Quantum circuit creation method and device, computer device and program

Abstract

A method, device, apparatus, medium and product for creating a quantum circuit are provided, which relate to the quantum technology field, and include the steps of obtaining a combination of an identity matrix and a Pauli Z matrix as a diagonal matrix basis (201); determining a dynamic time evolution relation of imaginary time diagonal control based on the diagonal matrix basis and the dynamic time evolution relation of quantum imaginary time control (202); determining a first quantum circuit of imaginary time diagonal control based on the dynamic time evolution relation of imaginary time diagonal control (203); determining a second quantum circuit based on a variational quantum approximation algorithm (204); and periodically alternating the first quantum circuit and the second quantum circuit to obtain a created quantum circuit (205).

Description

[Technical field]

[0001] This application claims priority to a Chinese patent application filed with the China Patent Office on January 20, 2022, bearing application number 202210066132.9 and entitled "Quantum circuit preparation method, device, apparatus, medium and product," the entire contents of which are incorporated herein by reference.

[0002] The present application relates to the field of quantum technology, and in particular to a method and apparatus for creating (also known as preparing) a quantum circuit, and a computer device and program. [Background technology]

[0003] With the rapid development of quantum computing, quantum algorithms have been used in important applications in many fields. A quantum circuit prepared based on the quantum imaginary time evolution (QITE) is provided, among which a unitary approximation circuit is created by the quantum imaginary time evolution unitary approximation method.

[0004] However, in the above method, the quantum imaginary time evolution unitary approximation method needs to select a sufficiently good unitary basis to ensure accuracy after time evolution mapping, and each step also needs to solve an additional set of linear equations. When constructing the simultaneous linear equations, the unitary approximation method needs to perform expansion and approximation operations on the unitary parameters, and even if only a second-order approximation is performed, the quantum imaginary time evolution unitary approximation method still needs to measure multiple observables to observe the time evolution results of the quantum circuit, and due to the increase in the system and the increasing demand for accuracy, some observables may rapidly increase in measurement data as time evolution progresses. Therefore, in a large-scale system, the number of measurements (measurements) is large and it is difficult to find a solution, and the feasibility of this method may gradually be lost. In addition, the depth of the circuit constructed by this method (i.e., the longest path in the quantum circuit, the length of the path is an integer, and represents the number of gates executed in the path when the circuit is measured) may also become deeper as the length of time evolution increases. Summary of the Invention [Problem to be solved by the invention]

[0005] An object of the embodiments of the present application is to provide a method and apparatus for creating a quantum circuit, and a computer device and program, capable of accelerating the process of quantum imaginary time evolution. [Means for solving the problem]

[0006] According to one aspect of an embodiment of the present application, there is provided a method for creating a quantum circuit, the method comprising: The combination of the identity matrix and the Pauli Z matrix is ​​obtained as the diagonal matrix basis; determining a dynamic time evolution relation of the quantum imaginary time control and a dynamic time evolution relation of the imaginary time diagonal control based on the diagonal matrix basis; determining a first quantum circuit of the imaginary time diagonal control based on a dynamic time evolution relationship of the imaginary time diagonal control; determining a second quantum circuit based on a variational quantum approximation algorithm; and The method includes using a periodically alternating circuit (a circuit that is periodically arranged alternately) of the first quantum circuit and the second quantum circuit as the created quantum circuit.

[0007] According to one aspect of an embodiment of the present application, there is provided a quantum circuit creation device, the device comprising: An acquisition module for acquiring a combination of the identity matrix and the Pauli Z matrix as a diagonal matrix basis; and A determination module for determining a dynamic time evolution relation of an imaginary time diagonal control based on a dynamic time evolution relation of a quantum imaginary time control and the diagonal matrix basis; The determination module is further used for determining a first quantum circuit of imaginary-time diagonal control based on a dynamic time evolution relationship of the imaginary-time diagonal control; the determination module is further adapted to determine a second quantum circuit based on a variational quantum approximation algorithm; The determination module is further used to cause a periodic alternation of the first quantum circuit and the second quantum circuit to be the created quantum circuit.

[0008] According to one aspect of an embodiment of the present application, a computer device is provided, the computer device including a processor and a memory device, the memory device storing at least one instruction, at least one program, code set or instruction set, the at least one instruction, the at least one program, code set or instruction set being loaded and executed by the processor to realize the above-mentioned method of creating a quantum circuit.

[0009] According to one aspect of an embodiment of the present application, a computer-readable storage medium is provided, the storage medium storing at least one instruction, at least one program, code set or instruction set, the at least one instruction, the at least one program, code set or instruction set being loaded and executed by the processor to realize the above-mentioned method of creating a quantum circuit.

[0010] According to one aspect of an embodiment of the present application, a computer program product or computer program is provided, the computer program product or computer program including computer instructions stored in a computer readable storage medium, a processor of a computing device reads the computer instructions from the computer readable storage medium, and the processor executes the computer instructions to cause the computing device to perform the method for creating a quantum circuit as described above. Effect of the Invention

[0011] The technical solutions provided in the embodiments of the present application can bring the following advantageous effects:

[0012] The quantum diagonal control method suitable for the quantum imaginary time evolution process reduces the number of measurements and accelerates the quantum imaginary time evolution, and the circuit structure of the alternating circulation of the variation circuit and the diagonal control circuit allows the same time evolution to be achieved using a shorter circuit architecture while also reducing the number of parameters and measurement requirements required for the variation circuit. The circuit structure of the alternating circulation of the variation circuit and the diagonal control circuit utilizes the alternating structure of the original imaginary time evolution plus the diagonal control method, and uses a relatively small number of diagonal control terms to replace the original imaginary time evolution in its controllable section, thereby achieving the creation of a circuit that reduces the number of measurements, among which is the matrix H, which combines the identity matrix and the Pauli Z matrix under the Pauli Z measurement. d and its acting H d H p , H d σ μ The term is H in the quantum imaginary time evolution unitary approximation method. d σμ and σ μ Since this increases the number of measurements slightly compared to σ μ σ v , H p , σ μ Since the measurement is reduced from five terms to three main terms, the number of parameters required for the variation circuit and the number of measurements can be reduced. [Brief description of the drawings]

[0013] [Figure 1] FIG. 2 illustrates a circuit fabrication architecture provided in one example of the present application. [Diagram 2] 1 is a flowchart of a method for creating a quantum circuit provided in one embodiment of the present application. [Diagram 3] FIG. 2 illustrates an alternating structure circuit provided in one exemplary embodiment of the present application. [Figure 4] 1 is a flowchart of a method for creating a quantum circuit provided in another exemplary embodiment of the present application. [Diagram 5] FIG. 2 illustrates a process of obtaining a first quantum circuit provided in one exemplary embodiment of the present application. [Figure 6] FIG. 2 illustrates the change in an observable provided in one embodiment of the present application. [Figure 7] FIG. 2 shows a flat plateau provided in one example of the present application. [Figure 8] FIG. 13 illustrates the change in energy level of imaginary time control provided in one embodiment of the present application. [Figure 9] FIG. 13 illustrates the convergence step number versus energy difference of the imaginary time control provided in one embodiment of the present application. [Figure 10] FIG. 10 is a comparison diagram of the convergence of the diagonal control algorithm provided in one embodiment of the present application and the original imaginary time evolution algorithm. [Figure 11] FIG. 10 is a comparison diagram of the convergence of the diagonal control algorithm provided in one embodiment of the present application and the original imaginary time evolution algorithm. [Figure 12]FIG. 2 illustrates an auxiliary bit diagonal matrix circuit provided in one embodiment of the present application. [Figure 13] FIG. 2 illustrates a single-step control circuit provided in one embodiment of the present application. [Figure 14] FIG. 2 illustrates a variational circuit provided in one embodiment of the present application. [Figure 15] 1 is a configuration block diagram of a quantum circuit creation device provided in one embodiment of the present application. [Figure 16] FIG. 11 is a block diagram of a quantum circuit creation device provided in another embodiment of the present application. [Figure 17] FIG. 2 is a block diagram of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] Before describing the embodiments of the present application, some terminology related to the present application will be introduced.

[0015] 1. Quantum computing: A computational method based on quantum logic, in which the basic unit for storing data is a quantum bit (qubit).

[0016] 2. Quantum bit: The basic unit of quantum computing. Conventional computers use 0 and 1 as the basic unit of binary. The difference is that quantum computing can process 0 and 1 simultaneously, and the system can store a linear superposition of 0 and 1, i.e.

[0017]

number

[0018] 3. Hamiltonian: A Hermitian conjugate matrix that describes the total energy of a quantum system. Hamiltonian is a physics term and an operator that describes the total energy of a system, usually denoted by H.

[0019] 4. Quantum State: In quantum mechanics, a quantum state is a microscopic state determined by a set of quantum numbers.

[0020] 5. Eigenstates: In quantum mechanics, the possible values ​​of a mechanical quantity are all the eigenvalues ​​of its operator. A state described by an eigenfunction is called an eigenstate of this operator. In an eigenstate, this mechanical quantity takes a definite value, i.e., the eigenvalue to which this eigenstate belongs. For a Hamiltonian matrix H, the equation

[0021]

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[0022]

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[0023] 6. Quantum Circuit: Also called Quantum Circuit, it is one of the expressions of quantum universal computer, and represents the hardware implementation of the corresponding quantum algorithm / program under the quantum gate model. If the quantum circuit contains adjustable control quantum gate parameters, it is called a Parameterized Quantum Circuit (PQC) or Variational Quantum Circuit (VQC), and both are the same concept.

[0024] 7. Quantum Gate: In quantum computing, particularly in the quantum circuit computational model, a quantum gate (or quantum logic gate) is a basic quantum circuit that manipulates a small number of quantum bits.

[0025] 8. Variational Quantum Eigensolver (VQE): This realizes the estimation of the ground state energy of a specific quantum system by using a variational circuit (i.e., PQC / VQC). It is a typical quantum-classical hybrid computing paradigm and has wide applications in the field of quantum chemistry.

[0026] 9.Non-unitary: A unitary matrix is

[0027]

number

[0028] 10. Pauli Operators: Also called Pauli matrices, they are a set of three 2x2 unitary Hermitian complex matrices (also called unitary matrices), commonly denoted by the Greek letter σ (sigma). The Pauli X operator is

[0029]

number

[0030]

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[0031]

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[0032] 11.Quantum imaginary time evolution process: The quantum dynamics time evolution equation is replaced from the real-time description to the imaginary-time description and is used mainly to find the lowest eigenstate.

[0033] 12. Quantum diagonal control: By adding a set of adjustable diagonal Hamiltonian operators, we achieve control over the time evolution process of quantum states, and also realize a reduction in observables by using the properties of diagonal matrices.

[0034] 13. Creation of a time-dependent non-unitary-approximate unitary conversion circuit: By mapping the time-dependent non-unitary time evolution to a time-dependent unitary time evolution using an approximation method, we make it possible to implement a circuit, and realize a circuit architecture that can be installed on current quantum computers.

[0035] Obtaining the ground state of a quantum system means obtaining the most stable state of the quantum system, which has very important applications in the study of the basic properties of quantum physics and quantum chemistry systems, solving combinatorial optimization problems, drug development, etc. One important application of quantum computers is to effectively solve or represent the ground state of a quantum system. Imaginary time evolution is one of the basic methods for solving the ground state of a quantum system.

[0036] The time-dependent Schrödinger equation is

[0037]

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[0038]

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[0039] Real time t in the time-dependent Schrödinger equation is imaginary time

[0040]

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[0041]

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[0043] Also,

[0044]

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[0045]

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[0046] By expanding the wave function in the imaginary time Schrodinger equation with the feature vector,

[0047]

number

[0048] Among them, E i is the specific energy, E0 <E i where E0 is the ground state energy and c i are the expansion coefficients.

[0049] E0 <E i Therefore, as time approaches infinity, all other eigenstates disappear at an exponential rate, i.e., as ψ(τ) evolves in time, the other states decay faster and faster, until eventually only the ground state remains:

[0050]

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[0051]

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[0052] This also allows us to obtain the initial lowest eigenstate by backtracking as follows:

[0053]

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[0054] <(1) Quantum imaginary time evolution unitary approximation method> In order to implement the non-unitary time evolution imaginary time dynamics on a quantum computer, one intuitive way is to find a set of unitary operators that can act on the current quantum state and ensure that the state after the action is close to the result after the action of the imaginary time non-unitary time evolution operator.Therefore, in the scheme, an approximation creation method is provided, which needs to first select a set of unitary operators as a basis, and then convert it into a quantum circuit by linearly combining a set of non-unitary operators from the pre-selected basis by an approximation method to approximate its time evolution.

[0055] <(2) Quantum imaginary time evolution variational approximation method> Compared with the above-mentioned approximation method of constructing and solving a linear system from a preselected basis, the core idea of ​​the quantum imaginary time evolution variational approximation method is also to find a set of unitary operators to approximate the non-unitary time evolution, but the difference is that in this method, the circuit architecture is designed in advance and the time evolution problem is converted into a parametric time evolution problem on a parametric circuit, thereby converting the long circuit problem into a parameter problem of a short circuit.

[0056] However, the above quantum imaginary time evolution unitary approximation method requires the selection of a sufficiently good unitary basis to guarantee the accuracy after the time evolution mapping, and also requires the additional solving of simultaneous linear equations at each step. Constructing this simultaneous linear equation is

[0057]

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[0059] The above-mentioned quantum imaginary time evolution variational approximation method has a predetermined fixed circuit structure, and the fixed circuit structure also usually faces a trade-off between accuracy, number of parameters and length. Due to the trade-off in circuit design, the convergence accuracy of this method is greatly affected by the selected circuit architecture, and this impact is difficult to estimate in advance. In addition to the impact on accuracy, if more parameters are selected to meet the need for accuracy, the number of measurements will also increase by approximating the matrix that needs to be solved, especially:

[0060]

number

[0061] In the embodiment of the present application, a relatively simple diagonal matrix basis combining a unit matrix and a Pauli Z matrix is ​​measured, and a set of time evolution operators is generated from this basis by quantum imaginary time control. In addition, by utilizing the properties of diagonal matrices and quantum control, the number of measurements can be reduced compared to current algorithms, and the circuit depth can be reduced.

[0062] For illustration, refer to Fig. 1, which is a diagram showing a circuit creation architecture provided in one embodiment of the present application. As shown in Fig. 1, starting from an imaginary time evolution function 110, an approximation circuit 120 can be obtained by a quantum imaginary time evolution unitary approximation method, and the obtained quantum circuit has a large number of measurements and a large depth; and a variation circuit 130 can be obtained by a quantum imaginary time variation approximation method, and the obtained quantum circuit has a large number of measurements and poor accuracy. In this embodiment, a diagonal control algorithm is used to judge using modules and select diagonal modules to obtain a diagonal matrix circuit 140.

[0063] Before describing an embodiment of the method of the present application, an execution environment of the method of the present application will first be introduced.

[0064] The method for creating a quantum circuit provided in the embodiments of the present application can be realized by executing a classical computer (e.g., a PC), for example, the method can be realized by executing a corresponding computer program by a classical computer, or can be executed in a hybrid device environment of a classical computer and a quantum computer, for example, the method can be realized by a combination of a classical computer and a quantum computer. For example, a quantum computer is used to realize solving eigenstates in the embodiments of the present application, and a classical computer is used to realize other steps in the embodiments of the present application other than the problem of solving eigenstates.

[0065] In the following method embodiment, for convenience of explanation, the execution subject of each step is only a computer device. It should be understood that the computer device may be a classical computer, or may be a hybrid execution environment including a classical computer and a quantum computer, and the embodiment of the present application is not limited thereto.

[0066] Please refer to FIG. 2, which is a flow chart of a method for creating a quantum circuit provided in one embodiment of the present application. Each step of the method may be performed by a computer device. The method may include the following steps:

[0067] Step 210: Obtain a combination of the identity matrix and the Pauli Z matrix as a diagonal matrix basis.

[0068] That is, a set of diagonal matrices formed by combining a unit matrix and a Pauli Z matrix is ​​obtained as a diagonal matrix basis.

[0069] Step 220: Determine the dynamic time evolution relation of the imaginary-time diagonal control based on the diagonal matrix basis and the dynamic time evolution relation of the quantum imaginary time control.

[0070] For example, a special quantum dynamical time evolution relationship is proposed under the description of imaginary time dynamics, and the idea of ​​quantum control theory is used to achieve the purpose of adjustment and control of its time evolution. The dynamical time evolution relationship of the imaginary time diagonal control is as follows:

[0071]

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[0072]

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[0073]

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[0074] Optionally, the real coefficients are determined based on the requirement of the first partial derivative with respect to time of the Lyapunov function, i.e., β d This provides a way of thinking about designing (τ) functions.

[0075] First, we start with a mean-based Lyapunov function:

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[0078] β d (τ) is

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[0080]

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[0082] Step 230: Determine a first quantum circuit of the imaginary-time diagonal control based on the dynamic time evolution relationship of the imaginary-time diagonal control.

[0083] As an option, a quantum circuit with imaginary-time diagonal control is obtained by performing a unitary transformation on the dynamical time evolution relation of the imaginary-time diagonal control using the quantum ordinal time evolution unitary approximation method.

[0084] Step 240: Determine a second quantum circuit based on the variational quantum approximation algorithm.

[0085] Optionally, a second quantum circuit is determined by a quantum imaginary time evolution variational approximation algorithm.

[0086] It should be noted that the above-mentioned steps 220 to 230 are steps parallel to the above-mentioned step 240, and steps 220 to 230 may be executed first, or step 240 may be executed first, or further, steps 220 to 230 and step 240 may be executed simultaneously.

[0087] Step 250: The periodically alternating circuit of the first quantum circuit and the second quantum circuit is regarded as the created quantum circuit.

[0088] As an option, the created quantum circuit is an alternating circuit of the first quantum circuit and the second quantum circuit, the alternating circuit having a cyclic period of a predetermined imaginary time step length.

[0089] The imaginary time diagonal control quantum circuit has certain limitations. One of them is H d can affect the convergence when the eigenstates of are in equilibrium, the other is that the initial state must be uniformly distributed, i.e., every position on the vector has a value, so that a simple diagonal matrix time evolution can evolve it to every position in space, and thirdly, to get a combination of all diagonal matrices, we need to use a combination of all identity matrices and Pauli Z matrices, which is a total of 2 combinations. nBecause of this term, when calculating large systems, even if not many measurements are made, there is still a need for post-processing (transformation) calculations on a classical computer, which places a significant burden on the overall convergence.

[0090] Therefore, in the embodiment of the present application, by utilizing the alternating structure of the original imaginary time evolution plus diagonal control method, and using a relatively small number of diagonal control terms to replace the original imaginary time evolution in its controllable section, it is possible to create a circuit that reduces the number of measurements, and experiments have shown that by taking advantage of the imaginary time control, it is possible to achieve better accuracy with less time evolution, and when the imaginary time evolution block is constructed by the variational quantum approximation algorithm, fewer time evolution states are required compared to the original pure variational quantum approximation unitary algorithm, so a simpler circuit structure, for example, fewer parameters and a shallower circuit depth, can also be used.

[0091] For illustration, refer to FIG. 3, which is a diagram showing an alternating structure circuit provided in one exemplary embodiment of the present application. As shown in FIG. 3, circuit 310 is a time evolution circuit constructed by a quantum unitary approximation algorithm, and circuit 320 is an alternating circulatory circuit structure of a variation circuit 321 and a diagonal control circuit 322. In the alternation, each time, the variation circuit 321 and the diagonal control circuit 322 correspond to a certain imaginary time step length Δτ. As is clear, compared with circuit 310, when the imaginary time step length Δτ is the same, the circuit 310 and circuit 320 shown in FIG. 3 have a shorter circuit length of the distributed quantum gates at each imaginary time step length Δτ, and the number of quantum gates is smaller, that is, circuit 320 can achieve the same time evolution using a shorter circuit architecture, and can also reduce the number of parameters and measurement requirements required for the variation circuit.

[0092] In summary, the method provided in this embodiment uses a quantum diagonal control method suitable for the quantum imaginary time evolution process to reduce the number of measurements and accelerate the quantum imaginary time evolution using the control method, and the circuit structure of the alternating circulation of the variation circuit and the diagonal control circuit can achieve the same time evolution using a shorter circuit architecture than the time evolution circuit constructed by the quantum unitary approximation algorithm.In addition, the quantum unitary approximation algorithm needs to find a set of unitary operators acting on the quantum state and ensure that the state after the action is very close to the result after the action of the imaginary time non-unitary time evolution operator, so first select a set of unitary operators as the basis, and then linearly combine a set of unitary operators from the pre-selected basis by an approximation method to approximate its time evolution, because the selection of the unitary operator is a random selection whose effect cannot be pre-estimated, after the unitary basis is selected, if the expression of the combination of the unitary basis is relatively weak, it may affect the accuracy after the time evolution mapping. Furthermore, the quantum unitary approximation algorithm also requires solving an additional system of linear equations at each step, and constructing this system of linear equations is

[0093]

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[0095] In one alternative embodiment, the first quantum circuit is obtained by performing a unitary transformation on the dynamic time evolution relation of the imaginary time diagonal control. Figure 4 is a flow chart of a method for creating a quantum circuit provided in another exemplary embodiment of the present application. As shown in Figure 4, the method includes the following steps.

[0096] Step 410: Obtain a combination of the identity matrix and the Pauli Z matrix as a diagonal matrix basis.

[0097] That is, a set of diagonal matrices consisting of a combination of a unit matrix and a Pauli Z matrix is ​​obtained as a diagonal matrix basis.

[0098] Step 420: Determine the dynamic time evolution relation of the imaginary-time diagonal control based on the diagonal matrix basis and the dynamic time evolution relation of the quantum imaginary time control.

[0099] For example, a special quantum dynamical time evolution relationship is proposed under the description of imaginary time dynamics, and the idea of ​​quantum control theory is used to achieve the purpose of adjustment and control of its time evolution. The dynamical time evolution relationship of the imaginary time diagonal control is as follows:

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[0103] Step 430: Using the quantum imaginary time evolution unitary approximation method, a unitary transformation is performed on the dynamical time evolution relation of the imaginary time diagonal control to obtain a first quantum circuit of the imaginary time diagonal control.

[0104] Optionally, the dynamical time evolution relation of the imaginary time diagonal control is converted into a candidate quantum circuit, and a unitary transformation is performed on the candidate quantum circuit by the quantum imaginary time evolution unitary approximation method to obtain a first quantum circuit of the imaginary time diagonal control.

[0105] For illustration, refer to Fig. 5, which is a diagram showing a process of obtaining a first quantum circuit provided in one exemplary embodiment of the present application. As shown in Fig. 5, first, a unitary basis 510 is selected in advance, and then converted into a circuit form (structure) 520 based on the unitary basis, and the circuit structure is converted by a quantum imaginary time unitary approximation algorithm to obtain a unitary approximation circuit module 530.

[0106] That is, by using the above-mentioned quantum imaginary time evolution variational approximation method, a unitary transformation is performed on the dynamical time evolution relationship of the above-mentioned imaginary time diagonal control as shown in the following formula.

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[0110] Each H d is a single simple matrix consisting of a combination of the identity matrix and the Pauli Z matrix.

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[0123] Step 440: Determine a second quantum circuit based on the variational quantum approximation algorithm.

[0124] Optionally, a second quantum circuit is determined by a quantum imaginary time evolution variational approximation algorithm.

[0125] That is, after designing the circuit architecture in advance, a set of unitary operators is determined to approximate the non-unitary time evolution, and the time evolution problem is transformed into a parametric time evolution problem on a parametric circuit to obtain a second quantum circuit.

[0126] Step 450: The periodically alternating circuit of the first quantum circuit and the second quantum circuit is regarded as a created quantum circuit.

[0127] As an option, the created quantum circuit is an alternating circuit of the first quantum circuit and the second quantum circuit, the alternating circuit having a cyclic period of a predetermined imaginary time step length.

[0128] In summary, the method provided in this embodiment reduces the number of measurements and accelerates the quantum imaginary time evolution using a quantum diagonal control method suitable for the quantum imaginary time evolution process, and also realizes the same time evolution using a shorter circuit architecture by a circuit structure of alternating circulation of the variation circuit and the diagonal control circuit, while suppressing the number of parameters and measurement requirements required for the variation circuit.

[0129] The method provided in this embodiment has the following advantages: (1) when used in conjunction with imaginary time evolution, it has been proven by numerical simulation that it can converge faster than the simple imaginary time evolution method, thereby achieving the goal of making the circuit depth relatively shallow; (2) by utilizing the properties of diagonal matrices and Z measurement,

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[0131] The method for creating a quantum circuit provided in the embodiments of the present application has at least the following advantageous effects.

[0132] <1. The number of measurements required when updating circuits can be reduced> Under the quantum unitary approximation policy, the number of measurements is

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[0136] Under the aid of diagonal control, the number of measurements changes into two different modules, one term being the observable of the original five unitary approximation policy, and the other term being the

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[0141] Of these, N dis the Z measurement without any additional measurements, and N d N p and N p N d The number of measurements for both is equal, N p and N μ All

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[0145] Thus, the reduction in the overall number of measurements is roughly proportional to the reduced convergence step length of the quantum unitary approximation due to the control method.

[0146] <2. The total number of steps required for convergence can be reduced> By utilizing quantum imaginary time control, the convergence step length can be effectively reduced in experimental tests, because it can adjust the energy difference of the original system, so that the imaginary time evolution can converge to the ground state at a faster rate. As shown in Figure 8, the change in the energy spectrum of hydrogen molecule under the assistance of imaginary time control is shown in the energy level change diagram 810 and change diagram 820, as the difference between the excited state energy and the ground state energy is larger, the convergence speed is faster.

[0147] The speedup nature of quantum imaginary time control allows the same accuracy to be achieved using fewer steps, as shown in Figure 9. The curve diagram 910 uses a 3SAT system to show how the number of steps that can be reduced by the overall control algorithm varies with the energy system.

[0148] Please refer to Figure 10, which is a curve diagram 1010 showing a comparison of the convergence of the diagonal control algorithm and the original imaginary time evolution algorithm. As can be seen, the convergence speed of the diagonal control algorithm + imaginary time evolution algorithm is faster than that of the original imaginary time evolution algorithm.

[0149] Under this architecture, the property of acceleration by quantum imaginary time control can still be realized, and the convergence circuit is reduced from the original 58-layer quantum imaginary time evolution circuit to 8-layer quantum imaginary time evolution + 8-layer diagonal control circuit. The total number of measurements is about 8 / 58 of the original, and the depth of the circuit is reduced to 16 layers. Therefore, it is possible to achieve the result of convergence to the target accuracy with a relatively short convergence time, a relatively short circuit, and a relatively small number of measurements.

[0150] <3. Circuit complexity can be reduced compared to the original imaginary time method> The diagonal circuit part in the above architecture may be realized by a shorter circuit architecture by using only one auxiliary bit and combining with post-selection, as shown in the 3-bit diagonal matrix circuit 1110 in Figure 11. As shown in Figure 11, the diagonal matrix circuit 1110 uses the post-selection method plus a control gate (X gate). Using the matrix

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[0154] In the embodiment of the present application, the circuit can be further shortened to a shorter fixed length based on the combination of the selected identity matrix and Pauli Z matrix. For example, under the architecture combining the identity matrix and the Pauli Z matrix, when half of the diagonal elements are adjusted by the Pauli Z matrix and the other half remain unchanged, for example, in the case of an IIZ combination matrix obtained by combining two identity matrices and one Pauli Z matrix, the third bit acts only on the elements with 1, that is, the four terms (001, 011, 101, 111), and the circuit can be simplified from the diagonal matrix circuit 1110 shown in FIG. 11 described above to the circuit 1210 shown in FIG. 12. In the circuit 1210 shown in FIG. 12, the Pauli Z matrix adjusts the diagonal elements with the third bit being 1, but the other diagonal elements are not affected.

[0155] In addition, because all control operators can be exchanged, a continuous multi-step control circuit can be simplified to a single-step control circuit and implemented on a quantum computer using a combination of shorter circuit architectures such as those in FIG. 12. It has been shown that a continuous two-layer circuit can be simplified to a one-layer control circuit 1310 by exchange, as in the circuit 1310 shown in FIG. 13. Among them, the two-layer circuit is

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[0158] In some embodiments, real-time control can also employ a similar method, and since it is unitary time evolution, there are also more intuitive non-approximate circuit creation methods for circuit selection.

[0159] 15 is a block diagram of a quantum circuit creation device provided in one exemplary embodiment of the present application. As shown in FIG. 15, the device includes the following:

[0160] An acquisition module 1510 is used to acquire a combination of the identity matrix and the Pauli Z matrix as a diagonal matrix basis; and A determination module 1520 is used to determine a dynamic time evolution relation of the quantum imaginary time control and a dynamic time evolution relation of the imaginary time diagonal control based on the diagonal matrix basis. The determining module 1520 is further used for determining a first quantum circuit of the imaginary-time diagonal control according to a dynamic time evolution relationship of the imaginary-time diagonal control; The determination module 1520 is further used to determine a second quantum circuit based on a variational quantum approximation algorithm; The determining module 1520 is further used to determine the periodic alternation of the first quantum circuit and the second quantum circuit as the created quantum circuit.

[0161] In one alternative embodiment, as shown in FIG. 16, the determination module 1520 includes:

[0162] Transformation unit 1521: Used to obtain the first quantum circuit by performing a unitary transformation on the dynamical time evolution relation of the imaginary time diagonal control by an imaginary time evolution unitary approximation device.

[0163] In one alternative embodiment, the transformation unit 1521 is further used to transform the dynamical time evolution relation of the imaginary time diagonal control into a candidate quantum circuit, and perform a unitary transformation on the candidate quantum circuit by the quantum imaginary time evolution unitary approximation device to obtain the first quantum circuit of imaginary time diagonal control.

[0164] In one alternative embodiment, the dynamic time evolution relationship of the imaginary time diagonal control is as follows:

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[0167] In one alternative embodiment, the real coefficients are determined based on a requirement for the first partial derivative of the Lyapunov function with respect to time.

[0168] In one alternative embodiment, the requirement for the first partial derivative of the Lyapunov function with respect to time is:

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[0170] In one alternative embodiment, the real coefficients are:

[0171]

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[0172] In summary, the device provided in this embodiment uses a quantum diagonal control method suitable for the quantum imaginary time evolution process to reduce the number of measurements and accelerate the quantum imaginary time evolution using a control method, and also uses a circuit structure of alternating circulation of the variation circuit and the diagonal control circuit to realize the same time evolution using a shorter circuit architecture while suppressing the number of parameters and measurement requirements required for the variation circuit.

[0173] In addition, the quantum circuit creation device provided in the above embodiment is described by taking the division of each of the above-mentioned functional modules as an example, but in actual applications, the above-mentioned functions can be assigned to different functional modules according to needs, that is, all or part of the above-mentioned functions can be completed by dividing the internal structure of the device into different functional modules. In addition, the quantum circuit creation device provided in the above embodiment belongs to the same concept as the embodiment of the quantum circuit creation method, and the specific realization process can be referred to the embodiment of the method, and the detailed description thereof will be omitted here.

[0174] Please refer to Figure 17, which is a block diagram of a computer device 1700 provided in one embodiment of the present application. The computer device 1700 may be a classical computer. The computer device can implement the method for creating a quantum circuit provided in the above embodiment.

[0175] Specifically, the computer device 1700 includes a central processing unit (e.g., a central processing unit (CPU), a graphics processing unit (GPU), a field programmable gate array (FPGA), etc.) 1701, a system memory 1704 including a random-access memory (RAM) 1702 and a read-only memory (ROM) 1703, and a system bus 1705 connecting the system memory 1704 and the central processing unit 1701. The computer device 1700 further includes a basic input / output system (I / O system) 1706 that enables information transmission between each device in the server, and a mass storage device 1707 for storing an operating system 1713, application programs 1714, and other program modules 1715.

[0176] Optionally, the basic input / output system 1706 includes a display 1708 for displaying information, and an input device 1709, such as a mouse, keyboard, etc., for a user to input information. The display 1708 and the input device 1709 are all connected to the central processing unit 1701 by an input / output controller 1710, which is connected to the system bus 1705. The basic input / output system 1706 may further include an input / output controller 1710 for receiving and processing input from a number of devices, such as a mouse, keyboard, electronic stylus, etc. Similarly, the input / output controller 1710 may also provide an output device for outputting to a display screen, a printer, or other type of output device.

[0177] Optionally, the mass storage device 1707 is connected to the central processing unit 1701 by a mass storage controller (not shown) that is connected to the system bus 1705. The mass storage device 1707 and its associated computer readable media provide non-volatile storage for the computing device 1700. In other words, the mass storage device 1707 may include a computer readable medium (not shown), such as a hard disk or a Compact Disc Read-Only Memory (CD-ROM) drive.

[0178] According to an embodiment of the present application, the computing device 1700 may further be implemented by a network, such as the Internet, to be connected to a remote computer over the network, i.e., the computing device 1700 may be connected to a network 1712 by a network interface unit 1711 connected to the system bus 1705, or may be connected to another type of network or remote computer system (not shown) by the network interface unit 1711.

[0179] As one skilled in the art will appreciate, the structure shown in FIG. 17 is not limiting of computing device 1700, and computing device 1700 may include more or fewer assemblies than shown, may combine some assemblies, or may employ different assembly arrangements.

[0180] In an exemplary embodiment, a computer-readable storage medium may be further provided, the storage medium storing at least one instruction, at least one program, code set or instruction set, which, when executed by a processor, may realize the above-mentioned method for creating a quantum circuit.

[0181] In an exemplary embodiment, a computer program product or computer program is further provided, the computer program product or computer program comprising computer instructions stored in a computer readable storage medium, the computer instructions being read by a processor of a computing device from the computer readable storage medium and executed by the processor to cause the computing device to perform the method for creating a quantum circuit as described above.

[0182] Although the preferred embodiment of the present application has been described above, the present application is not limited to this embodiment, and any modification to the present application falls within the technical scope of the present application as long as it does not depart from the spirit of the present application.

Claims

1. 1. A computational device implemented method for creating a quantum circuit, comprising: obtaining a combination of the identity matrix and the Pauli Z matrix as a diagonal matrix basis; determining a dynamic time evolution relation of an imaginary time diagonal control based on the dynamic time evolution relation of the quantum imaginary time control and the diagonal matrix basis; determining a first quantum circuit of the imaginary-time diagonal control based on the dynamic time evolution relationship of the imaginary-time diagonal control; determining a second quantum circuit based on a variational quantum approximation algorithm; and The method includes a step of forming the quantum circuit by periodically alternating the first quantum circuit and the second quantum circuit.

2. 2. The method of claim 1, The step of determining the first quantum circuit of the imaginary-time diagonal control based on the dynamic time evolution relationship of the imaginary-time diagonal control includes: The method includes a step of performing a unitary transformation on the dynamical time evolution relation of the imaginary time diagonal control by an imaginary time evolution unitary approximation method to obtain the first quantum circuit of the imaginary time diagonal control.

3. 3. The method of claim 2, The step of performing a unitary transformation on the dynamic time evolution relation of the imaginary time diagonal control by the imaginary time evolution unitary approximation method to obtain the first quantum circuit of the imaginary time diagonal control includes: Converting the imaginary-time diagonal-controlled dynamic time evolution relation into a candidate quantum circuit; and performing a unitary transformation on the candidate quantum circuit by the imaginary time evolution unitary approximation method to obtain the first quantum circuit.

4. 2. The method of claim 1, The dynamic time evolution relationship of the imaginary time diagonal control is as follows: [0010] and Here, τ represents imaginary time, [0025] represents the imaginary time eigenstate, and H d represents a time evolution operator determined based on the diagonal matrix basis, and β d (τ) represents a real coefficient that changes over time, and E represents the intrinsic energy.

5. 5. The method of claim 4, The method, wherein the real coefficients are determined based on a requirement for a first partial derivative of a Lyapunov function with respect to time.

6. 6. The method of claim 5, The requirement for the first partial derivative of the Lyapunov function with respect to time is [0030] and Here, E 0 H p is the smallest eigenvalue of H p represents the original Hamiltonian operator,method.

7. 7. The method of claim 6, The real coefficients are [0045] That is, the method.

8. 8. The method according to any one of claims 1 to 7, comprising: The step of determining a second quantum circuit based on the variational quantum approximation algorithm includes: obtaining a candidate quantum circuit, the candidate quantum circuit including circuit parameters awaiting training; obtaining a predetermined loss function, the predetermined loss function being used to define expected values ​​of circuit parameters of the candidate quantum circuits; determining a loss value for the candidate quantum circuit based on quantum operation results of the candidate quantum circuit and the predetermined loss function; and training the candidate quantum circuit based on the loss value to obtain the second quantum circuit.

9. 8. The method according to any one of claims 1 to 7, comprising: The step of forming a periodic alternating circuit of the first quantum circuit and the second quantum circuit into the created quantum circuit includes: The method includes a step of alternately placing the first quantum circuit and the second quantum circuit in a cyclic period having a predetermined imaginary time step length to obtain the quantum circuit.

10. An apparatus for creating a quantum circuit, comprising: an acquisition module for acquiring a combination of the identity matrix and the Pauli Z matrix as a diagonal matrix basis; and A determination module for determining a dynamic time evolution relation of an imaginary time diagonal control based on the dynamic time evolution relation of the quantum imaginary time control and the diagonal matrix basis; The determination module is further used for determining a first quantum circuit of imaginary-time diagonal control based on a dynamic time evolution relationship of the imaginary-time diagonal control; the determination module is further adapted to determine a second quantum circuit based on a variational quantum approximation algorithm; The apparatus, wherein the determination module is further used to cause a periodically alternating circuit of the first quantum circuit and the second quantum circuit to be the created quantum circuit.

11. 1. A computing device comprising: a processor; and a memory coupled to the processor, The storage device stores a computer program, A computing device, the processor being configured to execute the computer program to implement the method of any one of claims 1 to 7.

12. A program for causing a computer to execute the method according to any one of claims 1 to 7.

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