WO2023065463A1 - 量子计算方法、装置、设备、介质及产品 - Google Patents

量子计算方法、装置、设备、介质及产品 Download PDF

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WO2023065463A1
WO2023065463A1 PCT/CN2021/133711 CN2021133711W WO2023065463A1 WO 2023065463 A1 WO2023065463 A1 WO 2023065463A1 CN 2021133711 W CN2021133711 W CN 2021133711W WO 2023065463 A1 WO2023065463 A1 WO 2023065463A1
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quantum
hamiltonian
parameters
target
state
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PCT/CN2021/133711
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French (fr)
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陈玉琴
张胜誉
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腾讯科技（深圳）有限公司
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Priority to EP21937200.0A priority Critical patent/EP4195114A4/en
Priority to JP2022565677A priority patent/JP7408840B2/ja
Priority to US17/986,771 priority patent/US20230289639A1/en
Publication of WO2023065463A1 publication Critical patent/WO2023065463A1/zh

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/20—Models of quantum computing, e.g. quantum circuits or universal quantum computers
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/40—Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/60—Quantum algorithms, e.g. based on quantum optimisation, quantum Fourier or Hadamard transforms
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N5/00—Computing arrangements using knowledge-based models
    • G06N5/01—Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound

Definitions

  • the embodiments of the present application relate to the field of quantum technology, and in particular to a quantum computing method, device, equipment, medium and product.
  • quantum algorithms have important applications in many fields, among which, solving the eigenstates and eigenenergy of quantum systems is a very critical issue.
  • a method for obtaining the lowest eigenstate by imaginary time evolution is provided. After expressing the wave function in the imaginary time Schrödinger equation as an eigenvector expansion, the minimum eigenvalue is determined. Since the minimum eigenvalue is smaller than any eigenvalue Eigenvalue, when the time approaches infinity, other eigenvalues will disappear at an exponential rate, so given any wave function whose overlap with the minimum eigenvalue is not 0, the initial lowest eigenstate can be obtained by inversion.
  • Embodiments of the present application provide a quantum computing method, device, equipment, medium, and product. Described technical scheme is as follows:
  • a quantum computing method is provided, the method is executed by a computer device, and the method includes:
  • the quantum circuit includes quantum circuit parameters, and the Hamiltonian operator includes Hamiltonian A parameter of the Hamiltonian, wherein the parameters of the Hamiltonian include a quantum imaginary time parameter;
  • the final quantum state is determined to be the smallest eigenstate of the target quantum system.
  • a quantum computing device comprising:
  • the acquisition module is used to determine the initial quantum state of the target quantum system, the quantum circuit corresponding to the target quantum system, and the Hamiltonian operator used to describe the target quantum system, the quantum circuit includes quantum circuit parameters, and the Hamiltonian
  • the Tamon operator includes a Hamiltonian operator parameter, and the Hamiltonian operator parameter includes a quantum imaginary time parameter; the initial quantum state is input into the quantum circuit, and the quantum state output by the quantum circuit is obtained as the Quantum circuit-generated states of the target quantum system;
  • An update module configured to update the Hamiltonian operator parameters based on the output quantum circuit generation state
  • the update module is also used to update the quantum circuit parameters according to the updated Hamiltonian parameters to obtain the updated target quantum system
  • the update module is also used to cyclically update the parameters of the Hamiltonian operator and the parameters of the quantum circuit until the energy of the target quantum system is a minimum value, and the minimum value corresponds to the final quantum state of the target quantum system ; Determine the final quantum state as the minimum eigenstate of the target quantum system.
  • a computer device is provided, and the computer device is configured to implement the above quantum computing method.
  • a computer-readable storage medium stores at least one instruction, at least one section of program, code set or instruction set, the at least one instruction, the at least one section
  • the program, the code set or the instruction set is loaded and executed by the processor to realize the above-mentioned quantum computing method.
  • a computer program product or computer program includes computer instructions, and the computer instructions are stored in a computer-readable storage medium.
  • the processor of the computer device reads the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes the above-mentioned quantum computing method.
  • Fig. 1 is a flow chart of the quantum computing method provided by one embodiment of the present application.
  • FIG. 2 is a schematic diagram of a Hamiltonian operator parameter update process provided by an exemplary embodiment of the present application
  • Fig. 3 is a flowchart of a quantum computing method provided by another embodiment of the present application.
  • Fig. 4 is a schematic diagram of a quantum circuit provided by an embodiment of the present application.
  • FIG. 5 is a schematic diagram of evolution convergence provided by an embodiment of the present application.
  • Fig. 6 is a schematic diagram of the convergence process of the initial state evolution of different authenticity under the HF system provided by an embodiment of the present application;
  • Fig. 7 is a schematic diagram of energy convergence results provided by an embodiment of the present application.
  • Fig. 8 is a schematic diagram of the convergence situation of simulating virtual time evolution and virtual time control under a noise system provided by an embodiment of the present application;
  • Fig. 9 is a block diagram of a quantum computing device provided by an embodiment of the present application.
  • Fig. 10 is a block diagram of a quantum computing device provided by another embodiment of the present application.
  • Fig. 11 is a structural block diagram of a computer device provided by an embodiment of the present application.
  • Quantum computing Based on quantum logic computing, the basic unit of data storage is the quantum bit (qubit).
  • Qubit The basic unit of quantum computing. Traditional computers use 0 and 1 as the basic units of binary. The difference is that quantum computing can process 0 and 1 at the same time, and the system can be in a linear superposition state of 0 and 1:
  • ⁇ > ⁇
  • 2 represent the probability of being 0 and 1, respectively.
  • Hamiltonian A Hermitian matrix that describes the total energy of a quantum system.
  • the Hamiltonian is a physical vocabulary and an operator that describes the total energy of a system, usually denoted by H.
  • Quantum state In quantum mechanics, a quantum state is a microscopic state determined by a set of quantum numbers.
  • Eigenstate In quantum mechanics, the possible values of a mechanical quantity are all the eigenvalues of its operators. The state described by the eigenfunction is called the eigenstate of the operator. In its own eigenstate, this mechanical quantity takes on a definite value, that is, the eigenvalue to which this eigenstate belongs.
  • ⁇ > E
  • ⁇ > the solution that satisfies the equation: H
  • ⁇ > E
  • the ground state corresponds to the lowest energy eigenstate of the quantum system.
  • Quantum circuit also known as quantum circuit, a representation of quantum general-purpose computer, which represents the hardware implementation of the corresponding quantum algorithm/program under the quantum gate model. If the quantum circuit contains adjustable parameters to control the quantum gate, it is called a parameterized quantum circuit (Parameterized Quantum Circuit, referred to as PQC) or a variable quantum circuit (Variational Quantum Circuit, referred to as VQC), both of which are the same concept .
  • PQC Parameterized Quantum Circuit
  • VQC Variational Quantum Circuit
  • Quantum gate In quantum computing, especially in the computing model of quantum circuits, a quantum gate (Quantum gate, or quantum logic gate) is a basic quantum circuit that operates a small number of qubits.
  • VQE Variational Quantum Eigensolver
  • Non-unitary The so-called unitary matrix is a matrix that satisfies All matrices of , and all evolution processes directly allowed by quantum mechanics, can be described by unitary matrices.
  • U is a unitary matrix (Unitary Matrix), also known as a unitary matrix, a unitary matrix, etc., is the conjugate transpose of U.
  • matrices that do not meet this condition are non-unitary, which requires auxiliary means or even exponentially more resources to be realized experimentally, but non-unitary matrices often have stronger expressive power and faster ground state projection effects .
  • the above-mentioned “exponentially many resources” means that the demand for resources increases exponentially with the increase in the number of qubits.
  • the exponentially many resources can mean that the total number of quantum circuits that need to be measured is exponentially multiple, that is, the corresponding needs Exponentially much computation time.
  • Pauli operator also known as Pauli matrix, is a set of three 2 ⁇ 2 unitary Hermitian complex matrices (also known as unitary matrices), generally represented by the Greek letter ⁇ (sigma). Among them, the Pauli X operator is The Pauli Y operator is The Pauli Z operator is
  • ground state i.e. the lowest eigenstate
  • quantum computers An important application scenario of quantum computers is to efficiently solve or express the ground state of quantum systems. At present, some research institutions and manufacturers are also constantly researching new quantum computers, and are committed to exploring the solution of the ground state.
  • the imaginary time evolution is a basic method to solve the ground state of a quantum system.
  • H is the Hamiltonian of the target quantum system
  • ⁇ (t) represents the quantum state of the target quantum system at time t
  • i is the virtual time unit, that is, the quantum virtual time parameter.
  • E ⁇ represents the eigenvalue at time ⁇ .
  • E i is the intrinsic energy
  • E 0 is the ground state energy
  • ci is the expansion coefficient
  • H p represents the target Hamiltonian operator, that is, the original Hamiltonian operator
  • H d represents the control Hamiltonian operator
  • ⁇ (t) is a time-varying parameter.
  • the feedback control is designed to minimize ⁇ (t)
  • VQE Variational Quantum Eigensolver, Variational Quantum Eigensolver
  • the optimization problem is solved using classical optimization algorithms such as steepest descent, Newton's method, conjugate direction method, etc.
  • the difficulty of variable quantum eigensolution lies in the design of the quantum circuit. While ensuring that the quantum circuit can generate the target state, the parameter space must be as smooth as possible. At the same time, the depth of the quantum circuit should not be too deep to affect the execution of the quantum computer.
  • the scheme 2 introduced above is based on the quantum control method of the time-dependent Schrödinger equation in real time. It is necessary to ensure that the selected control Hamiltonian has sufficient control ability, and under incomplete control for all occurrences of the initial state and the convergence process The state requirements are extremely high, and when any state does not meet the controllable conditions, it may fail to converge.
  • variable quantum eigensolution based on the classical optimization algorithm is relatively simple to implement on the quantum computer, and the measurement required for a single update of the parameters is also less, but with the increase of the system size, it will encounter Quantum circuit design and barren plateau optimization problems.
  • This application proposes a brand-new technical solution, which applies control to the imaginary time-dependent Schrödinger equation. Due to the nature of its own dynamics that will converge to the ground state, it can reduce the requirements for control capabilities and accelerate the convergence as much as possible in the controllable state.
  • the process may reduce the requirements for the initial state; the use of quantum control assistance can reduce the requirements for various conditions and reduce the time required for convergence, while little or no increase in the computing resources originally required for each step to achieve the reduction of the overall computing resources;
  • the dynamics approximation by parameter updating is used to update the parameters of the barren plateau problem of the classical optimization algorithm and reduce the design requirements for the proposed quantum circuit.
  • the quantum computing method provided by the embodiment of the present application can be implemented by a classical computer (such as a PC), for example, the classical computer executes a corresponding computer program to realize the method; it can also be executed in a mixed device environment of a classical computer and a quantum computer , for example by the cooperation of classical computer and quantum computer to realize the method.
  • a quantum computer is used to solve the eigenstates in the embodiments of the present application
  • a classical computer is used to realize other steps in the embodiments of the present application except for solving the eigenstates.
  • the execution subject of each step is a computer device for introduction and description.
  • the computer device may be a classical computer, or may include a mixed execution environment of a classical computer and a quantum computer, which is not limited in this embodiment of the present application.
  • FIG. 1 shows a flowchart of a quantum computing method provided by an embodiment of the present application.
  • the execution subject of each step of the method is a computer device as an example for description.
  • the method can include:
  • Step 110 determining the initial quantum state of the target quantum system, the quantum circuit corresponding to the target quantum system, and the Hamiltonian operator used to describe the target quantum system, the quantum circuit includes quantum circuit parameters, and the Hamiltonian operator includes Hamiltonian operator parameters, The parameters of the Hamiltonian operator include quantum imaginary time parameters.
  • the initial quantum state is an input state for inputting into the target quantum system to obtain the output quantum state of the current target quantum system.
  • the quantum circuit corresponding to the target quantum system is the quantum circuit used by the target quantum system when performing quantum calculation, that is, the transformation of the initial quantum state through the quantum circuit is used as a quantum calculation process for the initial quantum state.
  • the quantum circuit parameters are the transformation parameters corresponding to each transformation node in the quantum circuit, and the quantum state is transformed according to the quantum circuit parameters, so as to realize different quantum calculation processes of different quantum circuits.
  • the Hamiltonian operator used to describe the target quantum system includes an original Hamiltonian operator and a control Hamiltonian operator.
  • the original Hamiltonian is used to provide evolutionary trends
  • the control Hamiltonian is used to provide additional evolutionary trends to control the evolution process.
  • the Hamiltonian operator includes Hamiltonian operator parameters, and the Hamiltonian operator parameters include quantum imaginary time parameters.
  • the Hamiltonian describes the target quantum system in terms of quantum dynamics.
  • the quantum dynamics expression includes original Hamiltonian operator and control Hamiltonian operator.
  • Step 120 input the initial quantum state into the quantum circuit, and obtain the quantum state output by the quantum circuit as the generated state of the quantum circuit of the target quantum system.
  • the quantum circuit generated state refers to the quantum state that is output by inputting the initial quantum state into the quantum circuit structure of the target quantum system and transforming the quantum circuit structure.
  • Step 130 updating the parameters of the Hamiltonian operator based on the generated state of the output quantum circuit.
  • the corresponding eigenstate of the target quantum system can be obtained, so as to adjust the parameters of the Hamiltonian with the goal of minimizing the eigenstate.
  • the quantum circuit-generated states of the target quantum system are used to approximately characterize the eigenstates of the target quantum system.
  • the above quantum dynamics is expressed by replacing real time in the time-dependent Schrödinger equation with imaginary time, and adding a dynamic expression obtained by controlling the Hamiltonian on the basis of the original Hamiltonian.
  • ⁇ represents the quantum virtual time parameter
  • ⁇ ( ⁇ )> represents the virtual time eigenstate
  • H p represents the original Hamiltonian
  • H d represents the control Hamiltonian
  • ⁇ ( ⁇ ) represents the The parameters of the Hamiltonian operator.
  • the parameters of the Hamiltonian operator are determined based on the requirement of the first-order partial derivative of the Lyapunov function with respect to time.
  • ⁇ ( ⁇ ) needs to be designed to control the evolution of the target quantum system to the lowest eigenstate.
  • the design ideas for the ⁇ ( ⁇ ) function can be provided through the Lyapunov function.
  • V( ⁇ ( ⁇ )) ⁇ ( ⁇ )
  • E 0 is the minimum eigenvalue of H p , so that H p -E 0 is a positive semi-definite matrix, and the first-order partial derivative of the Lyapunov function with respect to time can be obtained:
  • ⁇ ( ⁇ )>-2 ⁇ H d > ⁇ H p >) is used to represent the control Hamiltonian operator to provide additional evolutionary trends.
  • the parameters of the Hamiltonian are as follows:
  • the critical point of the control function is all eigenstates, where the maximum value corresponds to the eigenstate with the largest eigenvalue, the minimum value corresponds to the eigenstate with the smallest eigenvalue, and the remaining eigenstates are transition states.
  • the initial state must be as close as possible to the target eigenstate to achieve the control purpose.
  • the complementary acceleration can be achieved by adjusting the properties of the two.
  • the convergence speed of the quantum computer when performing the quantum calculation is improved, thereby improving the operational efficiency of the quantum calculation.
  • Step 140 update the parameters of the quantum circuit according to the updated parameters of the Hamiltonian operator, and obtain the updated target quantum system.
  • the quantum circuit parameters of the wave function can be obtained as follows:
  • ⁇ ( ⁇ ) represents the eigenstate
  • ⁇ i represents the ith quantum circuit parameter
  • the quantum circuit parameters corresponding to the target quantum system are updated according to the updated Hamiltonian operator parameters.
  • Step 150 cyclically update the parameters of the Hamiltonian operator and the parameters of the quantum circuit until the energy of the target quantum system is a minimum value, and the minimum value corresponds to the final quantum state of the target quantum system; determine that the final quantum state is the minimum eigenvalue of the target quantum system state.
  • FIG. 2 shows a schematic diagram of a Hamiltonian operator parameter update process provided by an exemplary embodiment of the present application.
  • the cyclic process mainly includes three parts:
  • Quantum circuit generates state 210 , updates Hamiltonian operator parameters 220 and updates quantum circuit parameters 230 .
  • the initial state is input into the quantum circuit structure, and the initial state is transformed through the quantum circuit structure, thereby outputting the quantum state as the quantum circuit generating state.
  • the process of updating the Hamiltonian operator parameter 220 is performed with the goal of minimizing the eigenstate, and the Hamiltonian operator parameter is adjusted.
  • a process of updating quantum circuit parameters 230 is performed to update the quantum circuit parameters of the target quantum system accordingly.
  • the quantum computing method provided by the embodiment of this application combines quantum imaginary time evolution and quantum real-time control theory, and through the analysis of the two mechanisms, a set of control that can be implemented on imaginary time evolution is proposed
  • the method not only reduces the requirements on the initial state and the system, but also reduces the requirements on the control ability. It can provide a strategy of large acceleration while achieving elastic selection, and applies the control to the imaginary time Schrödinger equation. Due to its own dynamics, it will The nature of converging to the ground state can reduce the requirements for control ability, improve the operation speed and accuracy of quantum computers when performing quantum calculations, and speed up the convergence process or reduce the requirements for the initial state as much as possible in the controllable state.
  • the method provided in the embodiment of this application replaces the real time in the time-dependent Schrödinger equation with the imaginary time. Since the dynamics of the imaginary time itself will converge to the nature of the ground state, it can reduce the requirements on the control ability, and in the controllable state. Speed up the convergence process as much as possible or reduce the requirements for the initial state; in addition, the use of quantum control assistance can reduce the requirements for various conditions and reduce the time required for convergence, while reducing or not increasing the computing resources of the quantum computer originally required for each step In order to reduce the overall computing resources.
  • the method provided in the embodiment of the present application needs to ensure that the target Hamiltonian and the control Hamiltonian are generating groups under the Lie algebra.
  • the control capability is only required to be Partially controllable, because of the nature of its dynamics will converge to the lowest eigenstate, can use partly controllable to achieve key control, realize the acceleration of the overall operation of the quantum computer and reduce the additional operation of the overall control.
  • the main control idea is to adjust according to the distance from the eigenstate.
  • the nature of its own evolution and the additional guidance provided by the control provide their own advantages in different situations to achieve stable speed-up and reduce dependence on the system and initial state selection.
  • Fig. 3 is a flow chart of a quantum computing method provided by another exemplary embodiment of the present application, and each step of the method may be executed by a computer device.
  • the method can include:
  • Step 301 Determine the control Hamiltonian based on the diagonal matrix formed by the identity matrix and the Pauli Z matrix.
  • control Hamiltonian operator In the choice of control Hamiltonian operator, the intuitive reference is from the point of view of control ability, choosing a set of control operators with complete control ability can converge to any state in theory.
  • control ability it is necessary to ensure that the original Hamiltonian operator and the control Hamiltonian operator are generating groups under the Lie algebra.
  • control ability it is necessary to ensure that the original Hamiltonian operator and the control Hamiltonian operator are generating groups under the Lie algebra.
  • how to select a suitable control Hamiltonian and unit discrete time to make it possible to adequately approximate the dynamic evolution process will be a difficult problem.
  • the partial controllability can be used to achieve the key control, and the overall acceleration can be realized at the same time. Reduced extra calculations for overall control.
  • the main control idea is to adjust according to the distance from the eigenstate.
  • the nature of its own evolution and the additional guidance provided by the control provide their own advantages in different situations to achieve stable speed-up and reduce dependence on the system and initial state selection.
  • D d has the property that all eigenstates are critical points, which may lead to evolution In the process, the proportion of the lowest eigenstate is too small and it converges to other eigenstates.
  • D d tends to zero around the eigenstate of H d , so it is necessary to judge when D d is suitable for providing evolutionary power, or it can be controlled around the eigenstate by the selection of H d poor ability to sidestep this problem.
  • D p also has the property of including other current states. Assuming that all eigenvalues are real numbers, first expand it to the eigenstates:
  • the system can control the evolution of the eigenstate, and the quantum system can be stabilized near the target state to achieve the goal of convergence towards the target, and reduce the eigenstate evolution of the system.
  • the residence time of the target interval has reached rapid and controllable convergence, and provides the idea of obtaining all eigenstates except the lowest eigenstate, such as amplifying the influence of the control operator around the eigenstate, the system will converge to this point Near the eigenstate, when the overlap between the converged state and all low-energy eigenstates with energy less than this eigenstate is small enough, the evolution of the original virtual time will tend to converge to this eigenstate.
  • the quantum system can be stabilized near the target state through H d regulation, which can improve the stability and reliability of the quantum computer in the process of performing quantum calculations.
  • step 302 the real time in the time-dependent Schrödinger equation is replaced by the imaginary time, and a control Hamiltonian is added on the basis of the original Hamiltonian to describe the target quantum system.
  • Step 303 input the initial quantum state into the quantum circuit, and obtain the quantum state output by the quantum circuit as the generated state of the quantum circuit of the target quantum system.
  • the quantum circuit generated state refers to the quantum state that is output by inputting the initial quantum state into the quantum circuit structure of the target quantum system and transforming the quantum circuit structure.
  • Step 304 updating the parameters of the Hamiltonian operator based on the generated state of the output quantum circuit.
  • the above algorithm is approximated by variable quantum eigensolution in each discrete time to avoid deep Trott circuits, and the convergence process of dynamics can also be used to avoid the traditional optimizer. the convergence problem.
  • the quantum circuit 410 shown in Figure 4 is taken as an example to avoid the approximation error caused by the poor expressiveness of the quantum circuit itself, and then use the change of quantum circuit parameters over time to update the parameters of the quantum circuit and at the same time update the parameters of the Hamiltonian operator with the design of imaginary time control.
  • Step 305 updating the parameters of the quantum circuit according to the updated parameters of the Hamiltonian operator to obtain the updated target quantum system.
  • Step 306 cyclically update the parameters of the Hamiltonian operator and the quantum circuit until the energy of the target quantum system is a minimum value, and the minimum value corresponds to the final quantum state of the target quantum system; determine that the final quantum state is the minimum eigenvalue of the target quantum system state.
  • the quantum computing method provided by the embodiment of this application combines quantum imaginary time evolution and quantum real-time control theory, and through the analysis of the two mechanisms, a set of control that can be implemented on imaginary time evolution is proposed
  • the method not only reduces the requirements on the initial state and the system, but also reduces the requirements on the control ability. It can provide a strategy of large acceleration while achieving elastic selection, and applies the control to the imaginary time Schrödinger equation. Due to its own dynamics, it will The nature of converging to the ground state can reduce the requirements for control ability, improve the operation speed and accuracy of quantum computers when performing quantum calculations, and speed up the convergence process or reduce the requirements for the initial state as much as possible in the controllable state.
  • the method provided in this embodiment proves its substantial acceleration properties in numerical simulations, and improves the performance of imaginary number time evolution when the eigenenergy difference is too small or the initial state is difficult to select, and improves the performance of quantum computers when performing quantum calculations. Computing speed and computing accuracy;
  • quantum control it is possible to (1) accelerate the evolution process of quantum imaginary time corresponding to the quantum computer; (2) increase the robustness of the quantum computer to noise; Influence; (4) How to use variational quantum eigensolution to approximate quantum control process to realize operation on near-term quantum hardware.
  • the fidelity of the selected initial state and the lowest eigenstate cannot be guaranteed. At this time, the smaller fidelity may affect the convergence speed of the original imaginary time evolution.
  • the burden of initial state selection is reduced by adding additional controls to speed up the process of scaling up the lowest eigenstate.
  • Figure 6 presents the convergence process of the initial state evolution for different authenticity degrees under the HF system. Since the control operator is set to be switched on, there will be an obvious discontinuous turning point, but it can be seen that after the control operator intervenes in the system
  • the curve 610 significantly shortens the convergence time, especially when the fidelity between the initial state and the ground state is lower, the improvement is more significant, and the time to intervene in the system is not long, and the consumption of overall resources hardly increases. Reduces the resource requirements of the quantum computer during the quantum computation.
  • the virtual time evolution is realized by using the control method as an example for further illustration.
  • non-control methods can also be used, such as designing a dynamic unit virtual time d t or using a depth learning and other methods to accelerate the convergence of virtual-time evolution and noise resistance.
  • Fig. 9 is a schematic structural diagram of a quantum computing device provided by an exemplary embodiment of the present application, which includes:
  • the acquisition module 910 is used to determine the initial quantum state of the target quantum system, the quantum circuit corresponding to the target quantum system, and the Hamiltonian operator used to describe the target quantum system, the quantum circuit includes quantum circuit parameters, the The Hamiltonian operator includes a Hamiltonian operator parameter, and the Hamiltonian operator parameter includes a quantum imaginary time parameter; the initial quantum state is input into the quantum circuit, and the quantum state output by the quantum circuit is obtained as Describe the quantum circuit generation state of the target quantum system;
  • An updating module 920 configured to update the parameters of the Hamiltonian operator based on the generated state of the output quantum circuit
  • the updating module 920 is further configured to update the quantum circuit parameters according to the updated Hamiltonian parameters to obtain the updated target quantum system;
  • the updating module 920 is further configured to cyclically update the parameters of the Hamiltonian operator and the parameters of the quantum circuit until the energy of the target quantum system is a minimum value, and the minimum value corresponds to the final quantum of the target quantum system state; determine the final quantum state as the smallest eigenstate of the target quantum system.
  • the Hamiltonian operator used to describe the target quantum system includes an original Hamiltonian operator and a control Hamiltonian operator, and the original Hamiltonian operator is used to provide an evolution trend, so The control Hamiltonian described above is used to provide additional evolution trends that control the evolution process.
  • the Hamiltonian operator used to describe the target quantum system is as follows:
  • ⁇ represents the quantum virtual time parameter
  • ⁇ ( ⁇ )> represents the virtual time eigenstate
  • H p represents the original Hamiltonian
  • H d represents the control Hamiltonian
  • ⁇ ( ⁇ ) represents the The parameters of the Hamiltonian operator.
  • the parameters of the Hamiltonian operator are determined based on the requirement of the first-order partial derivative of the Lyapunov function with respect to time.
  • the requirements for the first-order partial derivative of the Lyapunov function with respect to time are as follows:
  • the parameters of the Hamiltonian operator are as follows:
  • the device further includes:
  • the determining module 930 is configured to determine the control Hamiltonian based on a diagonal matrix composed of an identity matrix and a Pauli Z matrix.
  • the update module 920 is further configured to update the Hamiltonian with the goal of minimizing the energy of the target quantum system.
  • the quantum computing device provided by the embodiment of this application combines quantum imaginary time evolution and quantum real time control theory, and by analyzing the two mechanisms, a set of control that can be implemented on imaginary time evolution is proposed
  • the method not only reduces the requirements on the initial state and the system, but also reduces the requirements on the control ability. It can provide a strategy of large acceleration while achieving elastic selection, and applies the control to the imaginary time Schrödinger equation. Due to its own dynamics, it will The property of converging to the ground state can reduce the requirements for control ability, improve the calculation speed and accuracy of the quantum computer, and speed up the convergence process or reduce the requirements for the initial state as much as possible in the controllable state.
  • the quantum computing device provided by the above embodiment is only illustrated by the division of the above functional modules. In practical applications, the above function distribution can be completed by different functional modules according to the needs, that is, the internal structure of the device Divided into different functional modules to complete all or part of the functions described above.
  • the quantum computing device provided by the above embodiments and the quantum computing method embodiments belong to the same concept, and the specific implementation process is detailed in the method embodiments, and will not be repeated here.
  • FIG. 11 shows a structural block diagram of a computer device 1100 provided by an embodiment of the present application.
  • the computer device 1100 may be a classical computer.
  • the computer device can be used to implement the quantum computing method provided in the above embodiments. Specifically:
  • the computer device 1100 includes a central processing unit (such as a CPU (Central Processing Unit, central processing unit), a GPU (Graphics Processing Unit, a graphics processor) and an FPGA (Field Programmable Gate Array, Field Programmable Logic Gate Array) etc.) 1101, A system memory 1104 including a RAM (Random-Access Memory) 1102 and a ROM (Read-Only Memory) 1103, and a system bus 1105 connecting the system memory 1104 and the central processing unit 1101.
  • the computer device 1100 also includes a basic input/output system (Input Output System, I/O system) 1106 that helps to transmit information between various devices in the server, and is used to store an operating system 1113, an application program 1114 and other program modules 1115 mass storage device 1107.
  • I/O system Input Output System
  • the basic input/output system 1106 includes a display 1108 for displaying information and input devices 1109 such as a mouse and a keyboard for users to input information.
  • input devices 1109 such as a mouse and a keyboard for users to input information.
  • both the display 1108 and the input device 1109 are connected to the central processing unit 1101 through the input and output controller 1110 connected to the system bus 1105 .
  • the basic input/output system 1106 may also include an input-output controller 1110 for receiving and processing input from a keyboard, a mouse, or an electronic stylus, among other devices.
  • input output controller 1110 also provides output to a display screen, printer, or other type of output device.
  • the mass storage device 1107 is connected to the central processing unit 1101 through a mass storage controller (not shown) connected to the system bus 1105 .
  • the mass storage device 1107 and its associated computer-readable media provide non-volatile storage for the computer device 1100 . That is to say, the mass storage device 1107 may include a computer-readable medium (not shown) such as a hard disk or a CD-ROM (Compact Disc Read-Only Memory, CD-ROM) drive.
  • a computer-readable medium such as a hard disk or a CD-ROM (Compact Disc Read-Only Memory, CD-ROM) drive.
  • Computer readable media may comprise computer storage media and communication media.
  • Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data.
  • Computer storage media include RAM, ROM, EPROM (Erasable Programmable Read-Only Memory, Erasable Programmable Read-Only Memory), EEPROM (Electrically Erasable Programmable Read-Only Memory, Electrically Erasable Programmable Read-Only Memory), flash memory or Other solid-state storage technologies, CD-ROM, DVD (Digital Video Disc, high-density digital video disc) or other optical storage, tape cartridges, tapes, disk storage or other magnetic storage devices.
  • the computer storage medium is not limited to the above-mentioned ones.
  • the above-mentioned system memory 1104 and mass storage device 1107 may be collectively referred to as memory.
  • the computer device 1100 can also run on a remote computer connected to the network through a network such as the Internet. That is, the computer device 1100 can be connected to the network 1112 through the network interface unit 1111 connected to the system bus 1105, or in other words, the network interface unit 1111 can also be used to connect to other types of networks or remote computer systems (not shown) .
  • the memory also includes at least one instruction, at least one program, a set of codes, or a set of instructions stored in the memory and configured to be executed by one or more processors , to realize the above-mentioned quantum computing method.
  • FIG. 11 does not constitute a limitation to the computer device 1100, and may include more or less components than shown in the figure, or combine some components, or adopt a different arrangement of components.
  • the embodiment of the present application also provides a computer device, which can be used to implement the quantum computing method provided in the above embodiment. That is to say, the quantum computing method provided in this application can be executed by computer equipment.
  • the computer device may be a mixed device environment of a classical computer and a quantum computer, for example, a classical computer and a quantum computer cooperate to implement the method.
  • classical computers execute computer programs to realize some classical calculations and control quantum computers, and quantum computers realize operations such as control and measurement of qubits.
  • the above-mentioned preparation circuit, PQC and measurement circuit can be set in the quantum computer, and the computer program is executed by the classical computer to control the quantum computer, and the quantum computer is controlled to prepare the initial state of the quantum many-body system through the preparation circuit, and to control the initial state of the quantum many-body system through the PQC.
  • the state is processed, the output state of the PQC is obtained, and the output state of the PQC is measured through the measurement line.
  • classical computers can also execute computer programs to achieve some classical calculations.
  • the above-mentioned computer equipment may also be a separate classical computer, that is, each step of the quantum computing method provided by the present application is executed by a classical computer, for example, a numerical experiment simulation of the above-mentioned method is carried out by a classical computer executing a computer program;
  • the above-mentioned computer equipment may also be a separate quantum computer, that is, each step of the quantum computing method provided in this application is executed by a quantum computer, which is not limited in this application.
  • a computer-readable storage medium is also provided. At least one instruction, at least one program, code set or instruction set are stored in the storage medium, and the at least one instruction, the at least one program , when the code set or the instruction set is executed by the processor, the above quantum computing method can be realized.
  • the computer-readable storage medium may include: ROM (Read Only Memory, read-only memory), RAM (Random Access Memory, random access memory), SSD (Solid State Drives, solid state drive) or an optical disc, etc.
  • the random access memory may include ReRAM (Resistance Random Access Memory, resistive random access memory) and DRAM (Dynamic Random Access Memory, dynamic random access memory).
  • a computer program product or computer program comprising computer instructions stored in a computer readable storage medium.
  • the processor of the computer device reads the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes the above-mentioned quantum computing method.

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Abstract

一种量子计算方法、装置、设备、介质及产品，涉及量子技术领域。该方法包括：步骤110，确定目标量子系统的初始量子态、目标量子系统对应的量子电路和用于描述目标量子系统的哈密顿算符，哈密顿算符参数中包括量子虚时参数；步骤120，将初始量子态输入至量子电路中，得到量子电路输出的量子态为目标量子系统的量子电路生成态；步骤130，基于输出的量子电路生成态更新哈密顿算符参数；步骤140，根据更新后的哈密顿算符参数更新量子电路参数；步骤150，循环更新哈密顿算符参数和量子电路参数，直至目标量子系统的能量为最小值，最小值对应目标量子系统的最终量子态；确定最终量子态为目标量子系统的最小本征态。

Description

量子计算方法、装置、设备、介质及产品
本申请要求于2021年10月20日提交的申请号为202111222031.8、发明名称为“量子体系的本征态获取方法、装置、设备、介质及产品”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本申请实施例涉及量子技术领域，特别涉及一种量子计算方法、装置、设备、介质及产品。
背景技术
随着量子计算的快速发展，量子算法在很多领域都有了重要的应用，其中，求解量子系统的本征态和本征能量是一个非常关键的问题。
在相关技术中，提供了一种虚数时间演化得到最低本征态的方法，将虚时间薛定谔方程中的波函数以特征向量展开表示后，确定最小本征值，由于最小本征值小于任意本征值，当时间趋近无限时，其他本征值都会以指数速度消失，从而给定任意与最小本征值交叠量不为0的波函数，即能够反推得到初始最低本征态。
然而，上述方式中，需要保证起始态与最低本征态的交叠关系，以及其他本征态与最低本征态之差，其间的关系会较大程度的影响收敛速率。
发明内容
本申请实施例提供了一种量子计算方法、装置、设备、介质及产品。所述技术方案如下：
根据本申请实施例的一个方面，提供了一种量子计算方法，所述方法由计算机设备执行，所述方法包括：
确定目标量子系统的初始量子态、所述目标量子系统对应的量子电路和用于描述所述目标量子系统的哈密顿算符，所述量子电路包括量子电路参数，所述哈密顿算符包括哈密顿算符参数，所述哈密顿算符参数中包括量子虚时参数；
将所述初始量子态输入至所述量子电路中，得到所述量子电路输出的量子态为所述目标量子系统的量子电路生成态；
基于所述输出的量子电路生成态更新所述哈密顿算符参数；
根据更新后的哈密顿算符参数更新所述量子电路参数，得到更新后的目标量子系统；
循环更新所述哈密顿算符参数和所述量子电路参数，直至所述目标量子系统的能量为最小值，所述最小值对应所述目标量子系统的最终量子态；
确定最终量子态为所述目标量子系统的最小本征态。
根据本申请实施例的一个方面，提供了一种量子计算装置，所述装置包括：
获取模块，用于确定目标量子系统的初始量子态、所述目标量子系统对应的量子电路和用于描述所述目标量子系统的哈密顿算符，所述量子电路包括量子电路参数，所述哈密顿算符包括哈密顿算符参数，所述哈密顿算符参数中包括量子虚时参数；将所述初始量子态输入至所述量子电路中，得到所述量子电路输出的量子态为所述目标量子系统的量子电路生成态；
更新模块，用于基于所述输出的量子电路生成态更新所述哈密顿算符参数；
所述更新模块，还用于根据更新后的哈密顿算符参数更新所述量子电路参数，得到更新后的目标量子系统；
所述更新模块，还用于循环更新所述哈密顿算符参数和所述量子电路参数，直至所述目标量子系统的能量为最小值，所述最小值对应所述目标量子系统的最终量子态；确定最终量子态为所述目标量子系统的最小本征态。
根据本申请实施例的一个方面，提供了一种计算机设备，所述计算机设备用于执行以实现上述量子计算方法。
根据本申请实施例的一个方面，提供了一种计算机可读存储介质，所述存储介质中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或指令集由所述处理器加载并执行以实现上述量子计算方法。
根据本申请实施例的一个方面，提供了一种计算机程序产品或计算机程序，该计算机程序产品或计算机程序包括计算机指令，该计算机指令存储在计算机可读存储介质中。计算机设备的处理器从计算机可读存储介质读取该计算机指令，处理器执行该计算机指令，使得该计算机设备执行上述量子计算方法。
本申请实施例提供的技术方案可以带来如下有益效果：
将量子虚时间演化和量子实时间控制结合，提出一套可于虚时间演化上实行的控制方法，既减少了对初始态及系统的要求也降低了控制能力的要求，达到弹性选取的同时又能提供大幅度加速的策略，且将控制应用在虚数时间薛定谔方程，由于其本身的动力学会收敛到基态的性质，可以降低对控制能力的要求，提高了量子计算机执行量子计算时的运算速度和准确率，并在可控制的态上尽量加速收敛过程或降低对初始态的要求。
附图说明
图1是本申请一个实施例提供的量子计算方法的流程图；
图2是本申请一个示例性实施例提供的哈密顿算符参数更新过程示意图；
图3是本申请另一个实施例提供的量子计算方法的流程图；
图4是本申请一个实施例提供的量子电路的示意图；
图5是本申请一个实施例提供的演化收敛示意图；
图6是本申请一个实施例提供的在HF系统下对不同本真度的初始态演化的收敛过程示意图；
图7是本申请一个实施例提供的能量收敛结果示意图；
图8是本申请一个实施例提供的在噪声系统下模拟虚时间演化及虚时间控制的收敛情况示意图；
图9是本申请一个实施例提供的量子计算装置的框图；
图10是本申请另一个实施例提供的量子计算装置的框图；
图11是本申请一个实施例提供的计算机设备的结构框图。
具体实施方式
在对本申请实施例进行介绍说明之前，首先对本申请中涉及的一些名词进行解释说明。
1.量子计算：基于量子逻辑的计算方式，存储数据的基本单元是量子比特(qubit)。
2.量子比特：量子计算的基本单元。传统计算机使用0和1作为二进制的基本单元。不同的是量子计算可以同时处理0和1，系统可以处于0和1的线性叠加态：|ψ>＝α|0>+β|1>，这边α，β代表系统在0和1上的复数概率幅。它们的模平方|α| 2，|β| 2分别代表处于0和1的概率。
3.哈密顿量：描述量子系统总能量的一个厄密共轭的矩阵。哈密顿量是一个物理词汇，是一个描述系统总能量的算符，通常以H表示。
4.量子态：在量子力学中，量子态是由一组量子数所确定的微观状态。
5.本征态：在量子力学中，一个力学量所可能取的数值，就是它的算符的全部本征值。本征函数所描写的状态称为这个算符的本征态。在自己的本征态中，这个力学量取确定值，即这个本征态所属的本征值。对于一个哈密顿量矩阵H，满足方程：H|ψ>＝E|ψ>的解称之 为H的本征态|ψ>，具有本征能量E。基态则对应了量子系统能量最低的本征态。
6.量子线路：也称为量子电路，量子通用计算机的一种表示，代表了相应量子算法/程序在量子门模型下的硬件实现。若量子线路中包含可调的控制量子门的参数，则被称为参数化的量子线路(Parameterized Quantum Circuit，简称PQC)或变分量子线路(Variational Quantum Circuit，简称VQC)，两者为同一概念。
7.量子门：在量子计算，特别是量子线路的计算模型里面，一个量子门(Quantum gate，或量子逻辑门)是一个基本的，操作一个小数量量子比特的量子线路。
8.变分量子本征求解器(Variational Quantum Eigensolver，简称VQE)：通过变分线路(即PQC/VQC)实现特定量子系统基态能量的估计，是一种典型的量子经典混合计算范式，在量子化学领域有广泛的应用。
9.非幺正：所谓幺正矩阵，即是满足
Figure PCTCN2021133711-appb-000001
的全部矩阵，所有量子力学直接允许的演化过程，都可以通过幺正矩阵描述。其中，U为幺正矩阵(Unitary Matrix)，也称为酉矩阵、么正矩阵等，
Figure PCTCN2021133711-appb-000002
是U的共轭转置。另外，不满足该条件的矩阵则是非幺正的，其需要通过辅助手段甚至指数多的资源才可在实验上实现，但非幺正矩阵往往具有更强的表达能力和更快的基态投影效果。上述“指数多的资源”是指资源的需求量随着量子比特数量的增加，呈指数级增加，该指数多的资源可以是指需要测量的量子线路的总数是指数多个，也即相应需要指数多的计算时间。
10.泡利算符：也称为泡利矩阵，是一组三个2×2的幺正厄米复矩阵(又称酉矩阵)，一般都以希腊字母σ(西格玛)来表示。其中，泡利X算符为
Figure PCTCN2021133711-appb-000003
泡利Y算符为
Figure PCTCN2021133711-appb-000004
泡利Z算符为
Figure PCTCN2021133711-appb-000005
获取一个量子系统的基态(即最低本征态)，代表着获取该量子系统最稳定的状态，在量子物理和量子化学体系基本性质研究，组合优化问题求解，制药研究等方面具有非常重要的应用。量子计算机的一个重要应用场景就是有效地求解或者表达出量子系统基态。目前，一些研究机构和厂商也在不断研究新的量子计算机，致力于探索基态的求解。
相关技术提供的用于获取量子系统基态的方案的介绍说明。
方案1：基于量子虚时间演化获得最低本征态
虚时演化是求解量子系统基态的一种基本方法。
含时薛定谔方程为：
Figure PCTCN2021133711-appb-000006
其中H是目标量子系统的哈密顿量，ψ(t)表示目标量子系统在t时刻的量子态，i和
Figure PCTCN2021133711-appb-000007
为虚时单位，即量子虚时参数。
将含时薛定谔方程中的实数时间t以虚数时间
Figure PCTCN2021133711-appb-000008
替换，并改写上述含时薛定谔方程，得到如下虚时间薛定谔方程：
Figure PCTCN2021133711-appb-000009
此时，该虚时间薛定谔方程的解为：
|ψ(σ)>＝e -Hτ|ψ(0)>
由于e -Hτ非幺正算符，需要对其做归一化处理：
Figure PCTCN2021133711-appb-000010
|ψ(τ)>＝A(τ)e -Hτ|ψ(0)>
Figure PCTCN2021133711-appb-000011
其中，E τ表示τ时刻的本征值。
将虚时间薛定谔方程中的波函数以特征向量展开表示为：
Figure PCTCN2021133711-appb-000012
其中，E i为本征能量，E 0＜E i，E 0为基态能量，c i为展开系数。
由于E 0＜E i，当时间趋近无限时，其他本征态都会以指数速度消失，也即，随着ψ(τ)的演化，其它态会衰减的更快，最后只留下基态：
Figure PCTCN2021133711-appb-000013
因此，给定任意波函数，只要确保波函数与最低本征态交叠量c 0不为0，在时间τ时可得波函数：
Figure PCTCN2021133711-appb-000014
并由此能够反推得到初始最低本征态：
Figure PCTCN2021133711-appb-000015
方案2：实数时间含时薛定谔方程之量子控制方法
首先，将含时薛定谔方程中的原始哈密顿算符加上控制哈密顿算符，得到如下量子动力学控制方程：
Figure PCTCN2021133711-appb-000016
其中，H p表示目标哈密顿算符，也即原始哈密顿算符，H d表示控制哈密顿算符，β(t)为随时间变换参数。
在上述量子动力学控制方程的基础上，根据前一单位时间Δt的输出结果作为参考，设计反馈型控制来最小化<ψ(t)|H p|ψ(t)>，目标为设计β(t)来使
Figure PCTCN2021133711-appb-000017
根据
Figure PCTCN2021133711-appb-000018
使β(t)＝-wf(t,A(t))，其中，w＞0，f(t,A(t))为任意连续函数符合f(t,0)＝0且f(t,A(t))×A(t)＞0，对于任意A(t)不为0，如：f(t,A(t))＝-A(t)。
方案3：基于经典优化算法的变分量子本征求解
VQE(Variational Quantum Eigensolver，变分量子本征求解器)是一种可以运行在NISQ量子设备上的有容错能力的量子算法，能够模拟目标量子系统的基态。
根据变分原理可知
Figure PCTCN2021133711-appb-000019
将求解最低本征向量的问题描述为优化问题
Figure PCTCN2021133711-appb-000020
可选地，用经典优化算法如最速下降法、牛顿法、共轭方向法等解此优化问题。变分量子本征求解其难点在于量子电路的设计，在保证量子电路能生成目标态的同时还必须尽量让参数空间平滑，同时量子电路深度也不能过深以影响量子计算机端的执行。
然而，上文中介绍的方案1，量子虚时间演化需要保证起始态与最低本征态的交叠关系及其余本征值与最低本征值的差，且此关系会大程度影响收敛速率，其他本征态的交叠程度也会影响收敛的效果及速度。在量子计算机上操作也需要对算符做归一化处理，产生额外的计算消耗。
上文中介绍的方案2，基于实数时间含时薛定谔方程的量子控制方法，需要保证所选的控制哈密顿算符有足够的控制能力，且在非完全控制下对于初始态及收敛过程中所有出现的态要求极高，当其中有任意的态不符合可控条件便可能出现无法收敛的情况。
上文中介绍的方案3，基于经典优化算法的变分量子本征求解在量子计算机上实行较为简单，单次更新参数所需要的测量也较少，但是随着系统大小的提升会遇到拟设量子电路设计及贫瘠高原优化问题。
本申请提出一个全新的技术方案，将控制应用在虚数时间含時薛定諤方程，由于其本身的动力学会收敛到基态的性质，可以降低对控制能力的要求，并在可控制的态上尽量加速收敛过程或降低对初始态的要求；使用量子控制的辅助，可以降低对各条件的要求并减少收敛所需时间，同时少量或不增加原本每一步所需的计算资源以达到整体计算资源的减少；利用参数更新对动力学的近似来更新参数经典优化算法的贫瘠高原问题并降低对拟设量子电路的设计要求。
在介绍本申请方法实施例之前，先对本申请方法的执行环境进行介绍说明。
本申请实施例提供的量子计算方法，其可以由经典计算机(如PC)执行实现，例如通过经典计算机执行相应的计算机程序以实现该方法；也可以在经典计算机和量子计算机的混合设备环境下执行，例如由经典计算机和量子计算机配合来实现该方法。示例性地，量子计算机用于实现本申请实施例中对本征态的求解，经典计算机用于实现本申请实施例中除本征态求解问题之外的其他步骤。
在下述方法实施例中，为了便于说明，仅以各步骤的执行主体为计算机设备进行介绍说明。应当理解的是，该计算机设备可以是经典计算机，也可以包括经典计算机和量子计算机的混合执行环境，本申请实施例对此不作限定。
请参考图1，其示出了本申请一个实施例提供的量子计算方法的流程图。以方法各步骤的执行主体是计算机设备为例进行说明。该方法可以包括：
步骤110，确定目标量子系统的初始量子态、目标量子系统对应的量子电路和用于描述目标量子系统的哈密顿算符，量子电路包括量子电路参数，哈密顿算符包括哈密顿算符参数，哈密顿算符参数中包括量子虚时参数。
初始量子态是用于输入至目标量子系统，从而得到当前目标量子系统的输出量子态的输入态。
目标量子系统对应的量子电路为该目标量子系统在执行量子计算时所采用的量子电路，也即，通过该量子电路对初始量子态的变换，作为对该初始量子态的量子计算过程。
量子电路参数为量子电路中各个变换节点对应的变换参数，根据量子电路参数对量子态 进行变换，从而实现不同量子电路的不同量子计算过程。
本实施例中，用于描述目标量子系统的哈密顿算符中包括原始哈密顿算符和控制哈密顿算符。原始哈密顿算符用于提供演化趋势，控制哈密顿算符用于提供控制演化过程的额外演化趋势。且哈密顿算符包括哈密顿算符参数，哈密顿算符参数中包括量子虚时参数。
可选地，哈密顿算符以量子动力学表达的方式对目标量子系统进行描述。其中，该量子动力学表达中包括原始哈密顿算符和控制哈密顿算符。
步骤120，将初始量子态输入至量子电路中，得到量子电路输出的量子态为目标量子系统的量子电路生成态。
量子电路生成态是指将初始量子态输入至目标量子系统的量子电路结构中，通过在该量子电路结构上进行变换，从而输出的量子态。
步骤130，基于输出的量子电路生成态更新哈密顿算符参数。
在一些实施例中，根据目标量子系统的量子电路生成态，能够得到该目标量子系统对应的本征态，从而以最小化本征态为目标调整哈密顿算符参数。在一些实施例中，目标量子系统的量子电路生成态用于近似表征目标量子系统的本征态。
在一些实施例中，上述量子动力学表达为将含时薛定谔方程中的实数时间替换为虚数时间，并在原始哈密顿算符的基础上增加控制哈密顿算符后得到的动力学表达。
示意性的，用于以量子动力学表达描述目标量子系统的哈密顿算符如下：
Figure PCTCN2021133711-appb-000021
其中，τ表示量子虚时参数，|ψ(τ)>表示虚时本征态，H p表示所述原始哈密顿算符，H d表示所述控制哈密顿算符，β(τ)表示所述哈密顿算符参数。
接下来，对哈密顿算符参数β(τ)的设计思路进行介绍。哈密顿算符参数是基于李雅普诺夫函数对时间的一阶偏导要求确定的。
本实施例中，需要设计β(τ)来控制目标量子系统演化向最低本征态。通过李雅普诺夫函数可以提供对于β(τ)函数的设计思路。首先从基于平均值的李雅普诺夫函数出发：
V(ψ(τ))＝<ψ(τ)|(H p-E 0)|ψ(τ)>
其中，E 0为H p的最小本征值，使H p-E 0为半正定矩阵，通过李雅普诺夫函数对时间的一阶偏导可得：
Figure PCTCN2021133711-appb-000022
其中，
Figure PCTCN2021133711-appb-000023
用于表示原始哈密顿算符提供的演化趋势，且
Figure PCTCN2021133711-appb-000024
小于等于0；β(τ)(<ψ(τ)||{H d,H p}||ψ(τ)>-2<H d><H p>)用于表示控制哈密顿算符提供的额外演化趋势。
由于
Figure PCTCN2021133711-appb-000025
小于等于0，在一些实施例中，哈密顿算符参数如下：
β(τ)＝(<ψ(τ)||{H d,H p}||ψ(τ)>-2<H d><H p>)
从而确保β(0)＝0且
Figure PCTCN2021133711-appb-000026
此时控制函数的临界点为所有本征态，其中最大值对应最大本征值的本征态，最小值对应最小本征值的本征态，其余本征态为过渡态。此时从控制方法的角度来选择，必须使初始态尽量靠近目标本征态来达到控制目的。
另一方面，由于虚时间演化过程中会以指数速度收敛到当前最低能量的本征态，可以藉由调控两者的性质来达到互补加速的作用。提高了量子计算机在执行量子计算时的收敛速度， 从而提高了量子计算的运算效率。
步骤140，根据更新后的哈密顿算符参数更新量子电路参数，得到更新后的目标量子系统。
可选地，在基于变分算法架构来近似模拟虚时动力学函数演化的基础上，根据McLachlan变分原理：
Figure PCTCN2021133711-appb-000027
可得到波函数的量子电路参数随时间变化为：
Figure PCTCN2021133711-appb-000028
Figure PCTCN2021133711-appb-000029
Figure PCTCN2021133711-appb-000030
其中φ(τ)表示本征态，θ i表示第i个量子电路参数。
从而根据更新后的哈密顿算符参数更新目标量子系统对应的量子电路参数。
步骤150，循环更新哈密顿算符参数和量子电路参数，直至目标量子系统的能量为最小值，最小值对应所述目标量子系统的最终量子态；确定最终量子态为目标量子系统的最小本征态。
示意性的，请参考图2，其示出了本申请一个示例性实施例提供的哈密顿算符参数更新过程示意图，如图2所示，该循环过程中主要包括三个部分：
量子电路生成态210、更新哈密顿算符参数220和更新量子电路参数230。
其中，量子电路生成态210过程中，将初始态输入至量子电路结构中，通过量子电路结构对初始态进行变换，从而输出量子态作为量子电路生成态。
根据量子电路生成态210确定对应的本征态后，以最小化本征态为目标，执行更新哈密顿算符参数220的过程，对哈密顿算符参数进行调整。
以调整后的哈密顿算符参数为基础，执行更新量子电路参数230的过程，对目标量子系统的量子电路参数进行对应的更新。
上述三个过程形成循环，直至收敛至最小本征态。
综上所述，本申请实施例提供的量子计算方法，将量子虚时间演化和量子实时间控制理论结合，透过将两者机制做出分析，提出一套可于虚时间演化上实行的控制方法，既减少了对初始态及系统的要求也降低了控制能力的要求，达到弹性选取的同时又能提供大幅度加速的策略，且将控制应用在虚数时间薛定谔方程，由于其本身的动力学会收敛到基态的性质，可以降低对控制能力的要求，提高了量子计算机执行量子计算时的运算速度以及准确率，并在可控制的态上尽量加速收敛过程或降低对初始态的要求。
本申请实施例提供的方法，将含时薛定谔方程中的实数时间替换为虚数时间，由于虚数时间本身的动力学会收敛到基态的性质，可以降低对控制能力的要求，并在可控制的态上尽量加速收敛过程或降低对初始态的要求；另外，使用量子控制的辅助，可以降低对各条件的要求并减少收敛所需时间，同时减少或不增加原本每一步所需的量子计算机的运算资源以达到整体运算资源的减少。
本申请实施例提供的方法，根据控制能力的定义，需要保证目标哈密顿算符及控制哈密顿算符为所在李代数下的生成群，本实施例中，在虚时间下只要使控制能力为部份可控，因其动力学会收敛到最低本征态的性质，便可利用部份可控达到关键控制，实现量子计算机整 体运算加速的同时又能降低整体控制的额外运算。主要的控制思路是根据距离本征态的距离来调整，本身演化的性质及控制所提供的额外引导在不同的情况下提供各自的优势以达到稳定提速并减少对系统及初始态选择的依赖。
在一些实施例中，除了上述β(τ)函数的设计以外，控制哈密顿算符的选择也会较大程度的影响收敛过程。图3是本申请另一个示例性实施例提供的量子计算方法流程图，该方法各步骤的执行主体可以是计算机设备。该方法可以包括：
步骤301，基于单位矩阵和泡利Z矩阵所组成的对角矩阵确定控制哈密顿算符。
在控制哈密顿算符的选择上，直观的参考是从控制能力的角度出发，选择具有完全控制能力的控制算符集合在理论上就能够收敛到任何态。
在上述获取量子系统基态的方案1中，归一化虚时间演化的完全控制能力在特洛特分解后为：
Figure PCTCN2021133711-appb-000031
由贝克-坎贝尔-豪斯多夫公式可知当Δτ足够小时，假设H d和H p与其迭代交换子能展开整个李群，此时任意幺正转换皆可用此组目标算符及控制算符表示。
在实数时间量子控制中，假使选择控制能力不佳的控制算符，由于可能无法产生所需要的幺正算符，会使收敛过程收敛到不可控区域。然而，在虚时间演化中其本身的动力学性质提供了只要初始态与本征态重叠不为0，必有一组收敛到目标态的路径态集合，如果控制算符要达到加速的效果只需要在其可控区域提供合理的控制，既能加速原本虚时间演化的收敛速度，也可以设计其控制能力在重叠为0等虚实动力无法收敛之区域提供演化路径给虚时间演化收敛。
根据控制能力的定义，需要保证原始哈密顿算符及控制哈密顿算符为所在李代数下的生成群。然而随着系统增大，如何选取合适的控制哈密顿算符及单位离散时间使其能足够的近似动力学演化过程将会是一个难题。
本申请实施例中，在虚时间下只要使控制能力为部份可控，因其动力学会收敛到最低本征态的性质，便可利用部分可控达到关键控制，实现整体加速的同时又能降低整体控制的额外计算。主要的控制思路是根据距离本征态的距离来调整，本身演化的性质及控制所提供的额外引导在不同的情况下提供各自的优势以达到稳定提速并减少对系统及初始态选择的依赖。
根据李雅普诺夫函数的一阶导数我们可以观察出动力学演化本身的趋势及控制所提供的额外趋势分别为：
Figure PCTCN2021133711-appb-000032
D d(ψ(τ))＝β(τ)(<ψ(τ)|{H d,H p}|ψ(τ)>-2<H d><H p>)
原动力学收敛中非最低本征值与最低本征值的差会影响收敛速度，此时H p本身所能提供的收敛趋势D p将不会如差值大的系统明显，此时H d就能提供额外的收敛趋势D d来使系统加速收敛。
但当ψ(τ)接近H p本征态D p和D d皆会越靠近零，此时由于D d相较于D p有在所有本征态都是临界点的性质，可能会导致演化过程中遇到最低本征态占比过少而收敛至其他本征态的情况。此外，D d在H d的本征态周围也会趋向零，所以需要判断何时才是D d适合提供演化动力的时机或者也可以藉由H d的选择来使其在本征态周围控制能力较差来回避此问题。在此专案中我们选用单位矩阵及泡利Z矩阵所组成的对角矩阵作为控制算符的选项，在Jordan-Wigner燮换对应下为单电子动能项及原子核对单电子的力。此外D p还有包含其他当前态的性质，假设所有本征值皆为实数，先将其对本征态做展开可得：
Figure PCTCN2021133711-appb-000033
假设目前收敛到|E 0>和|E k>两个本征态叠加，此时上式为：
Figure PCTCN2021133711-appb-000034
由于λ 0为最低能量并且值为负，则当|E k>越靠近最低本征态时，其能量λ k也越负，在相同的C k下D p的数值越小，因此相同保真度下，D p的数值也可能不一样，当利用D p的大小当做控制截断的参考时，在相同保真度下混成态占比较多为高能量态时控制算符会更容易被触发，因此对不同的系统及起始态，可以利用不同的设计来达到加速或是控制的效果。
藉由结合H p及H d在不同状态下的动力学现象，能够实现系统对本征态演化的控制，由调控来让量子系统在目标态附近稳定以达到朝目标收敛的目的，并减少在非目标区间的停留时间已达到快速且可控的收敛，并提供最低本征态外所有本征态获得的思路，如在本征态周围使控制算符的影响放大，此时系统会收敛到此本征态附近，当收敛到的态与所有能量小于此本征态的低能本征态之重叠够小，此时原虚时演化会倾向于收敛到此本征态上。另外，由于结合了H p及H d在不同状态下的动力学现象，通过H d调控量子系统在目标态附近稳定，从而能够提高量子计算机执行量子计算的过程中的稳定性以及可靠性。
步骤302，将含时薛定谔方程中的实数时间替换为虚数时间，并在原始哈密顿算符的基础上增加控制哈密顿算符，对目标量子系统进行描述。
步骤303，将初始量子态输入至量子电路中，得到量子电路输出的量子态为目标量子系统的量子电路生成态。
量子电路生成态是指将初始量子态输入至目标量子系统的量子电路结构中，通过在该量子电路结构上进行变换，从而输出的量子态。
步骤304，基于输出的量子电路生成态更新哈密顿算符参数。
示意性的，将上述算法在每次离散时间内以变分量子本征求解近似，以避免产生较深的特洛特电路，也可以利用动力学的收敛过程来避免传统优化器所会遇到的收敛问题。首先，选择表现力较好的量子电路，示意性的，如图4示出的量子电路410为例，以避免量子电路本身表现力太差造成的近似误差，再利用量子电路参数随时间的变化来更新量子电路参数并同时以虚时间控制的设计来更新哈密顿算符参数。
步骤305，根据更新后的哈密顿算符参数更新量子电路参数，得到更新后的目标量子系统。
步骤306，循环更新哈密顿算符参数和量子电路参数，直至目标量子系统的能量为最小值，最小值对应所述目标量子系统的最终量子态；确定最终量子态为目标量子系统的最小本征态。
综上所述，本申请实施例提供的量子计算方法，将量子虚时间演化和量子实时间控制理论结合，透过将两者机制做出分析，提出一套可于虚时间演化上实行的控制方法，既减少了对初始态及系统的要求也降低了控制能力的要求，达到弹性选取的同时又能提供大幅度加速的策略，且将控制应用在虚数时间薛定谔方程，由于其本身的动力学会收敛到基态的性质，可以降低对控制能力的要求，提高了量子计算机执行量子计算时的运算速度以及准确率，并在可控制的态上尽量加速收敛过程或降低对初始态的要求。
本实施例提供的方法，在数值模拟上证明其大幅的加速性质，并且提升在本征能量差太小或初始态难以选取的情况下虚数时间演化的表现，提高了量子计算机执行量子计算时的运算速度以及运算准确率；
提供变分量子本征求解的近似手段，使其可取代变分算法中的经典优化器，实现短期量子计算机上的可执行性；利用控制方法来提供噪声对抗能力，提高了量子计算机执行量子计算时的收敛速度以及运算准确率，以及提高了量子计算机执行量子计算的过程中的稳定性以及可靠性。
从而，从量子控制的角度出发可以(1)加速量子计算机对应的量子虚时间演化的过程；(2)增加量子计算机对噪声的鲁棒性；(3)降低初始态对虚时间演化动力学的影响；(4)如何利用变分量子本征求解来近似量子控制过程以实现于近期的量子硬件上操作。
示意性的，本申请实施例提供的方法所产生的有益效果包括如下：
1、加速能量差较小系统之基态收敛
在HF分子键长为
Figure PCTCN2021133711-appb-000035
的系统下以8个量子比特对其进行模拟计算，在起始态为最大均匀混合态的模拟中可以看到巨大的提速，由于系统中第一激发态(第二低能量本征态)与基态(最低能量本征态)间的能量差距过小，ΔE＝0.015hatree，原版本虚时间演化的动力学其指数收敛的优势无法再少步数内便很好地表现出来。此时由外加的控制项在少量步数做调控便达到将初始态将其快速带往基态的收敛路径。示意性的，如图5所示，本申请实施例提供的方法的控制收敛速度曲线510明显优于相关技术中的收敛速度曲线520。提高了量子计算机在执行量子计算时的收敛速度，进而提高其整体运算速度。
2、降低虚时间演化初始态选择的依赖
当系统增大或较为复杂时，无法保证所选初始态与最低本征态的保真度，此时较小的保真度可能会影响原始虚时间演化的收敛速度，而本申请实施例中通过加入额外的控制加速最低本征态放大的过程,以此来降低对于初始态选择的负担。
图6呈现在HF系统下对不同本真度的初始态演化的收敛过程，由于控制算符设置为开关启动，因此会有明显的不连续转折点，但可以看到在控制算符介入系统后的曲线610显著的缩短了收敛时长，尤其在初始态与基态的保真度越低的情况下提升越显著，且介入系统的时间也不长，对整体资源的消耗也几乎没有增加。减少了量子计算机在量子计算过程中的资源需求。
3、相比实数时间量子控制系统降低控制算符要求及控制步数
在实时间量子控制中，选择控制能力较差的控制算符会出现部分态无法控制导致无法收敛的情况，然而在虚时间量子控制中由于有虚时间演化本身的动力学，控制算符并不像实数时间是唯一使系统收敛的动力源。
此时只需确定何时使用所选择的控制算符便能达到加速系统收敛的目的，与此同时实时控制会收敛在控制算符无法控制的区间，且无法保证此区间在目标态周围，除非控制算符有完全控制能力，图7为H 2键长
Figure PCTCN2021133711-appb-000036
系统的能量收敛结果，可以明显看到在最大均匀混和初始态及对角系列控制算符H d，实时间控制曲线710会收敛到其无法控制的区间，虚时控制曲线720不只收敛速度比虚时演化快且也没有如实时演化对控制能力的高度要求。
4、在噪声系统下有较好的表现
如图8所示，在噪声系统下模拟虚时间演化及虚时间控制两者的收敛情况，可以明显看出在噪声导致反弹时，由于虚时间控制可以更快的收敛，整体能量也最终能收敛到目标能量，如图8所示出的曲线810和曲线820。
值得注意的是，本申请实施例中，以利用控制方法实现虚时间演化为例进行更说明，在一些实施例中，还可以利用非控制方法如设计动态的单位虚时间d t或是采用深度学习等方式来加速虚时演化的收敛及噪声抗性。
图9是本申请一个示例性实施例提供了的量子计算装置的结构示意图，该装置包括：
获取模块910，用于确定目标量子系统的初始量子态、所述目标量子系统对应的量子电 路和用于描述所述目标量子系统的哈密顿算符，所述量子电路包括量子电路参数，所述哈密顿算符包括哈密顿算符参数，所述哈密顿算符参数中包括量子虚时参数；将所述初始量子态输入至所述量子电路中，得到所述量子电路输出的量子态为所述目标量子系统的量子电路生成态；
更新模块920，用于基于所述输出的量子电路生成态更新所述哈密顿算符参数；
所述更新模块920，还用于根据更新后的哈密顿算符参数更新所述量子电路参数，得到更新后的目标量子系统；
所述更新模块920，还用于循环更新所述哈密顿算符参数和所述量子电路参数，直至所述目标量子系统的能量为最小值，所述最小值对应所述目标量子系统的最终量子态；确定最终量子态为所述目标量子系统的最小本征态。
在一个可选的实施例中，用于描述所述目标量子系统的哈密顿算符中包括原始哈密顿算符和控制哈密顿算符，所述原始哈密顿算符用于提供演化趋势，所述控制哈密顿算符用于提供控制演化过程的额外演化趋势。
在一个可选的实施例中，用于描述所述目标量子系统的哈密顿算符如下：
Figure PCTCN2021133711-appb-000037
其中，τ表示量子虚时参数，|ψ(τ)>表示虚时本征态，H p表示所述原始哈密顿算符，H d表示所述控制哈密顿算符，β(τ)表示所述哈密顿算符参数。
在一个可选的实施例中，所述哈密顿算符参数是基于李雅普诺夫函数对时间的一阶偏导要求确定的。
在一个可选的实施例中，所述李雅普诺夫函数对时间的一阶偏导要求如下：
Figure PCTCN2021133711-appb-000038
其中，
Figure PCTCN2021133711-appb-000039
用于表示所述原始哈密顿算符提供的演化趋势，且
Figure PCTCN2021133711-appb-000040
小于等于0；β(τ)(<ψ(τ)||{H d,H p}||ψ(τ)>-2<H d><H p>)用于表示所述控制哈密顿算符提供的额外演化趋势。
在一个可选的实施例中，所述哈密顿算符参数如下：
β(τ)＝(<ψ(τ)||{H d,H p}||ψ(τ)>-2<H d><H p>)
在一个可选的实施例中，如图10所示，所述装置还包括：
确定模块930，用于基于单位矩阵和泡利Z矩阵所组成的对角矩阵确定所述控制哈密顿算符。
在一个可选的实施例中，所述更新模块920，还用于以最小化所述目标量子系统的能量为目标，更新所述哈密顿。
综上所述，本申请实施例提供的量子计算装置，将量子虚时间演化和量子实时间控制理论结合，透过将两者机制做出分析，提出一套可于虚时间演化上实行的控制方法，既减少了对初始态及系统的要求也降低了控制能力的要求，达到弹性选取的同时又能提供大幅度加速的策略，且将控制应用在虚数时间薛定谔方程，由于其本身的动力学会收敛到基态的性质，可以降低对控制能力的要求，提高了量子计算机的计算速度以及准确率，并在可控制的态上尽量加速收敛过程或降低对初始态的要求。
需要说明的是：上述实施例提供的量子计算装置，仅以上述各功能模块的划分进行举例说明，实际应用中，可以根据需要而将上述功能分配由不同的功能模块完成，即将设备的内部结构划分成不同的功能模块，以完成以上描述的全部或者部分功能。另外，上述实施例提 供的量子计算装置与量子计算方法实施例属于同一构思，其具体实现过程详见方法实施例，这里不再赘述。
请参考图11，其示出了本申请一个实施例提供的计算机设备1100的结构框图。该计算机设备1100可以是经典计算机。该计算机设备可用于实施上述实施例中提供的量子计算方法。具体来讲：
该计算机设备1100包括中央处理单元(如CPU(Central Processing Unit，中央处理器)、GPU(Graphics Processing Unit，图形处理器)和FPGA(Field Programmable Gate Array，现场可编程逻辑门阵列)等)1101、包括RAM(Random-Access Memory，随机存取存储器)1102和ROM(Read-Only Memory，只读存储器)1103的系统存储器1104，以及连接系统存储器1104和中央处理单元1101的系统总线1105。该计算机设备1100还包括帮助服务器内的各个器件之间传输信息的基本输入/输出系统(Input Output System，I/O系统)1106，和用于存储操作系统1113、应用程序1114和其他程序模块1115的大容量存储设备1107。
可选地，该基本输入/输出系统1106包括有用于显示信息的显示器1108和用于用户输入信息的诸如鼠标、键盘之类的输入设备1109。其中，该显示器1108和输入设备1109都通过连接到系统总线1105的输入输出控制器1110连接到中央处理单元1101。该基本输入/输出系统1106还可以包括输入输出控制器1110以用于接收和处理来自键盘、鼠标、或电子触控笔等多个其他设备的输入。类似地，输入输出控制器1110还提供输出到显示屏、打印机或其他类型的输出设备。
可选地，该大容量存储设备1107通过连接到系统总线1105的大容量存储控制器(未示出)连接到中央处理单元1101。该大容量存储设备1107及其相关联的计算机可读介质为计算机设备1100提供非易失性存储。也就是说，该大容量存储设备1107可以包括诸如硬盘或者CD-ROM(Compact Disc Read-Only Memory，只读光盘)驱动器之类的计算机可读介质(未示出)。
不失一般性，该计算机可读介质可以包括计算机存储介质和通信介质。计算机存储介质包括以用于存储诸如计算机可读指令、数据结构、程序模块或其他数据等信息的任何方法或技术实现的易失性和非易失性、可移动和不可移动介质。计算机存储介质包括RAM、ROM、EPROM(Erasable Programmable Read-Only Memory，可擦写可编程只读存储器)、EEPROM(Electrically Erasable Programmable Read-Only Memory，电可擦写可编程只读存储器)、闪存或其他固态存储技术，CD-ROM、DVD(Digital Video Disc，高密度数字视频光盘)或其他光学存储、磁带盒、磁带、磁盘存储或其他磁性存储设备。当然，本领域技术人员可知该计算机存储介质不局限于上述几种。上述的系统存储器1104和大容量存储设备1107可以统称为存储器。
根据本申请实施例，该计算机设备1100还可以通过诸如因特网等网络连接到网络上的远程计算机运行。也即计算机设备1100可以通过连接在该系统总线1105上的网络接口单元1111连接到网络1112，或者说，也可以使用网络接口单元1111来连接到其他类型的网络或远程计算机系统(未示出)。
所述存储器还包括至少一条指令、至少一段程序、代码集或指令集，该至少一条指令、至少一段程序、代码集或指令集存储于存储器中，且经配置以由一个或者一个以上处理器执行，以实现上述量子计算方法。
本领域技术人员可以理解，图11中示出的结构并不构成对计算机设备1100的限定，可以包括比图示更多或更少的组件，或者组合某些组件，或者采用不同的组件布置。
本申请实施例还提供了一种计算机设备，该计算机设备可用于实施上述实施例中提供的量子计算方法。也就是说，本申请提供的量子计算方法，可以由计算机设备执行。该计算机设备可以是经典计算机和量子计算机的混合设备环境，例如由经典计算机和量子计算机配合来实现该方法。在经典计算机和量子计算机的混合设备环境下，由经典计算机执行计算机程 序以实现一些经典计算以及对量子计算机进行控制，由量子计算机实现对量子比特的控制和测量等操作。例如，上述制备线路、PQC和测量线路可以设置在量子计算机中，由经典计算机执行计算机程序以对量子计算机进行控制，控制量子计算机进行通过制备线路制备量子多体系统的初态、通过PQC对初态进行处理，得到PQC的输出态、通过测量线路对PQC的输出态进行测量等操作。另外，经典计算机还可以执行计算机程序以实现一些经典计算。
在一些实施例中，上述计算机设备也可以是单独的经典计算机，即本申请提供的量子计算方法各步骤均由经典计算机来执行，例如通过经典计算机执行计算机程序来对上述方法进行数值实验模拟；或者，上述计算机设备也可以是单独的量子计算机，即本申请提供的量子计算方法各步骤均由量子计算机来执行，本申请对此不作限定。
在示例性实施例中，还提供了一种计算机可读存储介质，所述存储介质中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或所述指令集在被处理器执行时以实现上述量子计算方法。
可选地，该计算机可读存储介质可以包括：ROM(Read Only Memory，只读存储器)、RAM(Random Access Memory，随机存取记忆体)、SSD(Solid State Drives，固态硬盘)或光盘等。其中，随机存取记忆体可以包括ReRAM(Resistance Random Access Memory,电阻式随机存取记忆体)和DRAM(Dynamic Random Access Memory，动态随机存取存储器)。
在示例性实施例中，还提供了一种计算机程序产品或计算机程序，该计算机程序产品或计算机程序包括计算机指令，该计算机指令存储在计算机可读存储介质中。计算机设备的处理器从计算机可读存储介质读取该计算机指令，处理器执行该计算机指令，使得该计算机设备执行上述量子计算方法。

Claims (19)

  1. 一种量子计算方法，所述方法由计算机设备执行，所述方法包括：
    确定目标量子系统的初始量子态、所述目标量子系统对应的量子电路和用于描述所述目标量子系统的哈密顿算符，所述量子电路包括量子电路参数，所述哈密顿算符包括哈密顿算符参数，所述哈密顿算符参数中包括量子虚时参数；
    将所述初始量子态输入至所述量子电路中，得到所述量子电路输出的量子态为所述目标量子系统的量子电路生成态；
    基于所述输出的量子电路生成态更新所述哈密顿算符参数；
    根据更新后的哈密顿算符参数更新所述量子电路参数，得到更新后的目标量子系统；
    循环更新所述哈密顿算符参数和所述量子电路参数，直至所述目标量子系统的能量为最小值，所述最小值对应所述目标量子系统的最终量子态；
    确定所述最终量子态为所述目标量子系统的最小本征态。
  2. 根据权利要求1所述的方法，其中，
    用于描述所述目标量子系统的哈密顿算符中包括原始哈密顿算符和控制哈密顿算符，所述原始哈密顿算符用于提供演化趋势，所述控制哈密顿算符用于提供控制演化过程的额外演化趋势。
  3. 根据权利要求2所述的方法，其中，用于描述所述目标量子系统的哈密顿算符如下：
    Figure PCTCN2021133711-appb-100001
    其中，τ表示量子虚时参数，|ψ(τ)>表示虚时本征态，H p表示所述原始哈密顿算符，H d表示所述控制哈密顿算符，β(τ)表示所述哈密顿算符参数。
  4. 根据权利要求3所述的方法，其中，
    所述哈密顿算符参数是基于李雅普诺夫函数对时间的一阶偏导要求确定的。
  5. 根据权利要求4所述的方法，其中，所述李雅普诺夫函数对时间的一阶偏导要求如下：
    Figure PCTCN2021133711-appb-100002
    其中，
    Figure PCTCN2021133711-appb-100003
    用于表示所述原始哈密顿算符提供的演化趋势，且
    Figure PCTCN2021133711-appb-100004
    小于等于0；β(τ)(<ψ(τ)||{H d,H p}||ψ(τ)>-2<H d><H p>)用于表示所述控制哈密顿算符提供的额外演化趋势。
  6. 根据权利要求5所述的方法，其中，所述哈密顿算符参数如下：
    β(τ)＝(<ψ(τ)||{H d,H p}||ψ(τ)>-2<H d><H p>)。
  7. 根据权利要求5所述的方法，其中，所述方法还包括：
    基于单位矩阵和泡利Z矩阵所组成的对角矩阵确定所述控制哈密顿算符。
  8. 根据权利要求1至7任一所述的方法，其中，所述基于所述输出的量子电路生成态更新所述哈密顿算符参数，包括：
    以最小化所述目标量子系统的能量为目标，更新所述哈密顿算符参数。
  9. 一种量子计算装置，所述装置包括：
    获取模块，用于确定目标量子系统的初始量子态、所述目标量子系统对应的量子电路和用于描述所述目标量子系统的哈密顿算符，所述量子电路包括量子电路参数，所述哈密顿算符包括哈密顿算符参数，所述哈密顿算符参数中包括量子虚时参数；将所述初始量子态输入至所述量子电路中，得到所述量子电路输出的量子态为所述目标量子系统的量子电路生成态；
    更新模块，用于基于所述输出的量子电路生成态更新所述哈密顿算符参数；
    所述更新模块，还用于根据更新后的哈密顿算符参数更新所述量子电路参数，得到更新后的目标量子系统；
    所述更新模块，还用于循环更新所述哈密顿算符参数和所述量子电路参数，直至所述目标量子系统的能量为最小值，所述最小值对应所述目标量子系统的最终量子态；确定最终量子态为所述目标量子系统的最小本征态。
  10. 根据权利要求9所述的装置，其中，
    用于描述所述目标量子系统的哈密顿算符中包括原始哈密顿算符和控制哈密顿算符，所述原始哈密顿算符用于提供演化趋势，所述控制哈密顿算符用于提供控制演化过程的额外演化趋势。
  11. 根据权利要求10所述的装置，其中，用于描述所述目标量子系统的哈密顿算符如下：
    Figure PCTCN2021133711-appb-100005
    其中，τ表示量子虚时参数，|ψ(τ)>表示虚时本征态，H p表示所述原始哈密顿算符，H d表示所述控制哈密顿算符，β(τ)表示所述哈密顿算符参数。
  12. 根据权利要求11所述的装置，其中，
    所述哈密顿算符参数是基于李雅普诺夫函数对时间的一阶偏导要求确定的。
  13. 根据权利要求12所述的装置，其中，所述李雅普诺夫函数对时间的一阶偏导要求如下：
    Figure PCTCN2021133711-appb-100006
    其中，
    Figure PCTCN2021133711-appb-100007
    用于表示所述原始哈密顿算符提供的演化趋势，且
    Figure PCTCN2021133711-appb-100008
    小于等于0；β(τ)(<ψ(τ)||{H d,H p}||ψ(τ)>-2<H d><H p>)用于表示所述控制哈密顿算符提供的额外演化趋势。
  14. 根据权利要求13所述的装置，其中，所述哈密顿算符参数如下：
    β(τ)＝(<ψ(τ)||{H d,H p}||ψ(τ)>-2<H d><H p>)。
  15. 根据权利要求13所述的装置，其中，所述装置还包括：
    确定模块，用于基于单位矩阵和泡利Z矩阵所组成的对角矩阵确定所述控制哈密顿算符。
  16. 根据权利要求9至15任一所述的装置，其中，所述更新模块，还用于以最小化所述 目标量子系统的能量为目标，更新所述哈密顿。
  17. 一种计算机设备，所述计算机设备用于执行如权利要求1至8任一项所述的量子计算方法。
  18. 一种计算机可读存储介质，所述存储介质中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或指令集由处理器加载并执行以实现如权利要求1至8任一项所述的量子计算方法。
  19. 一种计算机程序产品或计算机程序，所述计算机程序产品或计算机程序包括计算机指令，所述计算机指令存储在计算机可读存储介质中，处理器从所述计算机可读存储介质读取并执行所述计算机指令，以实现如权利要求1至8任一项所述的量子计算方法。
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