Method for constructing excitation operator in variational quantum eigen solution algorithm

Abstract

The application provides a construction method of an excitation operator in a variational quantum eigenvalue solution algorithm, and the method comprises the following steps: constructing a quantum circuit of a single excitation operator by performing basis transformation on a CRY gate; and constructing a quantum circuit of a double excitation operator by performing basis transformation on a C3RY gate. In the technical scheme, the quantum circuit of the single excitation operator is constructed by performing the basis transformation on the CRY gate, and the quantum circuit of the double excitation operator is constructed by performing the basis transformation on the C3RY gate, so that the number of CNOT gates is reduced, and the depth of the quantum circuit is reduced.

Description

Technical Field

[0001] This application relates to the fields of quantum computing and quantum information technology, and in particular to a method for constructing excitation operators in a variable quantum eigenvalue solving algorithm. Background Technology

[0002] The chemical properties of matter are closely related to the energy levels of molecules. For example, predicting the rate of a chemical reaction requires information about the ground state energy levels of molecules, making the accurate calculation of molecular energy levels a crucial task. In classical computation, molecular energy levels can be precisely calculated using the Full Configuration Interaction (FCI) algorithm; however, the computational cost of this algorithm increases exponentially with molecular size, making it unsuitable for large molecules. This problem, however, can be naturally solved on quantum computers built upon quantum mechanics.

[0003] The first quantum algorithm applicable to solving the molecular Hamiltonian level problem is the Quantum Phase Estimating (QPE) algorithm. Compared to classical algorithms, QPE can provide exponential speedup. However, the quantum hardware requirements for QPE, such as error correction mechanisms and long coherence times, are difficult to meet with current noisy intermediate-scale quantum (NISQ) devices.

[0004] Recently, the Variational Quantum Eigensolver (VQE) algorithm, employing a quantum-classical hybrid architecture, has attracted widespread attention. In the VQE algorithm, to provide an easily prepared quantum state that closely resembles the ground state as much as possible as the starting point, the Hatree-Fock state |HF> is typically used as the reference state. The Hatree-Fock state (HF) assumes that the electrons of the molecule occupy the lowest-energy orbitals. This not only provides a good initial approximation for subsequent optimization but also reveals properties such as the number of electrons, spin, and point group symmetry. The population distribution of the Hatree-Fock state is then adjusted by a proposed circuit to generate a trial state for obtaining the ground-state energy through measurement.

[0005] The design of the proposed circuit is the core of the VQE algorithm. Generally, the VQE algorithm's approach to constructing the proposed circuit is derived from the imitation of the classic Coupled Cluster (CC) algorithm. The goal of the CC algorithm is to obtain the trial state by applying an exponential cluster operator to the trial state, i.e. Here, T is the cluster operator, composed of excitation operators of different orders, used to adjust the population distribution of the reference state. The cluster operator T contains parameters to be optimized, and variational methods can be used to minimize the energy expectation, thereby ultimately finding the ground state. Different cluster operators T correspond to different proposed structures. To reduce computational complexity, the cluster operator T generally retains only single-excitation and double-excitation operators, known as the CCSD method. Furthermore, to solve the unitary problem of exponential cluster operators and construct them as quantum circuits, the cluster operator is generally redesigned as the anti-Hermitian cluster operator S = TT. + The corresponding new exponential cluster operator is e. S =e T-T+ Since it is a unitary operator, the algorithm is called UCCSD.

[0006] The anti-Hermitian cluster operator S still consists of single-excitation and double-excitation operators, belonging to fermionic operators. To construct the corresponding quantum circuits, the currently common method is to use methods such as the Jordan-Wigner quantum circuit. [1] Parity basis [2] Or Bravyi-Kitaev [3] The transformations convert the excitation operator into a Pauli string, and after taking the imaginary part, into a quantum circuit. The number of CNOT gates used in these three transformations depends on the specific form of the excitation operator. For a single excitation operator, the minimum numbers are 4, 2, and 2, with no upper limit; for a double excitation operator, the minimum numbers are 48, 32, and 32, with no upper limit. Recently, Qubit-Excitation, based on locality, has been proposed... [4] The transformation can use a fixed number of CNOT gates, which are 4 for single-excitation operators and 48 for double-excitation operators. This has the lowest average number of gates compared to the previous three transformations.

[0007] In summary, implementing the VQE algorithm requires transforming fermion excitation operators to construct quantum circuits. Existing transformation methods, such as Jordan-Wigner, Parity basis, Bravyi-Kitaev, and Qubit-Excitation, all first convert the excitation operators into Pauli strings, and then convert the Pauli strings into quantum circuits. While this achieves the goal, it uses a large number of CNOT gates, resulting in excessively deep quantum circuits. For current NISQ devices, affected by various noises and operational errors, shallower quantum circuits (fewer CNOT gates) are more likely to yield high-quality computational results. Therefore, designing better excitation operator transformation methods is a crucial research direction.

[0008] References:

[0009] [1]Pascual Jordan and Eugene Paul Wigner. the Pauli's Springer, 1993.

[0010] [2] Andrew Tranter, Sarah Sofia, Jake Seeley, Michael Kaicher, Jarrod McClean, Ryan Babbush, Peter V Coveney, Florian Mintert, Frank Wilhelm, and Peter J Love. The bravyi-kitaev transformation: Properties and applications.

[0011] International Journal of Quantum Chemistry, 115(19): 1431 - 1441, 2015.

[0012] [3] Sergey B Bravyi and Alexei Yu Kitaev. Fermionic quantum computation. Annals of Physics, 298(1): 210 - 226, 2002.

[0013] [4] Yordan S Yordanov, Vasileios Armaos, Crispin HW Barnes, and David RM Arvidsson-Shukur. Qubit-excitation-based adaptive variational quantum eigensolver. Communications Physics, 4(1): 228, 2021.

[0014] [5] Israel F Araujo, Daniel K Park, Teresa B Ludermir, Wilson R Oliveira, Francesco Petruccione, and Adenilton J Da Silva. Configurable sublinear circuits for quantum state preparation. Quantum Information Processing, 22(2): 123, 2023. Summary of the Invention

[0015] This application provides a method for constructing excitation operators in a variable quantum eigenvalue solving algorithm, which reduces the number of CNOT gates used and decreases the depth of quantum circuits.

[0016] This application provides a method for constructing excitation operators in a variational quantum eigenvalue solving algorithm, comprising the following steps:

[0017] A quantum circuit with a single excitation operator is constructed by performing a basis transformation on the CRY gate.

[0018] In the above technical solution, by performing a basis transformation on the CRY gate, a quantum circuit with a single excitation operator is constructed, which reduces the number of CNOT gates used and decreases the depth of the quantum circuit.

[0019] In one specific implementation scheme, it also includes:

[0020] A quantum circuit with a dual excitation operator is constructed by performing a basis transformation on the C3RY gate.

[0021] In the above technical solution, a quantum circuit with a single excitation operator is constructed by performing a basis transformation on the CRY gate; and a quantum circuit with a double excitation operator is constructed by performing a basis transformation on the C3RY gate, thereby reducing the number of CNOT gates used and reducing the depth of the quantum circuit.

[0022] In one possible implementation, the CRY gate includes a CRY(2θ) gate;

[0023] The single-excitation operator The matrix is:

[0024]

[0025] The matrix of the CRY(2θ) gate is:

[0026]

[0027] The steps to construct a quantum circuit with a single excitation operator by performing a basis transformation on the CRY gate are as follows:

[0028] By interchanging the basis |01> and basis |11> of the CRY(2θ) gate, we obtain matrix (3):

[0029]

[0030] Complete the construction of the quantum circuit of the single excitation operator.

[0031] In one possible implementation, the C3RY gate includes a C3RY(2θ) gate;

[0032] The dual-excitation operator The matrix is:

[0033]

[0034] The matrix of the C3RY(2θ) gate is:

[0035]

[0036] The steps to construct a quantum circuit with a dual-excitation operator by performing a basis transformation on the C3RY gate are as follows:

[0037] By interchanging the bases |1110> and |1100> of the C3RY gate, and by interchanging the bases |1111> and |0011>, matrix (4) is obtained, thus completing the construction of the quantum circuit of the dual excitation operator.

[0038] In one possible implementation, the C3RY gate includes a C3RY(2θ) gate;

[0039] The dual-excitation operator The matrix is:

[0040]

[0041] The matrix of the C3RY(2θ) gate is:

[0042]

[0043] The steps to construct a quantum circuit with a dual-excitation operator by performing a basis transformation on the C3RY gate are as follows:

[0044] By interchanging the bases |1110> and |0011> of the C3RY gate, and the bases |1111> and |1100>, we obtain matrix (6):

[0045]

[0046] Complete the construction of the quantum circuit of the dual-excitation operator.

[0047] In one specific implementation scheme, it also includes:

[0048] The quantum circuits of the single-excitation operator and the double-excitation operator are directly constructed into quantum circuits using the basis transformation method.

[0049] In a specific feasible implementation,

[0050] The quantum circuit of the single excitation operator includes three CNOT gates and two RY gates.

[0051] In a specific feasible implementation,

[0052] The quantum circuitry of the dual-excitation operator includes twenty-six CNOT gates, fourteen RY gates, and four X gates.

[0053] In one specific implementation, the basis |01> and basis |11> of the CRY(2θ) gate are interchanged by a CNOT gate with qubit q as the control bit and qubit p as the controlled bit.

[0054] In one specific implementation scheme, the basis |1110> and basis |1100> of the C3RY gate are interchanged, and the basis |1111> and basis |0011> are interchanged, by first applying a CNOT gate with qubit s as the control bit and qubit p as the controlled bit; then applying a CNOT gate with qubit s as the control bit and qubit q as the controlled bit; and finally applying a 0-CNOT gate with qubit s as the control bit and qubit r as the controlled bit.

[0055] Alternatively, by first applying an X gate to qubits r and s respectively, and then applying a CNOT gate with qubit s as the control bit to qubits p, q and r respectively, the basis |1110> and the basis 0011> of the C3RY gate are interchanged, and the basis |1111> and the basis |1100> are interchanged. Attached Figure Description

[0056] Figure 1 The single-excitation operator provided in the embodiments of this application Overall circuit structure diagram;

[0057] Figure 2 A quantum circuit diagram for decomposing a CRY gate into a CNOT gate and an RY gate is provided for embodiments of this application;

[0058] Figure 3 The three-gate crossover CNOT gate provided in this application embodiment can exchange two qubits in the state diagram;

[0059] Figure 4 The single-excitation operator provided in the embodiments of this application Detailed route structure diagram;

[0060] Figure 5 The dual-excitation operator provided in the embodiments of this application The overall circuit structure diagram obtained by the first construction method;

[0061] Figure 6 The dual-excitation operator provided in the embodiments of this application The overall circuit structure diagram obtained by the second construction method;

[0062] Figure 7A schematic diagram of the structure of the C3RY gate, which is decomposed into a CNOT gate and a CRY gate using the V4 decomposition method, as provided in the embodiments of this application;

[0063] Figure 8 The single-excitation operator provided in the embodiments of this application A concrete implementation of the quantum circuit diagram;

[0064] Figure 9 The dual-excitation operator implemented based on method one is provided in the embodiments of this application. The overall quantum circuit diagram;

[0065] Figure 10 The dual-excitation operator based on method two provided in the embodiments of this application The overall quantum circuit diagram;

[0066] Figure 11 The decomposition result diagram of the C3RY(2.4) gate based on the V4 decomposition method provided for the embodiments of this application;

[0067] Figure 12 This is a flowchart illustrating the method for constructing excitation operators in the variational quantum eigenvalue solving algorithm provided in this application embodiment. Detailed Implementation

[0068] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present application will become clearer and more apparent.

[0069] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0070] Furthermore, the technical features involved in the different embodiments of this application described below can be combined with each other as long as they do not conflict with each other.

[0071] To facilitate understanding of the construction method of the excitation operator in the variational quantum eigenvalue solving algorithm provided in this application embodiment, its application scenario is first explained. The construction method of the excitation operator in the variational quantum eigenvalue solving algorithm provided in this application embodiment is used to reduce the number of CNOT gates used and reduce the depth of the quantum circuit. The implementation of the VQE algorithm requires the transformation of fermion excitation operators to construct quantum circuits. Existing transformation methods, such as Jordan-Wigner, Parity basis, Bravyi-Kitaev, and Qubit-Excitation, all first convert the excitation operator into a Pauli string, and then convert the Pauli string into a quantum circuit. Although this can achieve the goal, the number of CNOT gates used is large, resulting in an excessively deep quantum circuit. For current NISQ devices, affected by various noises and operational errors, the shallower the quantum circuit (the fewer CNOT gates used), the easier it is to obtain high-quality computational results. Therefore, designing a better excitation operator transformation method is a very important research direction. Therefore, this application provides a method for constructing excitation operators in a variational quantum eigenvalue solving algorithm to reduce the number of CNOT gates used and decrease the depth of quantum circuits. The following detailed description, in conjunction with specific accompanying drawings, illustrates the method.

[0072] refer to Figures 1 to 12 , Figure 1 The single-excitation operator provided in the embodiments of this application Overall circuit structure diagram; Figure 2 A quantum circuit diagram for decomposing a CRY gate into a CNOT gate and an RY gate is provided for embodiments of this application; Figure 3 The three-gate crossover CNOT gate provided in this application embodiment can exchange two qubits in the state diagram; Figure 4 The single-excitation operator provided in the embodiments of this application Detailed route structure diagram; Figure 5 The dual-excitation operator provided in the embodiments of this application The overall circuit structure diagram obtained by the first construction method; Figure 6 The dual-excitation operator provided in the embodiments of this application The overall circuit structure diagram obtained by the second construction method; Figure 7 A schematic diagram of the structure of the C3RY gate, which is decomposed into a CNOT gate and a CRY gate using the V4 decomposition method, as provided in the embodiments of this application; Figure 8 The single-excitation operator provided in the embodiments of this application A concrete implementation of the quantum circuit diagram; Figure 9 The dual-excitation operator implemented based on method one is provided in the embodiments of this application. The overall quantum circuit diagram; Figure 10 The dual-excitation operator based on method two provided in the embodiments of this application The overall quantum circuit diagram; Figure 11 The decomposition result diagram of the C3RY(2.4) gate based on the V4 decomposition method provided for the embodiments of this application; Figure 12 This is a flowchart illustrating the method for constructing excitation operators in the variational quantum eigenvalue solving algorithm provided in this application embodiment.

[0073] exist Figure 12 In this application, an embodiment provides a method for constructing excitation operators in a variational quantum eigenvalue solving algorithm, comprising the following steps:

[0074] A quantum circuit with a single excitation operator is constructed by performing a basis transformation on the CRY gate.

[0075] In the above technical solution, by performing a basis transformation on the CRY gate, a quantum circuit with a single excitation operator is constructed, which reduces the number of CNOT gates used and decreases the depth of the quantum circuit.

[0076] In one specific implementation scheme, it also includes:

[0077] A quantum circuit with a dual excitation operator is constructed by performing a basis transformation on the C3RY gate.

[0078] In the above technical solution, a quantum circuit with a single excitation operator is constructed by performing a basis transformation on the CRY gate; and a quantum circuit with a double excitation operator is constructed by performing a basis transformation on the C3RY gate, thereby reducing the number of CNOT gates used and reducing the depth of the quantum circuit.

[0079] In one possible implementation, the CRY gate includes a CRY(2θ) gate;

[0080] The single-excitation operator The matrix is:

[0081]

[0082] The matrix of the CRY(2θ) gate is:

[0083]

[0084] The steps to construct a quantum circuit with a single excitation operator by performing a basis transformation on the CRY gate are as follows:

[0085] By interchanging the basis |01> and basis |11> of the CRY(2θ) gate, we obtain matrix (3):

[0086]

[0087] Complete the construction of the quantum circuit of the single excitation operator.

[0088] It should be noted that by inverting each basis in Equation (3), that is, by interchanging the basis |00> with the basis |11> and the basis |01> with the basis |10> (achieved by simultaneously applying an X gate to qubits p and q), the same matrix as that of the single excitation operator can be obtained: Equation (1). However, considering that the essential function of the single excitation operator is to redistribute the population between |01> and |10>, and Equation (3) can already achieve this, the step of inverting each basis can be omitted in practical applications to reduce the use of quantum gates.

[0089] refer to Figure 1 The overall structure of a quantum circuit with a single excitation operator is realized by performing a basis transformation on the CRY(2θ) gate, as shown below. Figure 1 As shown. Further, refer to... Figure 2 and Figure 3 Because the CRY gate can be accessed through, for example Figure 2 The method is decomposed into CNOT gates and RY gates, and combined with Figure 3 The three interleaved CNOT gates shown can perform the swapping operation of the states of two qubits. Figure 1 The structure shown can be further decomposed into, for example: Figure 4 The circuit structure is shown. (As shown in the image.) Figure 4 As shown, this construction method can realize the function of a single-excitation operator using only 3 CNOT gates and 2 RY gates.

[0090] In one possible implementation, the C3RY gate includes a C3RY(2θ) gate;

[0091] The dual-excitation operator The matrix is:

[0092]

[0093] The matrix of the C3RY(2θ) gate is:

[0094]

[0095] The steps to construct a quantum circuit with a dual-excitation operator by performing a basis transformation on the C3RY gate are as follows:

[0096] By interchanging the bases |1110> and |1100> of the C3RY gate, and by interchanging the bases |1111> and |0011>, matrix (4) is obtained, thus completing the construction of the quantum circuit of the dual excitation operator.

[0097] In one possible implementation, the C3RY gate includes a C3RY(2θ) gate;

[0098] The dual-excitation operator The matrix is:

[0099]

[0100] The matrix of the C3RY(2θ) gate is:

[0101]

[0102] The steps to construct a quantum circuit with a dual-excitation operator by performing a basis transformation on the C3RY gate are as follows:

[0103] By interchanging the bases |1110> and |0011> of the C3RY gate, and the bases |1111> and |1100>, we obtain matrix (6):

[0104]

[0105] Complete the construction of the quantum circuit of the dual-excitation operator.

[0106] In one specific implementation scheme, it also includes:

[0107] The quantum circuits of the single-excitation operator and the double-excitation operator are directly constructed into quantum circuits using the basis transformation method.

[0108] In a specific feasible implementation,

[0109] The quantum circuit of the single excitation operator includes three CNOT gates and two RY gates.

[0110] In a specific feasible implementation,

[0111] The quantum circuitry of the dual-excitation operator includes twenty-six CNOT gates, fourteen RY gates, and four X gates.

[0112] In one specific implementation, the basis |01> and basis |11> of the CRY(2θ) gate are interchanged by a CNOT gate with qubit q as the control bit and qubit p as the controlled bit.

[0113] In one specific implementation scheme, the basis |1110> and basis |1100> of the C3RY gate are interchanged, and the basis |1111> and basis |0011> are interchanged, by first applying a CNOT gate with qubit s as the control bit and qubit p as the controlled bit; then applying a CNOT gate with qubit s as the control bit and qubit q as the controlled bit; and finally applying a 0-CNOT gate with qubit s as the control bit and qubit r as the controlled bit.

[0114] Alternatively, by first applying an X gate to qubits r and s respectively, and then applying a CNOT gate with qubit s as the control bit to qubits p, q and r respectively, the basis |1110> and the basis 0011> of the C3RY gate are interchanged, and the basis |1111> and the basis |1100> are interchanged.

[0115] It should be noted that for double-excitation operators... There are two possible construction methods:

[0116] Method 1: Interchange the bases |1110> and |1100> of the C3RY gate, and interchange the bases |1111> and |0011> (this can be achieved by first applying a CNOT gate with qubit s as the control bit and qubit p as the controlled bit; then applying a CNOT gate with qubit s as the control bit and qubit q as the controlled bit; and finally applying a 0-CNOT gate with qubit s as the control bit and qubit r as the controlled bit), to obtain matrix (4), thus completing the construction of the quantum circuit of the dual-excitation operator. Considering that the 0-CNOT gate can be implemented by one CNOT gate and two X gates, in this embodiment, for the dual-excitation operator... The overall structure of the quantum circuit obtained by the first construction method is as follows: Figure 5 As shown.

[0117] Method 2: Interchange the basis |1110> and the basis |0011> of the C3RY gate, and interchange the basis |1111> and the basis |1100> (this can be achieved by first applying X gates to qubits r and s respectively, and then applying CNOT gates with qubit s as the control bit to qubits p, q and r respectively), to obtain matrix (6); if it is to be consistent with the matrix expression of the double excitation operator: formula (4), it is only necessary to invert each basis bit by bit (this can be achieved by applying an X gate to each qubit). However, considering that the essential effect of the double excitation operator is to realize the redistribution of the population between |0011> and |1100>, and formula (6) can already achieve this, this step can be omitted in practical applications to reduce the use of quantum gates. Therefore, in this patent, for the double excitation operator The overall structure of the quantum circuit obtained by the second construction method is as follows: Figure 6 As shown.

[0118] The C3RY gate used in both of the above methods can be accessed through, for example... Figure 7 The V4 decomposition method shown [5] Decomposed into CNOT and CRY gates. Combined as follows: Figure 2 As shown in the decomposition method of CRY gates, it can be seen that both method one and method two use 26 CNOT gates, 14 RY gates and 4 X gates to implement the double-excitation operator.

[0119] In the above technical solution, this application proposes a low-cost construction method for the excitation operator used in the VQE algorithm by performing a basis transformation on the CRY gate and the C3RY gate:

[0120] For single-excitation operators, the method in this application only requires 3 CNOT gates and 2 RY gates to achieve the target function;

[0121] For the dual-excitation operator, this application proposes two schemes, both of which can achieve the target function using only 26 CNOT gates, 14 RY gates and 4 X gates.

[0122] For single-excitation and double-excitation operators, compared to the current best-performing Qubit-Excitation... [4] The transformation schemes (using 4 and 48 CNOT gates respectively) reduce the number of CNOT gates by 1 and 22 respectively, resulting in an overall reduction of implementation cost of approximately 45%. In the current era of NISQ (Noisy Intermediate-Scale Quantum) devices, this can significantly improve the experimental performance of the VQE (Variational Quantum Eigensolver) algorithm.

[0123] To further explain the method proposed in this application for low-cost implementation of excitation operators, using a single excitation operator... and double-excitation operator As a specific example, a concrete quantum circuit is shown:

[0124] For single-excitation operators The specific implementation of the quantum circuit based on this application is as follows: Figure 8 As shown.

[0125] For bi-excitation operators Based on the specific overall quantum circuits of Method 1 and Method 2 in this patent, as shown below: Figure 9 and Figure 10 As shown.

[0126] Figure 9 and Figure 10 The decomposition result of the C3RY(2.4) gate in the V4 decomposition method is as follows: Figure 11 As shown.

[0127] In the above technical solution, a quantum circuit with a single excitation operator is constructed by performing a basis transformation on the CRY gate; and a quantum circuit with a double excitation operator is constructed by performing a basis transformation on the C3RY gate, thereby reducing the number of CNOT gates used and reducing the depth of the quantum circuit.

[0128] Those skilled in the art will know that this application can be implemented as a system, method, or computer program product.

[0129] Therefore, this disclosure can be implemented in the following forms: it can be entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software, generally referred to herein as a "circuit," "module," or "system." Furthermore, in some embodiments, this application can also be implemented as a computer program product in one or more computer-readable media, which contains computer-readable program code.

[0130] Any combination of one or more computer-readable media may be used. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device.

[0131] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application. Based on this, various substitutions and improvements can be made to this application, all of which fall within the protection scope of this application.

Claims

1. A method for constructing excitation operators in a variational quantum eigenvalue solving algorithm, characterized in that, Includes the following steps: Through the The gate undergoes a basis transformation to construct a quantum circuit with a single excitation operator; Also includes: Through the The gate undergoes a basis transformation to construct a quantum circuit with a double excitation operator; The Doors include Door; The single-excitation operator The matrix is: ；(1) The The gate matrix is: ；(2) Through the The steps for constructing a quantum circuit with a single excitation operator by performing a basis transformation on the gate are as follows: Will The base of the door With base By interchanging the components, we obtain matrix (3): ；(3) Complete the construction of the quantum circuit for the single excitation operator; The Doors include Door; The dual-excitation operator The matrix is: ；(4) The The gate matrix is: ；(5) Through the The steps for constructing a quantum circuit with a double-excitation operator by performing a basis transformation on the gate are as follows: Will The base of the door With base To interchange, base With base The two operators are interchanged to obtain matrix (4), thus completing the construction of the quantum circuit of the dual excitation operator.

2. The method for constructing excitation operators in the variational quantum eigenvalue solving algorithm according to claim 1, characterized in that, The Doors include Door; The dual-excitation operator The matrix is: ； (4) The The gate matrix is: ； (5) Through the The steps for constructing a quantum circuit with a double-excitation operator by performing a basis transformation on the gate are as follows: Will The base of the door With base To interchange, base With base By interchanging the components, we obtain matrix (6): ；(6) Complete the construction of the quantum circuit of the dual-excitation operator.

3. The method for constructing excitation operators in the variational quantum eigenvalue solving algorithm according to claim 1 or 2, characterized in that, Also includes: The quantum circuits of the single-excitation operator and the double-excitation operator are directly constructed into quantum circuits using the basis transformation method.

4. The method for constructing excitation operators in the variational quantum eigenvalue solving algorithm according to claim 3, characterized in that, The quantum circuit of the single-excitation operator includes three Door and two Door.

5. The method for constructing excitation operators in the variational quantum eigenvalue solving algorithm according to claim 4, characterized in that, The quantum circuitry of the dual-excitation operator comprises twenty-six... Doors, fourteen The door and four Door.

6. The method for constructing excitation operators in the variational quantum eigenvalue solving algorithm according to claim 5, characterized in that, Through a quantum bit To control bits, using qubits For controlled bits Goalkeeper The base of the door With base They were interchanged.

7. The method for constructing the excitation operator in the variational quantum eigenvalue solving algorithm according to claim 6, characterized in that, By first applying qubits For control bits, qubits For controlled bits Gate; then apply qubits For control bits, qubits For controlled bits The gate is finally applied with qubits. For control bits, qubits For the controlled bits 0- Goalkeeper The base of the door With base To interchange, base With base To interchange; Alternatively, by first testing the qubits and Apply separately Gate, then to qubit , and Each is given a qubit. For control bits Goalkeeper The base of the door With base To interchange, base With base They were interchanged.

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