficient computing can be performed on the input data of the quantum system.
[0041] The quantum system data processing method based on optical quantum provided by the embodiment of the present application will be described in detail below in combination with multiple embodiments.
[0042] Figure 1 A flowchart of the quantum system data processing method based on optical quantum provided by the embodiment of the present application is shown in FIG. 1. Figure 1 The execution subject of the method can be any electronic device with processing capability, and the method includes the following steps. S101, obtaining an ordinary differential equation and attribute information of the ordinary differential equation.
[0043] It can be understood that the ordinary differential equation can come from actual problems such as quantum systems or financial scenarios or industrial simulations.
[0044] For example, taking the interest rate prediction and financial product pricing model in the financial field as an example, the interest rate prediction and financial product pricing model can be represented by the ordinary differential equation. Taking the mechanical vibration system in the robot dynamics field as an example, the response of the mass-spring-damping system in the mechanical vibration system can be represented by the ordinary differential equation.
[0045] Optionally, according to different requirements in actual application process, the corresponding ordinary differential equation and the attribute information of the ordinary differential equation are obtained.
[0046] The attribute information at least includes domain information and boundary conditions.
[0047] Specifically, the domain information refers to a value range of an input variable x of the ordinary differential equation, and the domain information can affect effectiveness and convergence of the Fourier expansion and determine how to discretize the input variable x.
[0048] Specifically, the boundary condition is used to limit a value or derivative behavior of the equation solution at some points, and the boundary condition includes an initial condition and a boundary value.
[0049] Optionally, the attribute information further includes a parameter range, a constraint condition, a smoothness requirement, a symmetry requirement, and a periodicity requirement of the solution of the ordinary differential equation.
[0050] S102, constructing an initial optical quantum circuit corresponding to the ordinary differential equation according to the spectrum number of the ordinary differential equation and attribute information of the ordinary differential equation.
[0051] Optionally, after obtaining the ordinary differential equation, the spectrum number of the ordinary differential equation can be determined, and the initial optical quantum circuit corresponding to the ordinary differential equation is constructed according to the spectrum number and attribute information of the ordinary differential equation.
[0052] The spectrum number refers to a number of independent frequency components contained after the ordinary differential equation is expanded by a Fourier series in a domain thereof.
[0053] Exemplarily, the spectrum number can be obtained after the ordinary differential equation is subjected to Fourier transform.
[0054] Exemplarily, the complexity of the initial optical quantum circuit can be determined according to the spectrum number of the ordinary differential equation, and the modulation range of the initial optical quantum circuit can be determined according to the attribute information of the ordinary differential equation, so as to construct the initial optical quantum circuit corresponding to the ordinary differential equation.
[0055] The initial optical quantum circuit, as a physical implementation of the ordinary differential equation, is a programmable photonic path network composed of multiple optical elements, and is used for controllable linear transformation and interference operation on an input photon state, so as to implement a quantum information processing task. The initial optical quantum circuit at least includes a unitary matrix and a phase shifter.
[0056] Exemplarily, the initial optical quantum circuit can be implemented based on a unitary matrix-phase shifter-unitary matrix architecture, and can implement an arbitrary multimode unitary transformation. The initial optical quantum circuit is used for controllable linear transformation and interference operation on the input photon state, and finally obtains a function expression about the input variable x through measurement of a photon number distribution at an output end.
[0057] The input photon state can be a Fock state, which specifically refers to an eigenstate describing a light field state with a certain number of photons. The Fock state is marked by a photon number, and represents a quantum state with a specific number of photons in a light field.
[0058] The unitary matrix represents the interference behavior of photons propagating between multiple waveguides. It can be implemented by a cascaded structure of beam splitters and phase shifters. Specifically, it can be obtained by mapping a linear interference network consisting of a series of beam splitters and phase shifters, for example, a combination of a series of 2×2 beam splitters and phase shifters. The parameters of the unitary matrix (e.g., beam splitter angles, phase shifter phases) can be optimized using gradient descent. The phase shifter is used to control the photon phase.
[0059] S103. Measure the initial photonic quantum circuit and determine the objective function corresponding to the initial photonic quantum circuit based on the measurement results.
[0060] Optionally, the initial quantum circuit can be evolved, and the output of the initial quantum circuit can be measured with photon number resolution to obtain the measurement results, thereby constructing the objective function corresponding to the initial quantum circuit based on the measurement results.
[0061] The measurement result can be the output probability distribution of the initial photonic quantum circuit, which is essentially a Fourier series expansion of the input phase.
[0062] The objective function corresponding to the initial quantum circuit refers to the function obtained by the initial quantum circuit through quantum state evolution and measurement of the input. The objective function can express the initial quantum circuit.
[0063] S104. Determine the loss information of the objective function. Based on the loss information, determine whether to apply the initial quantum circuit. If yes, use the initial quantum circuit as the target quantum circuit. If no, iteratively adjust the initial quantum circuit and use the initial quantum circuit at the end of the iteration as the target quantum circuit.
[0064] Optionally, after obtaining the objective function, the loss information of the objective function can be determined according to the preset loss function, and the initial quantum circuit can be used as the target quantum circuit based on the loss information of the objective function. If so, the initial quantum circuit is used as the target quantum circuit.
[0065] Optionally, if not, the initial quantum circuit is iteratively adjusted based on the loss information, and the objective function and the loss information of the objective function are redefined until the iteration ends. The initial quantum circuit at the end of the iteration is then used as the target quantum circuit.
[0066] The loss information is used to indicate the difference between the objective function and the ordinary differential equation.
[0067] For example, the objective function can be calculated based on a preset loss function and a regularization term to obtain loss information. The preset loss function can be, for example, mean squared error.
[0068] Exemplarily, the unitary matrix and the phase shifter in the initial optical quantum circuit can be adjusted, for example, the parameters of the unitary matrix can be adjusted, or the number of the phase shifters can be adjusted. The number of waveguides and the number of photons in the initial optical quantum circuit can also be adjusted.
[0069] S105, operating the input data of the quantum system based on the target optical quantum circuit.
[0070] Optionally, after obtaining the target optical quantum circuit, the input data of the quantum system can be operated based on the target optical quantum circuit.
[0071] The target optical quantum circuit is a specific physical implementation of the quantum system, that is, the quantum system can be physically instantiated through the target optical quantum circuit, so that the input data of the quantum system can be operated through the target optical quantum circuit.
[0072] Optionally, after obtaining the target optical quantum circuit, the target optical quantum circuit can be used as an optical quantum chip to construct an optical quantum computer.
[0073] In this embodiment, by obtaining the ordinary differential equation and the attribute information of the quantum system, and constructing the initial optical quantum circuit according to the number of frequency spectrum of the ordinary differential equation and the attribute information, and measuring the initial optical quantum circuit, the target function can be determined according to the measurement result, and the target optical quantum circuit can be obtained according to the loss information of the target function, so that the input data of the quantum system can be operated based on the target optical quantum circuit. Not only can the target optical quantum circuit corresponding to the ordinary differential equation of any complexity be determined equivalently and deterministically, but also the expression ability of the optical quantum circuit is improved, and the operation of the input data of the quantum system in the optical domain is completed, thereby reducing the energy consumption in the operation process of the quantum system, that is, the expression ability of the optical quantum circuit is greatly improved, and high-precision solution of the ordinary differential equation is realized.
[0074] Moreover, in the case of a photon number resolving detector, the more the number of photons, the more the Fourier coefficients that can be fitted, and the more the frequency spectrum, so that the present application can maximize the use of the original Fourier series expression ability of the optical quantum, and accurately express the solution of the ordinary differential equation through the combination of high, medium and low frequency terms.
[0075] In addition, the target optical quantum circuit obtained by the present application also has the advantages of smaller required quantum circuit complexity and no need for the participation of nonlinear optical devices, which can significantly improve the usability, practicality and value of quantum hardware in actual application in the current development stage of noisy and medium-scale quantum computing.
[0076] Meanwhile, due to the photon attribute of the target optical quantum circuit, the obtained target optical quantum circuit can also be applied to any time series task requiring high-speed real-time decision, such as speech recognition, financial prediction, etc. In addition, the present application can also be applied to a high-performance optical quantum computing cluster in parallel or distributed, and deployed to the fields of financial processing, logistics manufacturing, and artificial intelligence through super-fusion and other ways.
[0077] As a possible implementation manner, the process of constructing the initial optical quantum circuit corresponding to the ordinary differential equation is exemplarily described below. Figure 2 A flowchart for constructing the initial optical quantum circuit corresponding to the ordinary differential equation in the optical quantum-based quantum system data processing method provided by the embodiment of the present application is shown in Figure 2 According to the spectrum quantity of the ordinary differential equation and the attribute information of the ordinary differential equation, the initial optical quantum circuit corresponding to the ordinary differential equation is constructed in S102, which includes: S201, determining the optical quantum parameter according to the spectrum quantity of the ordinary differential equation.
[0078] It can be understood that the more the spectrum quantity of the ordinary differential equation is, the higher the complexity of the optical quantum circuit is.
[0079] Optionally, the optical quantum parameter can be matched from the preset mapping relationship between the spectrum quantity and the optical quantum parameter according to the spectrum quantity of the ordinary differential equation.
[0080] The optical quantum parameter at least includes the waveguide number, the phase shifter number, and the photon number. The optical quantum parameter can also include the size of the unitary matrix.
[0081] Exemplarily, the waveguide number can be the same as the spectrum quantity, the photon number can be determined according to the spectrum quantity, the photon number*the phase shifter number can be greater than or equal to the spectrum quantity, and the number of phase shifters can be the waveguide number minus 1. For example, when the spectrum quantity is 2, the waveguide number can be 2, the photon number can be 2, the phase shifter number can be 1, and the size of the unitary matrix can be 2*2.
[0082] By determining the optical quantum parameter according to the spectrum quantity of the ordinary differential equation, the expression ability of the obtained target optical quantum circuit can be matched with the complexity of the ordinary differential equation, so as to improve the expression ability of the obtained target optical quantum circuit to the ordinary differential equation.
[0083] S202, constructing the optical quantum circuit according to the optical quantum parameter, the attribute information of the ordinary differential equation, and the preset optical quantum circuit architecture.
[0084] Optionally, the initial optical quantum circuit can be constructed according to the obtained optical quantum parameter, the attribute information of the ordinary differential equation, and the preset optical quantum circuit architecture.
[0085] Exemplarily, a preset optical quantum circuit architecture can be acquired, and the optical quantum circuit architecture is adjusted according to information indicated by the optical quantum parameter and the attribute information of the ordinary differential equation, so as to obtain an initial optical quantum circuit.
[0086] The preset optical quantum circuit architecture is a unitary matrix-phase shifter-unitary matrix architecture.
[0087] By determining the optical quantum parameter according to the spectrum quantity of the ordinary differential equation, the initial optical quantum circuit is constructed according to the optical quantum parameter, the attribute information of the ordinary differential equation and the preset optical quantum circuit architecture, which can improve the construction efficiency and stability of the optical quantum circuit, reduce the training cost and improve the convergence success rate. At the same time, the low energy consumption characteristic of the photonic computing and the general programmable ability of the electronic computing can be fused to realize the high energy efficiency and high precision nonlinear layer processing.
[0088] As a possible implementation manner, Figure 3 FIG. 1 is a flowchart of a method for processing data of a quantum system based on an optical quantum provided by an embodiment of the present application, which shows that the optical quantum parameter is determined according to the spectrum quantity of the ordinary differential equation in S201. Figure 3 The method for processing data of a quantum system based on an optical quantum provided by an embodiment of the present application includes the following steps. S301, acquiring preset photon number preference information.
[0089] Optionally, the preset photon number preference information can be acquired.
[0090] The photon number preference information is used to indicate the expected initial input photon state when the initial optical quantum circuit is constructed. Exemplarily, the photon number preference information can be 2, that is, the expected input photon state is a quantum state containing exactly two photons.
[0091] S302, determining the optical quantum parameter according to the spectrum quantity of the ordinary differential equation and the photon number preference information.
[0092] Optionally, the optical quantum parameter can be determined according to the spectrum information of the ordinary differential equation, the photon number preference information and a preset optical quantum parameter determination rule.
[0093] Exemplarily, the waveguide number can be the same as the spectrum quantity, the photon number can be determined according to the spectrum quantity, and the number of phase shifters can be the waveguide number minus 1. For example, when the spectrum quantity is 2, the waveguide number can be 2, the photon number can be 2, the number of phase shifters can be 1, and the scale of the unitary matrix can be 2*2.
[0094] By determining the optical quantum parameters through the spectral number of the ordinary differential equation and the photon number preference information, the expression capability of the optical quantum circuit can be matched with the complexity of the ordinary differential equation, and the optical quantum resources can be allocated on demand, so that the expression capability of the obtained target optical quantum circuit for the ordinary differential equation is improved on the premise of efficient utilization of the optical quantum resources.
[0095] As a possible implementation manner, Figure 4 A flowchart for constructing an optical quantum circuit in a quantum system data processing method based on optical quantum provided by an embodiment of the present application is shown in FIG. 2. Figure 4 The optical quantum circuit is constructed in S202 according to the optical quantum parameters, the attribute information of the ordinary differential equation and the preset optical quantum circuit architecture, and includes the following steps: S401, according to the optical quantum parameters and the preset optical quantum circuit architecture, an intermediate optical quantum circuit is configured.
[0096] The preset optical quantum circuit architecture can include three layers, the first layer is a unitary matrix, which is composed of a beam splitter and a phase shifter, and is used to construct an arbitrary unitary transformation, the second layer is a phase shifter, which is composed of an adjustable phase shifter, and is used to introduce a controllable relative phase, and the third layer is a unitary matrix, which is composed of a beam splitter and a phase shifter, and is used to adjust the output mode.
[0097] Optionally, the dimension of the initial optical quantum circuit can be determined according to the waveguide number, the number of beam splitters and phase shifters required can be calculated according to the waveguide number, and the parameters of each beam splitter and phase shifter can be configured, so as to obtain the intermediate optical quantum circuit.
[0098] For example, when the waveguide number is 4, the photon number is 2 and the number of phase shifters is 3, the intermediate optical quantum circuit can be obtained by using Clements decomposition on a 2*2 unitary matrix. The first layer of the intermediate optical quantum circuit includes six beam splitters and six phase shifters, the second layer includes three phase shifters, and the third layer includes six beam splitters and six phase shifters.
[0099] S402, the intermediate optical quantum circuit is configured again according to the attribute information of the ordinary differential equation, and an initial optical quantum circuit is obtained.
[0100] Optionally, the input state of the intermediate optical quantum circuit can be encoded according to the attribute information of the ordinary differential equation, so as to realize the secondary configuration of the initial optical quantum circuit and obtain the intermediate optical quantum circuit.
[0101] As a possible implementation manner, Figure 5 A flowchart for obtaining an initial optical quantum circuit in a quantum system data processing method based on optical quantum provided by an embodiment of the present application is shown in FIG. 3. Figure 5As shown, the intermediate optical quantum circuit is configured again according to the attribute information of the ordinary differential equation in S402 to obtain the initial optical quantum circuit, including: S501, determining the input variable of the intermediate optical quantum circuit according to the definition domain information.
[0102] Optionally, the definition domain information can be discretized according to a preset discretization granularity to obtain the input variable of the intermediate optical quantum circuit.
[0103] S502, determining the phase of the phase shifter in the intermediate optical quantum circuit according to the input variable, and configuring the intermediate optical quantum circuit according to the phase of the phase shifter to obtain the initial optical quantum circuit.
[0104] Optionally, the input variable can be mapped to the phase of the phase shifter in the intermediate optical quantum circuit, and the intermediate optical quantum circuit is configured according to the phase of the phase shifter to obtain the initial optical quantum circuit.
[0105] Exemplarily, the input variable can be mapped to the phase of the phase shifter in the intermediate optical quantum circuit in the order of the input variable, and the phase angle of the phase shifter in the intermediate optical quantum circuit is adjusted according to the phase of the phase shifter to obtain the initial optical quantum circuit.
[0106] As a possible implementation manner, the determination of the phase of the phase shifter in the intermediate optical quantum circuit according to the input variable in S502 includes: determining the phase of the phase shifter in the intermediate optical quantum circuit according to the input variable and the index information corresponding to the phase shifter in the intermediate optical quantum circuit.
[0107] Optionally, the phase of the phase shifter in the intermediate optical quantum circuit can be calculated according to the input variable and the index information corresponding to the phase shifter in the intermediate optical quantum circuit.
[0108] Exemplarily, taking the input variable x as an example, assuming that the current phase shifter is the i th phase shifter in the optical quantum circuit, the phase of the i th phase shifter can be calculated as i * x.
[0109] By determining the phase of the phase shifter in the optical quantum circuit through the input variable and the index information corresponding to the phase shifter in the optical quantum circuit, the input variable can be mapped to the parameters of multiple phase shifters, and the parameter of each phase shifter is proportional to its index, so that the influence of the input variable on the initial optical quantum circuit has linear scalability, thereby improving the number of Fourier spectrum, realizing the function expression and optimization capability of the optical quantum circuit.
[0110] The process of constructing the initial optical quantum circuit is exemplarily described above. It can be understood that, after the initial optical quantum circuit is constructed, the initial optical quantum circuit can be measured, and the target function corresponding to the initial optical quantum circuit is determined according to the measurement result, which will be described in detail below.
[0111] As a possible implementation manner, Figure 6 A flowchart for determining the target function corresponding to the initial optical quantum circuit in the quantum system data processing method based on optical quantum provided by the embodiment of the present application is shown in Figure 6 The measurement of the initial optical quantum circuit in S103 and the determination of the target function corresponding to the initial optical quantum circuit according to the measurement result include the following steps. S601, photon number resolving measurement is performed on the initial optical quantum circuit to obtain a measurement result.
[0112] Optionally, the initial optical quantum circuit can be evolved multiple times, and the evolved initial optical quantum circuit can be subjected to photon number resolving measurement. A multi-photon event is obtained after each evolution, and a plurality of multi-photon events obtained by sampling are counted to obtain a measurement result.
[0113] The measurement result is used to indicate the probability distribution of the multi-photon event.
[0114] Exemplarily, a preset input state is input into the initial optical quantum circuit, and the input state is transformed into an output photon state through the evolution of the optical elements in the initial optical quantum circuit.
[0115] Optionally, the output state is subjected to photon number resolving measurement, and the multi-photon events are counted to obtain a measurement result.
[0116] Exemplarily, the plurality of output states are subjected to photon number resolving measurement by the detector, and the sampling is counted to obtain a sampling result. The frequency of each event is calculated according to the sampling result to obtain a measurement result.
[0117] The measurement result can be the probability distribution of the multi-photon event, which can reflect the distribution of the quantum state output by the initial optical quantum circuit in different modes under the current input state.
[0118] S602, the measurement results are weighted and summed to calculate the target function corresponding to the initial optical quantum circuit.
[0119] Optionally, each event in the measurement result is respectively given a preset weight corresponding to the event, and the sum is calculated to obtain the target function corresponding to the initial optical quantum circuit.
[0120] The weighted sum of the measurement result is essentially the Fourier series expansion of the input phase.
[0121] By performing photon number resolving measurement on the initial optical quantum circuit, obtaining a measurement result, and performing weighted summation on the measurement result, a target function corresponding to the initial optical quantum circuit is calculated. The "physical output" of the initial optical quantum circuit can be converted into a "mathematical function" through measurement and statistics, so that the initial optical quantum circuit is no longer a "black box", but a mathematical function with clear input-output mapping, thereby improving the explainability and controllability of the initial optical quantum circuit.
[0122] As a possible implementation manner, Figure 7 A flowchart for determining loss information of a target function in a quantum system data processing method based on optical quantum provided by an embodiment of the present application is shown in FIG. 7. Figure 7 As shown in FIG. 7, the determination of the loss information of the target function in S104 includes: S701, determining a current solution of the ordinary differential equation according to the target function.
[0123] Optionally, after obtaining the target function, the current solution of the ordinary differential equation can be calculated according to the target function and the order of the ordinary differential equation.
[0124] For example, the target function can be differentiated according to the order of the ordinary differential equation, and the result obtained after differentiation is substituted into the ordinary differential equation to obtain the current solution of the ordinary differential equation.
[0125] For example, if the ordinary differential equation is second-order, the target function can be differentiated twice, and the result obtained after differentiation is substituted into the ordinary differential equation to obtain the current solution of the ordinary differential equation.
[0126] S702, determining the loss information of the target function according to the current solution.
[0127] For example, the current solution can be calculated according to the preset loss function and the regularization term to obtain the loss information. The preset loss function can be mean square error, etc.
[0128] As a possible implementation manner, Figure 8 A flowchart for determining whether to apply an initial optical quantum circuit in a quantum system data processing method based on optical quantum provided by an embodiment of the present application is shown in FIG. 8. Figure 8 As shown in FIG. 8, the determination of whether to apply the initial optical quantum circuit according to the loss information in S104 includes: S801, if the loss information is less than a preset loss threshold, it is determined that the initial optical quantum circuit is applied.
[0129] Optionally, if the loss information is less than the preset loss threshold, it can be determined that the initial optical quantum circuit is applied.
[0130] S802. If the loss information is greater than the preset loss threshold, then adjust the unitary matrix in the initial photonic quantum circuit according to the loss information.
[0131] Optionally, if the loss information is greater than the preset loss threshold, the unitary matrix in the initial optical quantum circuit can be adjusted according to the loss information through the end-to-end backpropagation algorithm, and S103-S104 can be re-executed.
[0132] Specifically, the parameters of the unitary matrix in the initial quantum circuit can be updated based on the loss information, thereby enabling the objective function to better approximate the nonlinear function.
[0133] For example, the parameters of the unitary matrix can be used as trainable variables. Based on the loss information, the gradient of the loss information with respect to the parameters of the unitary matrix can be calculated through backpropagation. Then, the parameters of the unitary matrix can be updated based on the gradient using optimizers such as Adam and RMSProp.
[0134] By adjusting the unitary matrix in the photonic quantum circuit, the function output by the target photonic quantum circuit can be made to approximate the target function by controlling the photon interference path, thereby realizing the physical expression of the nonlinear function.
[0135] Based on the same inventive concept, this application also provides a quantum system data processing device based on photons, which corresponds to the quantum system data processing method based on photons. Since the principle of the device in this application is similar to the quantum system data processing method based on photons described above, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be described again.
[0136] Reference Figure 9 As shown, Figure 9 This is a schematic diagram of a quantum system data processing device based on photonic quantum, provided for an embodiment of this application. The device includes: an acquisition module 901, a construction module 902, a determination module 903, and a calculation module 904. The acquisition module 901 is used to acquire the ordinary differential equation and its attribute information. The attribute information includes at least the domain information and boundary conditions. The construction module 902 is used to construct the initial optical quantum circuit corresponding to the ordinary differential equation based on the number of spectra of the ordinary differential equation and the attribute information of the ordinary differential equation. The initial optical quantum circuit includes at least: a unitary matrix and a phase shifter. The determination module 903 is used to measure the initial optical quantum circuit and determine the objective function corresponding to the initial optical quantum circuit based on the measurement results; The determining module 903 is further configured to determine loss information of the target function, determine whether to apply the initial optical quantum circuit according to the loss information, if yes, take the initial optical quantum circuit as the target optical quantum circuit, and if no, iteratively adjust the initial optical quantum circuit according to the loss information, and take the initial optical quantum circuit at the end of the iteration as the target optical quantum circuit. The operation module 904 is configured to perform operation on input data of the quantum system based on the target optical quantum circuit.
[0137] Optionally, the constructing module 902 is specifically configured to: determine the optical quantum parameters according to the number of spectra of the ordinary differential equation, the optical quantum parameters at least including a waveguide number, a phase shifter number and a photon number; construct the optical quantum circuit according to the optical quantum parameters, attribute information of the ordinary differential equation and a preset optical quantum circuit architecture.
[0138] Optionally, the constructing module 902 is specifically configured to: obtain preset photon number preference information; determine the optical quantum parameters according to the number of spectra of the ordinary differential equation and the photon number preference information.
[0139] Optionally, the constructing module 902 is specifically configured to: obtain preset photon number preference information; determine the optical quantum parameters according to the number of spectra of the ordinary differential equation and the photon number preference information.
[0140] Optionally, the constructing module 902 is specifically configured to: determine the input variable of the intermediate optical quantum circuit according to the domain information; determine the phase of the phase shifter in the intermediate optical quantum circuit according to the input variable, and configure the intermediate optical quantum circuit according to the phase of the phase shifter to obtain the initial optical quantum circuit.
[0141] Optionally, the constructing module 902 is specifically configured to: determine the phase of the phase shifter in the intermediate optical quantum circuit according to the input variable and index information corresponding to the phase shifter in the intermediate optical quantum circuit.
[0142] Optionally, the determining module 903 is specifically configured to: perform photon number resolution measurement on the initial optical quantum circuit to obtain a measurement result, the measurement result being used to indicate a multi-photon event probability distribution; perform weighted summation on the measurement result to calculate a target function corresponding to the initial optical quantum circuit.
[0143] Optionally, the determining module 903 is specifically configured to: Determine the current solution of the ordinary differential equation based on the objective function; Based on the current solution, determine the loss information of the objective function.
[0144] Optionally, module 903 is specifically used for: If the loss information is less than the preset loss threshold, then the initial optical quantum circuit is determined to be applied; If the loss information is greater than the preset loss threshold, the unitary matrix in the initial photonic quantum circuit is adjusted according to the loss information.
[0145] The processing flow of each module in the device and the interaction flow between each module can be referred to the relevant descriptions in the above method embodiments, and will not be detailed here.
[0146] This application also provides an optical quantum computer, which includes: the aforementioned target optical quantum circuit, a single-photon source, and a photon detector.
[0147] This includes the target photonic quantum circuit, the single-photon source, and the optical connection of the photon detector. The photon detector can be a single-photon detector.
[0148] Among them, optical quantum computers are quantum computing devices that use photons (light particles) as qubits for information processing. Single photon sources generate high-quality single photons as qubit carriers by exciting quantum dots with lasers or by spontaneous parametric downconversion (SPDC).
[0149] The target optical quantum circuit is obtained by executing the steps of the above-mentioned nonlinear data generation and processing method based on optical quantum. Specifically, it is composed of optical components such as optical fiber, waveguide, beam splitter, phase modulator, and mirror to realize optical transmission and interference, information encoding and logic operation (such as Hadamard gate and CNOT gate).
[0150] The single-photon detector measures the final state of a photon (such as the Fock state or path) and outputs the calculation results. For details on the specific processing procedures of an optical quantum computer, please refer to the relevant technical descriptions, which will not be elaborated upon here.
[0151] This application also provides an electronic device, such as... Figure 10 As shown, Figure 10 The schematic diagram of the electronic device structure provided in the embodiments of this application includes: a processor 1001, a memory 1002, and optionally, a bus 1003. The memory 1002 stores machine-readable instructions executable by the processor 1001 (e.g., ...). Figure 9The acquisition module 901, the construction module 902, the determination module 903, and the operation module 904 in the device correspond to the execution instructions and the like, and when the electronic device is running, the processor 1001 and the memory 1002 communicate through the bus 1003, and when the processor 1001 executes the machine readable instructions, the steps of the above-mentioned quantum system data processing method based on light quanta are executed.
[0152] The application further provides a computer readable storage medium, and the computer readable storage medium stores a computer program. When the computer program is run by a processor, the steps of the above-mentioned quantum system data processing method based on light quanta are executed.
[0153] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the above-mentioned system and device can refer to the corresponding process in the method embodiments, and the application will not be described again. In the several embodiments provided in the application, it should be understood that the disclosed system, device and method can be implemented by other ways. The above-mentioned device embodiments are only schematic, for example, the division of the modules is only a logical function division, and in actual implementation, there can be another division way, for example, a plurality of modules or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the shown or discussed mutual units can be indirect coupling or communication connection through some communication interfaces, devices or modules, and can be electrical, mechanical or other forms.
[0154] In addition, each functional unit in each embodiment of the application can be integrated in one processing unit, or each unit can exist physically, or two or more units can be integrated in one unit. If the functions are realized in the form of software function units and sold or used as independent products, they can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the application essentially or the parts that make contributions to the prior art or parts of the technical solutions can be embodied in the form of software products, and the computer software products are stored in a storage medium, including a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in each embodiment of the application. The foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various storage medium that can store program codes.
[0155] The above merely provides the specific implementation of the present application, but the protection scope of the present application is not limited to this. Any person skilled in the art can easily think of the changes or replacements within the technical range disclosed by the present application, which should be covered in the protection scope of the present application.
Claims
1. A data processing method for quantum systems based on photons, characterized in that, include: Obtain the ordinary differential equation and its attribute information, wherein the attribute information includes at least: domain information and boundary conditions; Based on the number of spectra of the ordinary differential equation and the attribute information of the ordinary differential equation, an initial optical quantum circuit corresponding to the ordinary differential equation is constructed. The initial optical quantum circuit includes at least a unitary matrix and a phase shifter. The initial optical quantum circuit is measured, and the objective function corresponding to the initial optical quantum circuit is determined based on the measurement results. Determine the loss information of the objective function, and determine whether to apply the initial quantum circuit based on the loss information. If yes, use the initial quantum circuit as the target quantum circuit; otherwise, iteratively adjust the initial quantum circuit based on the loss information, and use the initial quantum circuit at the end of the iteration as the target quantum circuit. The input data of the quantum system is processed based on the target optical quantum circuit.
2. The quantum system data processing method based on photons according to claim 1, characterized in that, The step of constructing the initial optical quantum circuit corresponding to the ordinary differential equation based on the number of spectra and the attribute information of the ordinary differential equation includes: Based on the number of spectra in the ordinary differential equation, the photon parameters are determined, and the photon parameters include at least: waveguide number, phase shifter number, and photon number; The photonic quantum circuit is constructed based on the photonic quantum parameters, the property information of the ordinary differential equation, and the preset photonic quantum circuit architecture.
3. The quantum system data processing method based on photons according to claim 2, characterized in that, The determination of photonic quantum parameters based on the number of spectra in the ordinary differential equation includes: Obtain preset photon number preference information; The photon parameters are determined based on the number of spectra in the ordinary differential equation and the photon number preference information.
4. The quantum system data processing method based on photons according to claim 2, characterized in that, The step of constructing the quantum circuit based on the quantum parameters, the property information of the ordinary differential equation, and the preset quantum circuit architecture includes: Based on the aforementioned photon parameters and the preset photon circuit architecture, an intermediate photon circuit is configured. Based on the property information of the ordinary differential equation, the intermediate photonic quantum circuit is configured a second time to obtain the initial photonic quantum circuit.
5. The quantum system data processing method based on photons according to claim 4, characterized in that, The step of performing a secondary configuration on the intermediate quantum circuit based on the property information of the ordinary differential equation to obtain the initial quantum circuit includes: Based on the defined domain information, the input variables of the intermediate optical quantum circuit are determined; Based on the input variables, the phase of the phase shifter in the intermediate quantum circuit is determined, and the intermediate quantum circuit is configured according to the phase of the phase shifter to obtain the initial quantum circuit.
6. The quantum system data processing method based on photons according to claim 5, characterized in that, Determining the phase of the phase shifter in the intermediate quantum optical circuit based on the input variables includes: The phase of the phase shifter in the intermediate quantum circuit is determined based on the input variables and the index information corresponding to the phase shifter in the intermediate quantum circuit.
7. The quantum system data processing method based on photons according to claim 1, characterized in that, The step of measuring the initial quantum circuit and determining the target function corresponding to the initial quantum circuit based on the measurement results includes: A photon number-resolved measurement is performed on the initial optical quantum circuit to obtain the measurement result, which is used to indicate the probability distribution of multiphoton events. The objective function corresponding to the initial quantum circuit is calculated by weighted summation of the measurement results.
8. The quantum system data processing method based on photons according to claim 1, characterized in that, The loss information for determining the objective function includes: Based on the objective function, determine the current solution of the ordinary differential equation; Based on the current solution, the loss information of the objective function is determined.
9. The quantum system data processing method based on photons according to claim 1, characterized in that, The step of determining whether to apply the initial quantum circuit based on the loss information includes: If the loss information is less than a preset loss threshold, then the initial optical quantum circuit is determined to be applied; If the loss information is greater than a preset loss threshold, then the unitary matrix in the initial photonic quantum circuit is adjusted according to the loss information.
10. A quantum system data processing device based on photons, characterized in that, The device includes: The acquisition module is used to acquire the ordinary differential equation and the attribute information of the ordinary differential equation, wherein the attribute information includes at least: domain information and boundary conditions; A construction module is used to construct an initial quantum circuit corresponding to the ordinary differential equation based on the number of spectra of the ordinary differential equation and the attribute information of the ordinary differential equation. The initial quantum circuit includes at least a unitary matrix and a phase shifter. The determination module is used to measure the initial optical quantum circuit and determine the target function corresponding to the initial optical quantum circuit based on the measurement results; The determining module is further configured to determine the loss information of the objective function, and determine whether to apply the initial quantum circuit based on the loss information. If yes, the initial quantum circuit is used as the target quantum circuit; if no, the initial quantum circuit is iteratively adjusted based on the loss information, and the initial quantum circuit at the end of the iteration is used as the target quantum circuit. The computation module is used to perform computations on the input data of the quantum system based on the target optical quantum circuit.
11. An optical quantum computer, characterized in that, The optical quantum computer includes: a target optical quantum circuit obtained by performing the method described in any one of claims 1-9.
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