WO2023165500A1 - Appareil et procédé de traitement pour tâche de traitement de données, support d'enregistrement et dispositif électronique - Google Patents

Appareil et procédé de traitement pour tâche de traitement de données, support d'enregistrement et dispositif électronique Download PDF

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WO2023165500A1
WO2023165500A1 PCT/CN2023/078928 CN2023078928W WO2023165500A1 WO 2023165500 A1 WO2023165500 A1 WO 2023165500A1 CN 2023078928 W CN2023078928 W CN 2023078928W WO 2023165500 A1 WO2023165500 A1 WO 2023165500A1
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differential equation
quantum
differentiable
predicted
quantum circuit
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PCT/CN2023/078928
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Chinese (zh)
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卢攀攀
李叶
窦猛汉
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本源量子计算科技（合肥）股份有限公司
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Priority claimed from CN202210214969.3A external-priority patent/CN116738128A/zh
Priority claimed from CN202210214967.4A external-priority patent/CN116738127A/zh
Priority claimed from CN202210214645.XA external-priority patent/CN116738125A/zh
Priority claimed from CN202210214966.XA external-priority patent/CN116738126A/zh
Application filed by 本源量子计算科技（合肥）股份有限公司 filed Critical 本源量子计算科技（合肥）股份有限公司
Publication of WO2023165500A1 publication Critical patent/WO2023165500A1/fr

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/13—Differential equations

Definitions

  • the embodiments of this specification relate to the field of data processing, and specifically relate to a processing method, device, storage medium, and electronic device for a data processing task.
  • Quantum computing is a new type of computing. The principle is to construct a computing framework with the theory of quantum mechanics. Compared with the optimal classical algorithm, quantum computing has the effect of exponential speed-up when solving certain problems.
  • Embodiments of this specification provide a data processing task processing method, device, storage medium, and electronic equipment, which are used to reduce resource consumption caused by grid division.
  • An embodiment of this specification provides a processing method for a data processing task, the processing method comprising: acquiring data processing task data; wherein, the data processing task is a task of solving a differential equation; the data processing task data includes The differential equation; constructing a differentiable quantum circuit according to the data processing task data; predicting the target processing result of the data processing task based on the differentiable quantum circuit, and constructing the predicted processing result according to the prediction When the value of the loss function meets the specified accuracy condition, the prediction processing result that makes the value of the loss function meet the specified accuracy condition is taken as the target processing result.
  • predicting the target processing result of the data processing task based on the differentiable quantum circuit includes: predicting the target of the differential equation based on the variational parameters in the differentiable quantum circuit solution to predict.
  • the data processing task data further includes the initial conditions and boundary conditions satisfied by the solution of the differential equation;
  • the step of constructing a differentiable quantum circuit according to the data processing task data includes: The differential equation and the initial conditions and boundary conditions satisfied by the solution of the differential equation construct the differentiable quantum circuit, and determine the variational parameters in the differentiable quantum circuit.
  • constructing the differentiable quantum circuit according to the differential equation and the initial conditions and boundary conditions satisfied by the solution of the differential equation includes: acquiring a group of qubits and The initial state of is set to
  • the step of predicting the target solution of the differential equation based on the variational parameters in the differentiable quantum circuit includes: updating the variational parameters through an optimization algorithm, based on the updated The latter variational parameters predict the target solution of the differential equation.
  • the updating of the variational parameters through an optimization algorithm includes: updating the variational parameters ⁇ through the following formula: Wherein, the n is an integer not less than 1, ⁇ is the learning rate, and L is the loss function, is the gradient of the loss function to ⁇ .
  • the loss function is:
  • the L ⁇ (diff) represents that the predicted solution of the differential equation does not satisfy the error of the differential equation
  • the d x f represents the derivative term in the differential equation
  • the f represents the difference between the differential equation and the differential equation
  • said x represents a variable
  • said L ⁇ (boundary) represents the error that the predicted solution of said differential equation does not satisfy said boundary condition and said initial condition
  • the differential equation is a time-dependent partial differential equation
  • the target processing result of the data processing task is predicted based on the differentiable quantum circuit, and the predicted processing obtained according to the prediction
  • the step of taking the predicted processing result that makes the value of the loss function meet the specified accuracy condition as the target processing result includes: based on the initial variable of the differentiable quantum circuit Predict the target solution of the time-dependent partial differential equation by sub-parameters, until according to If the value of the loss function at the current moment constructed by the prediction processing result obtained by the prediction meets the specified accuracy condition, the predicted solution of the time-dependent partial differential equation that makes the value of the loss function meet the specified accuracy condition is used as The objective solution of the time-dependent partial differential equation.
  • the time-dependent partial differential equation includes:
  • the u(x, t) is the solution of the time-dependent partial differential equation
  • x is a space variable
  • t is a time variable
  • N'[u(x, t)] is a nonlinear term
  • ⁇ is a computational domain
  • T is time.
  • the data processing task data also includes the initial conditions and boundary conditions of the time-dependent partial differential equation; after the step of obtaining the data processing task data, it also includes: A semi-discrete form of the time-dependent partial differential equation is determined.
  • u(x, t+ ⁇ t) u(x, t)+ ⁇ t ⁇ N′[u(x, t+ ⁇ t)], wherein, the u(x, t+ ⁇ t) is the time-dependent partial differential The solution of the equation at time t+ ⁇ t.
  • predicting the target solution of the time-dependent partial differential equation based on the initial variational parameters of the differentiable quantum circuit includes: obtaining a group of qubits and Set the state to
  • the determination of the predicted solution of the time-dependent partial differential equation includes: obtaining a pre-selected measurement operator; determining the expected value corresponding to the measurement operator according to the final quantum state; according to The expected value determines a predicted solution of the time-dependent partial differential equation.
  • the first type of quantum logic gates includes: Rx quantum logic gates, Ry quantum logic gates and Rz quantum logic gates; the second type of quantum logic gates includes: Rx quantum logic gates, Ry quantum logic gates Quantum logic gates, Rz quantum logic gates and CNOT quantum logic gates.
  • the loss function at the current moment constructed according to the prediction processing result obtained from the prediction includes: if the current moment is the initial moment, the loss function at the initial moment is:
  • the N' is the number of discrete points
  • M is the number of boundary points
  • i is the ith discrete point
  • j' is the j'th boundary point
  • g( xi ) is the initial condition
  • h(x j' ,0) is the boundary condition at the initial moment
  • the loss function at ⁇ t time is:
  • the N'[u(x,t)] is determined according to the differentiable quantum circuits at the previous moment.
  • the method further includes: updating the variational parameter ⁇ through the following formula: Wherein, the n is an integer not less than 1, ⁇ is the learning rate, and L is the loss function, is the gradient of the loss function to ⁇ .
  • the method further includes: acquiring the computational domain of the differential equation and dividing the computational domain into several non-overlapping sub-computational domains;
  • the step of constructing a differentiable quantum circuit according to the data processing task data includes: constructing a differentiable quantum circuit corresponding to the sub-computational domain; wherein, one sub-computational domain corresponds to a predicted solution of the differential equation; based on the The differentiable quantum circuit predicts the target processing result of the data processing task, and when the value of the loss function constructed according to the predicted processing result meets the specified accuracy condition, the value of the loss function meets the specified accuracy condition.
  • the step of specifying the predicted processing result of the accuracy condition as the target processing result includes: predicting the target solution of the differential equation based on the differentiable quantum circuit, and then constructing the sub-calculation based on the predicted solution of the differential equation
  • the value of the joint loss function of the domain conforms to the specified precision
  • the predicted solution of the differential equation that makes the value of the loss function meet the specified accuracy condition is taken as the target solution of the differential equation.
  • the differential equation is:
  • the F is a functional function
  • the d x u is a derivative term
  • the u is the solution of the differential equation
  • the x is a variable.
  • predicting the target processing result of the data processing task based on the differentiable quantum circuit includes: the target solution of the differential equation based on the variational parameters in the differentiable quantum circuit Make predictions.
  • the step of constructing a differentiable quantum circuit corresponding to the sub-computational domain includes: obtaining a group of qubits and setting the initial state of the qubits to
  • the step of predicting the target solution of the differential equation based on the variational parameters in the differentiable quantum circuit includes: obtaining a pre-selected measurement operator; The final quantum state corresponding to the variational parameter in the circuit determines the expected value corresponding to the measurement operator; and determines the predicted solution of the differential equation according to the expected value.
  • the first type of quantum logic gates includes: Rx quantum logic gates, Ry quantum logic gates and Rz quantum logic gates; the second type of quantum logic gates includes: Rx quantum logic gates, Ry quantum logic gates Quantum logic gates, Rz quantum logic gates and CNOT quantum logic gates.
  • the joint loss function is:
  • the n is the number of sub-computational domains
  • the nb is the number of interfaces
  • the L i (diff) [d x f i , f i , x] is the differential equation corresponding to the i-th sub-computational domain
  • the error caused by the prediction solution not satisfying the differential equation, the L i (boundary) [f i , x] is the prediction solution of the differential equation corresponding to the i-th sub-calculation domain does not satisfy the solution of the differential equation
  • the L i (interface) [f, x] is the predicted solution of the differential equation corresponding to the adjacent areas on both sides of the i-th interface does not satisfy the continuity condition of the interface and caused by the error and
  • the n i is the number of discrete points on the i-th interface
  • f + (x j ) and f - (x j ) are the predicted solutions of the differential equations corresponding to the sub-calculation
  • the step of predicting the target solution of the differential equation based on the variational parameters in the differentiable quantum circuit includes: using an optimization algorithm to update the variational parameters in the differentiable quantum circuit Parameters; according to the updated variational parameters in the differentiable quantum circuit, an updated predicted solution of the differential equation is obtained.
  • the step of using an optimization algorithm to update the variational parameters in the differentiable quantum circuit includes:
  • the variational parameter ⁇ is updated by the following formula: Wherein, the n is an integer not less than 1, ⁇ is the learning rate, and L is the joint loss function, is the gradient of the joint loss function to ⁇ .
  • the data processing task data further includes the derivative term of the differential equation;
  • the step of constructing a differentiable quantum circuit according to the data processing task data includes: according to the differential equation and the The derivative terms of the differential equation respectively construct the differentiable quantum circuit; predict the target processing result of the data processing task based on the differentiable quantum circuit, and to the loss function constructed according to the predicted processing result obtained by the prediction
  • the step of taking the predicted processing result that makes the value of the loss function meet the specified precision condition as the target processing result includes: the target solution of the differential equation based on the differentiable quantum circuit and
  • the value of the derivative term of the differential equation is predicted to the value of the loss function constructed from the predicted solution of the differential equation and the predicted value of the derivative term of the differential equation will make the loss
  • a predicted solution of the differential equation whose value of the function satisfies the specified accuracy condition is used as a target solution of the differential equation.
  • the differential equation is:
  • the F is a functional function
  • the d x u is the derivative term of the differential equation
  • the u is the predicted solution of the differential equation
  • the x is the variable quantity.
  • the step of respectively constructing the differentiable quantum circuit according to the differential equation and the derivative term of the differential equation includes: respectively constructing the predicted solution for solving the differential equation and the solving the differentiable quantum circuit of the predicted value of the derivative term of the differential equation, and respectively determining the predicted solution of the differential equation and the prediction of the derivative term of the differential equation corresponding to the variational parameters in the differentiable quantum circuit value.
  • said respectively constructing differentiable quantum circuits for solving the predicted solution of the differential equation and for solving the predicted value of the derivative term includes: respectively obtaining a group of qubits and The initial state of the qubit is set to
  • the space basis set is combined into the second sub-quantum circuit module of the predicted solution of the differential equation and the predicted value of the derivative term of the differential equation; respectively constructed for obtaining the predicted solution of the differential equation and the derivative of the differential equation
  • the respectively determining the predicted solution of the differential equation corresponding to the variational parameter in the differentiable quantum circuit and the predicted value of the derivative term of the differential equation includes: obtaining a pre-selected measurement operator; determine the expected value corresponding to the measurement operator according to the final quantum state corresponding to the variational parameter in the differentiable quantum circuit; determine the predicted solution of the differential equation and the derivative of the differential equation according to the expected value item's predicted value.
  • the loss function is:
  • L[f i , f, x] L (diff) [f i , f, x]+L (boundary) [f, x], wherein said f i represents the i-th order derivative in said differential equation item, the L (diff) represents that the predicted solution of the differential equation does not satisfy the error of the differential equation, the f is the differential equation, the x represents a variable, and the L (boundary) represents the differential equation The error in which the predicted solution of the equation does not satisfy the boundary conditions and initial conditions of the solution of the differential equation.
  • determining the predicted solution of the differential equation and the predicted value of the derivative term of the differential equation corresponding to the variational parameters in the differentiable quantum circuit respectively includes: updating the predicted value of the differential equation by using an optimization algorithm Variational parameters in the differentiable quantum circuit; according to the updated variational parameters in the differentiable quantum circuit, an updated predicted solution of the differential equation and a predicted value of a derivative term of the differential equation are obtained.
  • the step of using an optimization algorithm to update the variational parameters in the differentiable quantum circuit includes: updating the variational parameters ⁇ by the following formula: Wherein, the n is an integer not less than 1, ⁇ is the learning rate, and L is the loss function, is the gradient of the loss function to ⁇ .
  • An embodiment of this specification provides a processing device for a data processing task, and the determining device includes:
  • An acquisition module configured to acquire data processing task data; wherein, the data processing task is a task of solving a differential equation; the data processing task data includes the differential equation;
  • a building block configured to build a differentiable quantum circuit according to the data processing task data
  • a prediction module configured to predict the target processing result of the data processing task based on the differentiable quantum circuit, until the value of the loss function constructed according to the predicted processing result obtained from the prediction meets the specified accuracy condition;
  • the prediction processing result that makes the value of the loss function conform to the specified accuracy condition is taken as the target processing result.
  • An embodiment of the present specification provides a storage medium, in which a computer program is stored, wherein the computer program is configured to execute the method described in any one of the above when running.
  • One embodiment of the present specification provides an electronic device, including a memory and a processor, the memory stores a computer program, and the processor is configured to run the computer program to perform any of the above-mentioned method.
  • the present application obtains data processing task data, constructs a differentiable quantum circuit based on the data processing task data, and then predicts the target processing result of the data processing task based on the differentiable quantum circuit, until When the value of the loss function constructed according to the prediction processing result obtained by the prediction meets the specified accuracy condition, the prediction processing result that makes the value of the loss function meet the specified accuracy condition is taken as the target processing result, and can be based on the prediction processing result Build a loss function and update the value of the loss function to solve the differential equation and reduce the resource consumption caused by grid division.
  • FIG. 1 is a block diagram of the hardware structure of a computer terminal according to a data processing task processing method provided by an embodiment of this specification;
  • FIG. 2 is a schematic flowchart of a processing method for a data processing task provided by an embodiment of this specification
  • Fig. 3 is a schematic diagram of a differentiable quantum circuit provided by an embodiment of this specification.
  • Fig. 4 is a schematic diagram of another differentiable quantum circuit provided by the embodiment of this specification.
  • FIG. 5 is a schematic flowchart of another data processing task processing method provided by the embodiment of this specification.
  • FIG. 6 is a schematic flowchart of another data processing task processing method provided by the implementation mode of this specification.
  • FIG. 7 is a schematic diagram of a calculation domain division provided by an embodiment of this specification.
  • Fig. 8 is a schematic diagram of another differentiable quantum circuit provided by the embodiment of this specification.
  • FIG. 9 is a schematic flowchart of another method for processing a data processing task provided by an embodiment of this specification.
  • FIG. 10 is a schematic structural diagram of a processing device for a data processing task provided by an embodiment of this specification.
  • An embodiment of this specification provides a method for processing data processing tasks, and the method can be applied to electronic devices, such as computer terminals, specifically, ordinary computers, quantum computers, and the like.
  • FIG. 1 is a block diagram of a hardware structure of a computer terminal according to a data processing task processing method provided by an embodiment of this specification.
  • the computer terminal may include one or more (only one is shown in FIG. 1 ) processors 102 and a memory 104 for storing data, wherein the processor 102 may include but not limited to a microprocessor (Microcontroller Unit, MCU) or a processing device such as a programmable logic device (Field Programmable Gate Array, FPGA).
  • MCU Microcontroller Unit
  • FPGA Field Programmable Gate Array
  • the above-mentioned computer terminal may further include a transmission device 106 and an input and output device 108 for communication functions.
  • FIG. 1 is only for illustration, and it does not limit the structure of the above computer terminal.
  • the computer terminal may also include more or fewer components than shown in FIG. 1 , or have a different configuration than that shown in FIG. 1 .
  • the memory 104 can be used to store software programs and modules of application software, such as program instructions/modules corresponding to a processing method for implementing a data processing task in the embodiment of this specification, and the processor 102 runs the software programs stored in the memory 104 and module, so as to execute various functional applications and data processing, that is, to realize the above-mentioned method.
  • the memory 104 may include high-speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory.
  • the memory 104 may further include a memory that is remotely located relative to the processor 102, and these remote memories may be connected to a computer terminal through a network. Examples of the aforementioned networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.
  • the transmission device 106 is used to receive or transmit data via a network.
  • the specific example of the above-mentioned network may include a wireless network provided by the communication provider of the computer terminal.
  • the transmission device 106 includes a network adapter (Network Interface Controller, NIC), which can be connected to other network devices through a base station so as to communicate with the Internet.
  • the transmission device 106 may be a radio frequency (Radio Frequency, RF) module, which is used to communicate with the Internet in a wireless manner.
  • RF Radio Frequency
  • a real quantum computer has a hybrid structure, which consists of two parts: one is a classical computer, which is responsible for performing classical calculation and control; the other is a quantum device, which is responsible for running quantum programs and realizing quantum computing.
  • the quantum program is a series of instruction sequences written in a quantum language such as QRunes that can be run on a quantum computer, which supports the operation of quantum logic gates and finally realizes quantum computing.
  • a quantum program is a series of instruction sequences that operate quantum logic gates in a certain sequence.
  • Quantum computing simulation is the process of simulating the quantum program corresponding to a specific problem using a virtual architecture built with the resources of an ordinary computer (that is, a quantum virtual machine). Often, quantum programs corresponding to specific problems need to be constructed.
  • the quantum program referred to in the implementation mode of this specification refers to a program written in a classical language that characterizes qubits and their evolution, in which qubits, quantum logic gates, etc. related to quantum computing are represented by corresponding classical codes.
  • quantum circuits are also called quantum logic circuits. They are the most commonly used general-purpose quantum computing models. They represent circuits that operate on qubits under an abstract concept. The components include qubits, circuits (timelines) , and various quantum logic gates, the results often need to be read out through quantum measurement operations.
  • the circuits can be regarded as connected by time, that is, the state of qubits evolves naturally with time, in the process according to The instruction of the Hamiltonian operator is operated until it encounters a logic gate.
  • a quantum program as a whole corresponds to a total quantum circuit
  • the quantum program mentioned in this specification refers to the total quantum circuit, wherein the total number of qubits in the total quantum circuit is the same as the total number of qubits in the quantum program.
  • a quantum program can be composed of quantum circuits, measurement operations for qubits in quantum circuits, registers for saving measurement results, and control flow nodes (jump instructions).
  • a quantum circuit can contain tens, hundreds or even thousands of Tens of thousands of quantum logic gate operations.
  • the execution process of a quantum program is the process of executing all quantum logic gates according to a certain time sequence. It should be noted that timing refers to the time sequence in which a single quantum logic gate is executed.
  • Quantum logic gates can be used to evolve quantum states. Quantum logic gates are the basis of quantum circuits. Quantum logic gates include single-bit quantum logic gates, such as Hadamard Gate (H gate, Hadema gate), Pauli-X gate (X gate), Pauli-Y gate (Y gate), Pauli-Z gate (Z gate), RX gate, RY gate, RZ gate, etc. etc.; multi-bit quantum logic gates, such as CNOT gates, CR gates, iSWAP gates, Toffoli gates, etc.
  • H gate Hadamard Gate
  • X gate Pauli-X gate
  • Y gate Pauli-Y gate
  • Z gate Pauli-Z gate
  • RX gate RY gate, RZ gate, etc. etc.
  • multi-bit quantum logic gates such as CNOT gates, CR gates, iSWAP gates, Toffoli gates, etc.
  • Quantum logic gates are generally represented by unitary matrices, and unitary matrices are not only in the form of matrices, but also a kind of operation and transformation. Generally, the effect of a quantum logic gate on a quantum state is calculated by multiplying the left side of the unitary matrix by the matrix corresponding to the right vector of the quantum state.
  • the basic unit of information is a bit, and a bit has two states of 0 and 1, and the most common physical implementation method is to represent these two states through the level.
  • the basic unit of information is the qubit.
  • a qubit also has two states of 0 and 1, denoted as
  • the state of the qubit will collapse to a certain state (eigenstate, here is
  • 2 1, and
  • the quantum state refers to the state of a qubit, and its eigenstate is expressed in binary in a quantum algorithm (or called a quantum program).
  • a group of qubits is q0, q1, and q2, representing the 0th, 1st, and 2nd qubits, and the order from high to low is q2q1q0
  • the quantum states of this group of qubits are 2 3 eigenstates
  • the 8 eigenstates (determined states) refer to:
  • a quantum state is a superposition state composed of eigenstates. When the probability amplitude of other states is 0, it is in one of the definite eigenstates.
  • solving fluid dynamics problems with numerical methods generally involves the solution of differential equations, which are involved in many scientific and technological fields. Therefore, it is very important to develop effective methods for solving differential equations.
  • This specification proposes a processing method for data processing tasks, wherein the data processing tasks include solving general differential equations (including but not limited to partial differential equations containing time items) to solve the problem of spatial derivatives in the case of complex computational domain shapes.
  • general differential equations including but not limited to partial differential equations containing time items
  • FIG. 2 is a schematic flowchart of a data processing task processing method provided in an embodiment of this specification, which may include the following steps:
  • S101 Acquire data processing task data; wherein, the data processing task is a task of solving a differential equation; the data processing task data includes the differential equation.
  • any equation that expresses the relationship between the unknown function, the derivative of the unknown function, and the independent variable is called a differential equation.
  • the unknown function is a one-variable function, called an ordinary differential equation;
  • the unknown function is a derivative of a multivariate function containing an unknown function, called a partial differential equation, for example etc.
  • the data processing task may include solving the following differential equations:
  • u is the data processing result of the data processing task, that is, the solution of the differential equation
  • x is a variable.
  • Step 1 Obtain a group of qubits and set the initial state of the qubits to
  • Step 2 using the first type of quantum logic gates to construct the first sub-quantum circuit module that generates the basis set of the function space.
  • the first type of quantum logic gates to construct the first sub-quantum circuit module for obtaining the basis set of the function space, which is used to convert the predefined nonlinear function
  • the magnitude of the quantum state transformed into the initial state As a function space basis group, where, N is the number of qubits, j is the serial number of the qubit, is the Ry quantum logic gate on the jth qubit.
  • T n (x) and U n (x) are Chebyshev n-degree polynomials of the first and second kind respectively, and they have three very key properties, which are linkability, nesting, and easiness of differentiability, These characteristics greatly enrich the characterization capabilities of Chebyshev polynomial basis sets, specifically:
  • T n (T m (x)) T mn (x)
  • the first type of quantum logic gates may include: Rx quantum logic gates, Ry quantum logic gates and Rz quantum logic gates.
  • Step 3 Using the second type of quantum logic gates, constructing a second sub-quantum circuit module for combining function space basis sets into predicted solutions of differential equations.
  • the second type of quantum logic gates to construct the second sub-quantum circuit module for combining the function space basis set into the predicted solution of the differential equation, so that the quantum state amplitude of the initial state into the final quantum state and solve the predicted solution of the differential equation according to the final quantum state, where, is the unitary matrix corresponding to the second sub-quantum circuit module.
  • the second sub-quantum circuit may include but not limited to: Hardware Efficient Ansatz (HEA) circuit and Alternating Blocks Ansatz (ABA) circuit
  • HEA consists of a single quantum rotating connection layer and global entanglement Layer composition, with the deepening of the number of layers, the expressive ability of the circuit is constantly improving, and it will also increase the difficulty of training the circuit
  • ABA does not use the global entanglement layer, but divides the circuit into multiple sub-blocks , and use HEA-style circuits in sub-blocks, that is, ABA first establishes local entanglement, and then gradually forms correlated states by interleaving sub-blocks, which helps improve the trainability of circuits and maintains a high degree of expressiveness , and prevent the phenomenon of gradient disappearance in the iterative process.
  • the second type of quantum logic gates may include: Rx quantum logic gates, Ry quantum logic gates, Rz quantum logic gates and CNOT quantum logic gates.
  • Step 4 Build the measurement operation module for obtaining the predicted solution of the differential equation.
  • a measurement operation module acting on the qubit is constructed to measure the final quantum state of the qubit.
  • Step 5 sequentially combining the first sub-quantum circuit module, the second sub-quantum circuit module and the measurement operation module to obtain a differentiable quantum circuit.
  • the first sub-quantum circuit module, the second sub-quantum circuit module, and the measurement operation module are combined in turn to construct a schematic diagram of a differentiable quantum circuit as shown in Figure 3.
  • the black dot and ⁇ icon in the figure represent CNOT Quantum logic gate, wherein, the black dot is on the control bit of the CNOT quantum logic gate, and ⁇ is on the target bit of the CNOT quantum logic gate.
  • S103 Predict the target processing result of the data processing task based on the differentiable quantum circuit, and when the value of the loss function constructed according to the predicted processing result obtained from the prediction meets the specified accuracy condition, make the The predicted processing result whose value of the above loss function meets the specified accuracy condition is used as the target processing result.
  • Predicting the target processing result of the data processing task based on the differentiable quantum circuit may include the following steps:
  • Step 1 Obtain the information of the differential equation to be solved and the initial conditions and boundary conditions satisfied by the solution of the differential equation to be solved.
  • Step 2 Constructing a differentiable quantum circuit and determining variational parameters in the differentiable quantum circuit.
  • Step 3 Predict the solution of the differential equation through the differentiable quantum circuit according to the initial condition and the boundary condition.
  • predicting the solution of the differential equation through the differentiable quantum circuit may include:
  • the measurement operator is required Measure the final state to obtain a predicted solution to the differential equation
  • the key to this process is the preselection of the measurement operator
  • the magnetization of the entire system can be selected as the measurement operator
  • Z is the Pauli operator
  • the Ising Hamiltonian with additional transverse and longitudinal magnetic fields can also be selected as the measurement operator.
  • the expected value Determine the predicted solution f(x) for the differential equation.
  • the output result of the quantum circuit that is, the predicted solution f(x) is:
  • Constructing a loss function according to the prediction processing result obtained from the prediction may include:
  • the L ⁇ (diff) represents that the prediction processing result does not satisfy the error of the above differential equation
  • the d x f is the derivative term in the above differential equation
  • the f is the function to be found of the above differential equation
  • Said x represents a variable
  • said L ⁇ (boundary) represents the error that said prediction processing result does not satisfy boundary conditions and initial conditions, said is the regular term error.
  • f(x) is the prediction processing result obtained by predicting the above differential equation.
  • the following loss function will be generated:
  • M is the number of regular points
  • u reg ( xi ) is the value of known regular points
  • F[d x f( xi ), f( xi ), xi ] in the above formula is as follows:
  • the prediction processing result that makes the value of the loss function meet the specified accuracy condition is just the target processing result of the above differential equation; otherwise, it can be updated through the optimization algorithm Variational parameters in differentiable quantum circuits.
  • the variational parameter ⁇ is updated by the following formula, namely Among them, n is an integer not less than 1, ⁇ is the learning rate, is the gradient of the loss function to ⁇ , and L is the loss function.
  • the updated variational parameters are passed to the differentiable quantum circuit, the evolution and measurement of the above steps are continued, and the prediction processing results and their corresponding loss functions are updated by continuously iterating the variational parameters until the value of the loss function is obtained.
  • the predicted processing results that meet the preset accuracy conditions are used as the target processing results of the differential equation.
  • the variational parameter ⁇ can be updated; the updated variational parameter can be substituted into the loss function, and the updated loss function can be obtained; the variational parameter can be further updated according to the updated loss function , repeating the above process until the loss function satisfies the predetermined accuracy condition, that is, the prediction processing result that makes the loss function satisfy the preset accuracy condition is taken as the target processing result of the differential equation.
  • This embodiment is different from the traditional numerical calculation method to solve differential equations, because this method does not need to numerically discretize the spatial derivative, especially for the complex shape of the calculation domain, it can avoid the resource consumption caused by grid division; in addition, By adding a regular term to the loss function, the existing prior data can be fully utilized to achieve another way to solve the differential equation.
  • the data of the data processing task is first obtained, and then a differentiable subcircuit is constructed according to the data processing task, and then the target processing result of the data processing task is predicted based on the differentiable subcircuit, until the result obtained according to the prediction is
  • the prediction processing result that makes the value of the loss function meet the specified accuracy condition is set as the target processing result.
  • This embodiment can construct a loss function based on the predicted solution and update the value of the loss function to realize another processing method for solving the differential equation and reduce resource consumption caused by grid division.
  • DQC Differentiable Quantum Circuits
  • FIG. 5 is a schematic flowchart of a solution task of using a quantum circuit to process a time-dependent partial differential equation provided in this embodiment, which may include the following steps:
  • S201 Acquire data task data, wherein the data processing task is a task of solving a time-dependent partial differential equation; the data processing task data includes the time-dependent partial differential equation.
  • Partial differential equations are an important branch of modern mathematics. Both in theory and in practical applications, partial differential equations are used to describe problems in the fields of mechanics, control processes, ecological and economic systems, chemical cycle systems, and epidemiology. The use of partial differential equations to describe problems can fully take into account the influence of space, time, etc., so for partial differential equations that contain time items, they can be called time-dependent partial differential equations.
  • time-dependent partial differential equation is obtained as follows:
  • u(x,t) is the solution of the time-dependent partial differential equation
  • x is the space variable
  • t is the time variable
  • N'[u(x,t)] is the nonlinear item
  • ⁇ is the computational domain, T for time.
  • constructing a differentiable quantum circuit may include the following steps:
  • S2022 Using the first type of quantum logic gates, constructing a first sub-quantum circuit module that generates a function space basis set.
  • the process of constructing the first sub-quantum circuit module is the same as the above-mentioned process of constructing the first sub-quantum circuit, and will not be repeated here.
  • S2024 Construct a measurement operation module for obtaining a prediction solution of the time-dependent partial differential equation.
  • a measurement operation module acting on the qubit is constructed to measure the final quantum state of the qubit.
  • S2025 Combine the first sub-quantum circuit module, the second sub-quantum circuit module, and the measurement operation module in sequence to construct a differentiable quantum circuit.
  • the first sub-quantum circuit module, the second sub-quantum circuit module, and the measurement operation module are combined in turn to construct a schematic diagram of a differentiable quantum circuit as shown in Figure 3.
  • the black dot and ⁇ icon in the figure represent CNOT Quantum logic gates, where the black dots are in the CNOT On the control bit of the quantum logic gate, ⁇ is on the target bit of the CNOT quantum logic gate.
  • S203 Predict the target processing result of the time-dependent partial differential equation based on the initial variational parameters of the differentiable quantum circuit, until the value of the loss function at the current moment constructed according to the predicted processing result obtained from the prediction meets the specified accuracy condition
  • the predicted solution of the time-dependent partial differential equation that makes the value of the loss function meet the specified accuracy condition is used as the target solution of the time-dependent partial differential equation.
  • Predicting the target processing result of the time-dependent partial differential equation based on the initial variational parameters of the differentiable quantum circuit may include the following steps:
  • Step 1 Determine the initial conditions and boundary conditions of the time-dependent partial differential equation.
  • Step 2 Determine the time-dependent partial differential equation in semi-discrete form according to a pre-selected differential scheme.
  • the difference format is a discretization method that uses numerical methods to calculate the derivative of a function, that is, an algorithm that uses the difference between two or more adjacent numerical points to replace the derivative or partial derivative in the partial differential equation.
  • the choice of the difference format is The first step in discretizing or semi-discretizing partial differential equations.
  • the time item in the time-containing partial differential equation is firstly Discrete, get If the pre-selected differential format is an implicit differential format, the determination of the time-dependent partial differential equation in semi-discrete form according to the pre-selected differential format includes:
  • the u(x, t+ ⁇ t) is the value of the function to be obtained at the time t+ ⁇ t.
  • Step 3 According to the initial conditions and boundary conditions, the solution of the time-dependent partial differential equation is predicted through the differentiable quantum circuit.
  • the forecasting process is the same as the aforementioned forecasting process, and will not be repeated here.
  • Constructing a loss function at the current moment according to the prediction result obtained from the prediction may include:
  • N' is the number of discrete points
  • M is the number of boundary points
  • i is the ith discrete point
  • j' is the j'th boundary point
  • g( xi ) is the initial condition
  • h(x j' ,0) is the boundary condition at the initial moment
  • the N'[u(x,t)] is determined according to the differentiable quantum circuits at the previous moment.
  • the value of the loss function at the current moment constructed according to the prediction processing results meets the preset accuracy conditions, specifically:
  • the target solution of the time-dependent partial differential equation is obtained, mainly by using the pre-selected measurement operator acting on the final quantum state , the predicted solution of the time-dependent partial differential equation at the current moment can be obtained And substitute the predicted solution at the current moment into the loss function at the corresponding moment to determine whether the value of the loss function meets the preset accuracy conditions, where the preset accuracy conditions can be set by the user according to the calculation requirements, for example, 10 -6 or 0 .
  • the predicted solution that makes the value of the loss function meet the specified accuracy conditions is just the target solution of the above time-dependent partial differential equation; otherwise, through the optimization algorithm Update variational parameters in differentiable quantum circuits.
  • the variational parameter ⁇ is updated by the following formula, namely Among them, n is an integer not less than 1, ⁇ is the learning rate, is the gradient of the loss function to ⁇ , and L is the loss function.
  • the updated variational parameters are passed to the differentiable quantum circuit, and the evolution and measurement of the above steps are continued, and through continuous iterative variation Update the prediction solution and its corresponding loss function by sub-parameters until the prediction solution that makes the value of the loss function meet the preset accuracy conditions is obtained, which is used as the target solution of the above time-dependent partial differential equation.
  • the loss function at time ⁇ t is obtained, namely:
  • the approximate value of the predicted solution at time ⁇ t can be obtained in Determine according to the differentiable quantum circuit at the current moment, then update the variational parameters (parameters in the proposed design), and finally repeat the above steps until the predicted solution u of the time-dependent partial differential equation to be solved at a given time T is obtained (x,T).
  • the time-dependent partial differential equation is semi-discretized and transformed into a semi-discrete time-dependent partial differential equation, and by constructing a differentiable quantum circuit and obtaining the predicted solution of the time-dependent partial differential equation corresponding to the initial variational parameters, the
  • the classical data structure is connected with the quantum state in the quantum field, and the evolution operation of the classical data structure encoding to the quantum state is performed, and the quantum state of the evolved quantum circuit is obtained, which can use the superposition characteristics of the quantum to speed up processing.
  • the high processing speed of solving tasks of time-dependent partial differential equations expands the simulation application scenarios of quantum computing.
  • the DQC method has advantages in solving ordinary differential equations and ordinary differential equations, but because the differentiable quantum circuit model needs to use the parameter shift method to calculate the values of the derivatives in the differential equation many times, the calculation efficiency may be reduced.
  • an embodiment of this specification combines domain decomposition technology with differentiable quantum circuits, and proposes a method for solving differential equations using quantum computing.
  • the differential quantum circuit is solved on the entire computational domain, resulting in a waste of computational resources; on the other hand, it also effectively improves the computational efficiency of optimizing variational parameters.
  • FIG. 6 is a schematic flowchart of a method for solving differential equations based on computational domain decomposition provided in this embodiment, which may include the following steps:
  • S301 Acquire data processing task data; wherein, the data processing task is a task of solving a differential equation; the data processing task data includes the differential equation.
  • the F is a functional function
  • the d x u is a derivative term
  • the u is the solution of the differential equation to be solved
  • the x is a variable
  • the u(x,t) is the solution of the differential equation
  • x is the space variable
  • t is the time variable
  • N'[u(x,t)] is the non-linear item
  • ⁇ is the computational domain
  • T is the time
  • S303 Construct differentiable quantum circuits corresponding to sub-regions, wherein one sub-computational domain corresponds to one predicted solution of the differential equation. Specifically, the process of constructing a differentiable quantum circuit corresponding to a sub-region is the same as the process of constructing a differentiable quantum circuit in the previous two embodiments, and will not be repeated here.
  • S304 Predict the target solution of the differential equation based on the differentiable quantum circuit, until the value of the joint loss function of the sub-calculation domain constructed according to the predicted solution of the differential equation meets the specified accuracy condition, the value of the loss function will meet
  • the predicted solution of the differential equation for the specified accuracy condition serves as the target solution of the differential equation.
  • the prediction process is basically the same as the prediction process in the foregoing embodiments, and will not be repeated here.
  • the joint loss function constructed according to the predicted solution of the differential equation may include:
  • the n is the number of sub-regions
  • the n b is the number of interfaces
  • the L i (diff) [d x f i , f i , x] is the predicted solution of the i-th sub-region does not satisfy the differential equation but
  • the error caused by L i (boundary) [f i , x] is the error caused by the prediction solution of the i-th sub-region not satisfying the boundary conditions
  • the L i (interface) [f, x] is the error caused by the i-th sub-region
  • the error caused by the prediction solution of the adjacent areas on both sides of the interface does not meet the continuity condition of the interface and
  • the n i is the number of discrete points on the i-th interface
  • f + (x j ) and f - (x j ) are the predicted solutions corresponding to the sub-regions on both sides of the interface.
  • the target solution of the differential equation is obtained, which is mainly by using the pre-selected measurement operator
  • f i (x)> each predicted solution f i (x) of the differential equation is obtained, and the predicted solution is substituted into the joint loss function to determine whether the value of the joint loss function meets the preset accuracy conditions , where the preset accuracy condition can be set by the user according to the calculation requirements, for example, 10 -6 or 0.
  • the predicted solution that makes the value of the loss function meet the specified accuracy condition is just the target solution of the above differential equation; otherwise, the differentiable quantum is updated by the optimization algorithm Variational parameters in the circuit.
  • the optimization process of variational parameters is basically the same as the optimization process of variational parameters in the foregoing embodiments, and will not be repeated here.
  • the classical data structure is connected with the quantum state in the quantum field, and the evolution operation of encoding the classical data structure into the quantum state is performed.
  • the quantum state of the evolved quantum circuit which can use the quantum superposition property to speed up the processing speed of the task of solving the differential equation with high complexity, and expand the simulation application scenarios of quantum computing.
  • FIG. 9 is a schematic flowchart of a method for using a quantum circuit to solve a differential equation solution task provided by an embodiment of this specification, which may include the following steps:
  • S401 Acquire data processing task data; wherein, the data processing task is a task of solving a differential equation; the data processing task data includes the differential equation and a derivative term of the differential equation.
  • the solution of the predicted value of the derivative term of the differential equation in the task of solving the differential equation by using the differentiable quantum circuit described below wherein the derivative term of the differential equation can be divided into different categories, such as the derivative term and can be classified into one class, the derivative term and Belonging to one class, etc.
  • the key to its classification is whether the same section of differentiable quantum circuit can be used to solve the predicted value of the derivative term.
  • the F is a functional function
  • the d x u is a derivative term
  • the u is the predicted solution of the differential equation to be solved
  • the x is a variable
  • S402 Construct differentiable quantum circuits respectively according to the differential equation and derivative terms of the differential equation.
  • constructing a differentiable quantum circuit according to the differential equation and the derivative term of the differential equation may include:
  • the first differentiable quantum circuit is constructed according to the above differential equation
  • the second differentiable quantum circuit is constructed according to the derivative term of the above differential equation
  • the predicted solution and the second differential equation corresponding to the current variational parameters in the first differentiable quantum circuit are respectively determined.
  • the current variational parameter in the differentiable quantum circuit corresponds to the predicted value of the derivative term of the differential equation.
  • S403 Predict the target solution of the differential equation and the value of the derivative term of the differential equation based on the differentiable quantum circuit, until the value of the loss function constructed based on the predicted solution of the differential equation and the predicted value of the derivative term of the differential equation meets the specified accuracy In the case of the condition, the predicted solution of the differential equation that makes the value of the loss function meet the specified accuracy condition is taken as the target solution of the differential equation.
  • the prediction process is basically the same as the prediction process in the foregoing embodiments, and will not be repeated here.
  • said f i represents the i-th order derivative term in the differential equation
  • said L (diff) represents that said predicted solution does not satisfy the error of the differential equation
  • said f is said differential equation
  • said x represents a variable
  • the L (boundary) represents the error that the predicted solution does not satisfy the boundary conditions and initial conditions.
  • the target solution of the differential equation is obtained, which is mainly by using the pre-selected measurement operator
  • each predicted solution f i (x) of the differential equation and each predicted value f′ i (x) of the derivative term are obtained, and the predicted solution and predicted value are substituted into the loss function to determine the value of the loss function Whether it meets the preset accuracy condition, where the preset accuracy condition can be set by the user according to the calculation requirements, for example, 10 -6 or 0.
  • the predicted solution that makes the value of the loss function meet the specified accuracy condition is just the target solution of the differential equation; Variational parameters in quantum circuits.
  • the optimization process of variational parameters is basically the same as the optimization process of variational parameters in the foregoing embodiments, and will not be repeated here.
  • the classical data structure is connected with the quantum state in the quantum field, and the classical data structure is executed.
  • the evolution operation of structure encoding to quantum state obtains the quantum state of the evolved quantum circuit, which can take advantage of the superposition characteristics of quantum to speed up the processing speed of solving tasks of highly complex differential equations and expand the simulation application scenarios of quantum computing.
  • FIG. 10 is a schematic structural diagram of a data processing task processing device provided in an embodiment of this specification, corresponding to the process shown in FIG. 2, and the device may include:
  • An acquisition module 501 configured to acquire data processing task data; wherein, the data processing task is a task of solving a differential equation; the data processing task data includes the differential equation;
  • a construction module 502 configured to construct a differentiable quantum circuit according to the data processing task data
  • the prediction module 503 is configured to predict the target processing result of the data processing task based on the differentiable quantum circuit, and when the value of the loss function constructed according to the predicted prediction processing result meets the specified accuracy condition, the loss The predicted processing result whose value of the function meets the specified accuracy condition is used as the target processing result.
  • the acquisition module 501 includes:
  • the acquisition unit is used to acquire the information of the differential equation and the initial conditions and boundary conditions satisfied by the solution of the differential equation.
  • the building block 502 includes:
  • a construction unit for constructing a differentiable quantum circuit and determining variational parameters in the differentiable quantum circuit
  • the building units include:
  • the first acquisition subunit is used to acquire a group of qubits and set the initial state of the qubits to
  • the first construction sub-unit is used to construct the first sub-quantum circuit module of the generating function space basis set by using the first type of quantum logic gate;
  • the second construction subunit is used to construct a second sub-quantum circuit module for combining function space basis sets into predicted solutions of differential equations by using the second type of quantum logic gates;
  • the third construction subunit is used to construct the measurement operation module for obtaining the prediction solution of the differential equation
  • the combination subunit is used to sequentially combine the first sub-quantum circuit module, the second sub-quantum circuit module and the measurement operation module to obtain a differentiable quantum circuit.
  • the prediction module 503 includes:
  • a prediction unit configured to obtain a predicted solution of the differential equation through the differentiable quantum circuit according to the initial condition and the boundary condition;
  • a determining unit configured to determine that the loss function constructed according to the predicted solution of the differential equation meets a preset accuracy condition
  • the update unit is used to update the variational parameters through an optimization algorithm for the predicted solution of the differential equation whose loss function does not meet the preset accuracy condition, and obtain the predicted solution of the differential equation corresponding to the updated variational parameter.
  • the update unit includes:
  • the update subunit is used to update the variational parameter ⁇ through the following formula:
  • n is an integer not less than 1
  • ⁇ is the learning rate
  • ⁇ is the gradient of the loss function to ⁇
  • L is the loss function
  • the embodiments of this specification also provide a storage medium, where a computer program is stored in the storage medium, wherein the computer program is configured to execute the steps in any one of the above embodiments when running.
  • the above-mentioned storage medium may include but not limited to: U disk, read-only memory (Read-Only Memory, ROM), random access memory (Random Access Memory, RAM), mobile hard disk, magnetic disk Or various media such as optical discs that can store computer programs.
  • the implementation mode of this specification also provides an electronic device, including a memory and a processor, the computer program is stored in the memory, and the processor is configured to run the computer program to perform any one of the above method embodiments A step of.
  • the electronic device may further include a transmission device and an input and output device, wherein the transmission device is connected to the processor, and the input and output device is connected to the processor.

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Abstract

Des modes de réalisation de la présente description concernent un appareil et un procédé de traitement destinés à une tâche de traitement de données, un support d'enregistrement et un dispositif électronique. Le procédé consiste à : obtenir des données de tâche de traitement de données, une tâche de traitement de données représentant une tâche de résolution d'une équation différentielle, et les données de tâche de traitement de données comprenant l'équation différentielle ; construire un circuit quantique dérivable en fonction des données de tâche de traitement de données ; et prédire un résultat de traitement cible de la tâche de traitement de données sur la base du circuit quantique dérivable jusqu'à ce que la valeur d'une fonction de perte construite en fonction d'un résultat de traitement prédit satisfasse une condition de précision spécifiée, le résultat de traitement prédit permettant que la valeur de la fonction de perte satisfasse la condition de précision spécifiée étant utilisée en tant que résultat de traitement cible. Selon le procédé utilisé par les modes de réalisation de la présente description, la fonction de perte peut être construite sur la base d'une solution prédite de l'équation différentielle, et un autre mode de traitement de la tâche de résolution de l'équation différentielle est réalisé par mise à jour de la valeur de la fonction de perte, de telle sorte que la consommation de ressources provoquée par la division de grille soit réduite.
PCT/CN2023/078928 2022-03-04 2023-03-01 Appareil et procédé de traitement pour tâche de traitement de données, support d'enregistrement et dispositif électronique WO2023165500A1 (fr)

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