Construction method of leftmost excitation operator of a tentative circuit in a VQE algorithm

Abstract

The application provides a construction method of an excitation operator at the left end of a tentative circuit in a VQE algorithm, and the method comprises the following steps: under a limitation, an equivalent quantum circuit is constructed through an RY(2θ) gate to prepare an output state of the excitation operator which is the same as that in a standard construction quantum circuit, and the depth of the quantum circuit of the excitation operator at the left end of the tentative circuit is reduced. In the technical scheme, under the limitation, the equivalent quantum circuit is constructed through the RY(2θ) gate to prepare the output state of the excitation operator which is the same as that in the standard construction quantum circuit, and the depth of the quantum circuit of the excitation operator at the left end of the tentative circuit is reduced, so that the solving quality of the variational quantum eigenvalue solution algorithm is effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of quantum computing and quantum information technology, and in particular to a construction method of a leftmost excitation operator in a variational quantum eigensolver (VQE) algorithm. BACKGROUND

[0002] The variational quantum eigensolver (VQE) algorithm can prepare different trial states by adjusting the parameters in the ansatz circuit. When the energy expectation value of the Hamiltonian of a given molecule at a trial state reaches a minimum, the trial state is the ground state of the molecule, and the expectation value of the Hamiltonian at this time is the ground state energy of the molecule. After obtaining the ground state energy of the molecule, information such as the chemical reaction rate, optical properties, and stable structure of the molecule can be predicted. Therefore, the VQE algorithm has important applications in high-temperature superconductivity, solid-state physics, transition metal catalysis, and biochemistry.

[0003] The key to the VQE algorithm is the construction of the ansatz circuit. Due to the influence of noise and operation errors on current noisy intermediate-scale quantum (NISQ) devices, the depth of quantum circuits that can be accurately executed is limited, making it difficult to effectively solve the energy level problem of large molecules. Designing and constructing ansatz circuits with shallower depth to improve the solving quality of the VQE algorithm is an important research direction.

[0004] The current mainstream design idea of the ansatz circuit is to separate single and double excitation operators from the second-quantized molecular Hamiltonian. At this time, the excitation operator is in the form of fermions, which cannot be directly constructed into a quantum circuit that can be executed by a quantum computer. Transformation methods such as Jordan-Wigner [1] , Parity basis [2] , Bravyi-Kitaev [3] , or Qubit-Excitation [4] are used to convert these fermion excitation operators into Pauli strings, and then the ansatz circuit is constructed based on these Pauli strings. Among them, the Qubit-Excitation transformation has the best effect, and for single and double excitation operators, it requires quantum circuits with depths of 4 and 48, respectively, to implement. However, for larger molecules, even using the Qubit-Excitation transformation, the depth of the final ansatz circuit still exceeds the range that current NISQ devices can withstand. Therefore, designing an excitation operator construction scheme with shallower depth is the key to promoting the practicality of the VQE algorithm.

[0005] In summary, the implementation of VQE algorithm requires the construction of excitation operators in fermionic form into quantum circuits. Current mainstream construction schemes, such as Jordan-Wigner, Parity basis, Bravyi-Kitaev and Qubit-Excitation, achieve a depth of quantum circuits for implementing excitation operators that is too large, resulting in the final overall ansatz circuit being unable to be accurately executed by current NISQ devices.

[0006] References:

[0007] [1] Pascual Jordan and Eugene Paul Wigner. das paulische Springer, 1993.

[0008] [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. International Journal of Quantum Chemistry, 115(19): 1431-1441, 2015.

[0009] [3] Sergey B Bravyi and Alexei Yu Kitaev. Fermionic quantum computation. Annals of Physics, 298(1): 210-226, 2002.

[0010] [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. SUMMARY

[0011] The application provides a construction method of an excitation operator at the left end of a tentative circuit in a VQE algorithm, which is used to reduce the depth of a quantum circuit and effectively improve the solution quality of a variational quantum eigenvalue solution algorithm.

[0012] The application provides a construction method of an excitation operator at the left end of a tentative circuit in a VQE algorithm, which comprises the following steps:

[0013] Under the limitation, an equivalent quantum circuit is constructed by using an RY(2θ) gate, an output state of the excitation operator under a standard construction quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator at the left end of the tentative circuit is reduced.

[0014] In the above technical solution, under the limitation, an equivalent quantum circuit is constructed by using an RY(2θ) gate, an output state of the excitation operator under a standard construction quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator at the left end of the tentative circuit is reduced, thereby effectively improving the solution quality of the variational quantum eigenvalue solution algorithm.

[0015] In a specific embodiment, the limitation comprises:

[0016] The input of the tentative circuit is a full zero state;

[0017] The construction circuit is located at the left end of the tentative circuit;

[0018] The construction circuit cannot act on a quantum bit that has been acted on.

[0019] In a specific embodiment, under the limitation, an equivalent quantum circuit is constructed by using an RY(2θ) gate, an output state of the excitation operator under a standard construction quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator at the left end of the tentative circuit is reduced, and the step comprises:

[0020] Under the limitation, an equivalent quantum circuit of a single excitation operator is constructed by using an RY(2θ) gate, an output state of the single excitation operator under a standard construction quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator at the left end of the tentative circuit is reduced.

[0021] In a specific embodiment, under the limitation, an equivalent quantum circuit is constructed by using an RY(2θ) gate, an output state of the excitation operator under a standard construction quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator at the left end of the tentative circuit is reduced, and the step comprises:

[0022] Under the limitation, an equivalent quantum circuit of a double excitation operator is constructed by using an RY(2θ) gate, an output state of the double excitation operator under a standard construction quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator at the left end of the tentative circuit is reduced.

[0023] In one specific implementation, the standard constructed quantum circuit is an excitation operator quantum circuit constructed using the Qubit Excitation transformation.

[0024] In one specific implementation, the matrix of the single excitation operator is:

[0025]

[0026] When the single excitation operator is located at the leftmost end of the hypothetical circuit, the input state is |01> and the output state is cos(θ)|01> + sin(θ)|10>;

[0027] The matrix of the RY(2θ) gate acting on the qubit q is:

[0028]

[0029] Under the constraint, the steps of preparing the same output state of the single excitation operator under the standard constructed quantum circuit by constructing a single excitation operator equivalent quantum circuit through the RY(2θ) gate are as follows:

[0030] When the input state is |00>, the RY(2θ) gate transforms it into cos(θ)|00> + sin(θ)|01>;

[0031] Then construct a single excitation operator equivalent quantum circuit to prepare the same output state cos(θ)|01> + sin(θ)|10> of the single excitation operator under the standard constructed quantum circuit.

[0032] In one specific implementation, the specific steps of constructing a single excitation operator equivalent quantum circuit are as follows:

[0033] Act on cos(θ)|00> + sin(θ)|01> with a CNOT gate with q as the control qubit and p as the target qubit, and an X gate with q as the action qubit, to prepare the output state cos(θ)|01> + sin(θ)|10>.

[0034] In one specific implementation, the matrix of the double excitation operator is:

[0035]

[0036] When the double excitation operator is located at the leftmost end of the hypothetical circuit, the input state is |0011> and the output state is cos(θ)|0011> - sin(θ)|1100>;

[0037] Under the restriction condition, the same output state of the double-excitation operator under the standard construction quantum circuit is prepared by constructing a double-excitation operator equivalent quantum circuit, and the specific steps are as follows:

[0038] When the input state is |0000>, the RY(2θ) gate converts it into cos(θ)|0000>+sin(θ)|0001>;

[0039] Then, the double-excitation operator equivalent quantum circuit is constructed to prepare the same output state cos(θ)|0011>-sin(θ)|1100> of the double-excitation operator under the standard construction quantum circuit.

[0040] In a specific embodiment, the specific steps of constructing the double-excitation operator equivalent quantum circuit are as follows:

[0041] Two CNOT gates are applied to cos(θ)|0000>+sin(θ)|0001> with s as the control bit and r and q as the controlled bits, and the quantum state cos(θ)|0000>+sin(θ)|0111> is obtained;

[0042] Again, the CNOT gate is applied with r as the control bit and p as the controlled bit, and the quantum state cos(θ)|0000>+sin(θ)|1111> is obtained;

[0043] Then, the X gate is applied to s and r, and the quantum state cos(θ)|0011>+sin(θ)|1100> is obtained;

[0044] Finally, the Z gate is applied to p, and the output state cos(θ)|0011>-sin(θ)|1100> is obtained.

[0045] In a specific embodiment, the quantum state of the single-excitation operator is mapped to the quantum bits as |pq>;

[0046] The quantum state of the double-excitation operator is mapped to the quantum bits as |pqrs>. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 The quantum circuit diagram of the single-excitation operator is provided for the input quantum state |00> of the embodiment of the present application;

[0048] Figure 2 The quantum circuit diagram of the double-excitation operator is provided for the input quantum state |0000> of the embodiment of the present application;

[0049] Figure 3 The single-excitation operator provided in the embodiments of this application A concrete implementation of the quantum circuit diagram;

[0050] Figure 4 The dual-excitation operator provided in the embodiments of this application A concrete implementation of the quantum circuit diagram;

[0051] Figure 5 A flowchart illustrating the method for constructing the leftmost excitation operator of the proposed line in the VQE algorithm provided in this application embodiment. Detailed Implementation

[0052] 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.

[0053] 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.

[0054] 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.

[0055] To facilitate understanding of the construction method of the leftmost excitation operator in the VQE algorithm provided in this application embodiment, its application scenario is first explained. The construction method of the leftmost excitation operator in the VQE algorithm provided in this application embodiment is used to reduce the depth of quantum circuits and effectively improve the solution quality of variational quantum eigenvalue solving algorithms. Currently, the mainstream design approach for proposed circuits is to separate single and double excitation operators based on the molecular Hamiltonian of the second quantization. At this time, the excitation operators are in fermion form and cannot be directly constructed into quantum circuits that can be executed by quantum computers. It is necessary to use methods such as Jordan-Wigner... [1] Parity basis [2] Bravyi-Kitaev [3] or Qubit-Excitation [4]The isomorphism method converts these fermion excitation operators into Pauli strings, and finally constructs the ansatz circuit according to the Pauli strings. The Qubit-Excitation transformation has the best effect, and for single and double excitation operators, it requires quantum circuits with depths of 4 and 48, respectively, to implement. However, for larger molecules, even using the Qubit-Excitation transformation, the depth of the final ansatz circuit still exceeds the range that can be tolerated by current NISQ devices. Therefore, designing an excitation operator construction scheme with shallower circuit depth is the key to promoting the practicality of the VQE algorithm. To this end, the embodiment of the present application provides a construction method of the leftmost excitation operator of the ansatz circuit in the VQE algorithm, to reduce the depth of the quantum circuit and effectively improve the solving quality of the variational quantum eigenvalue solving algorithm. The following will be described in detail in conjunction with specific drawings.

[0056] Reference Figures 1 to 5 , Figure 1 For the input quantum state |00> provided by the embodiment of the present application, the quantum circuit diagram of the single excitation operator is implemented; Figure 2 For the input quantum state |0000> provided by the embodiment of the present application, the quantum circuit diagram of the double excitation operator is implemented; Figure 3 The specific implementation quantum circuit diagram of the single excitation operator provided by the embodiment of the present application; Figure 4 The specific implementation quantum circuit diagram of the double excitation operator provided by the embodiment of the present application; Figure 5 The flow chart of the construction method of the leftmost excitation operator of the ansatz circuit in the VQE algorithm provided by the embodiment of the present application.

[0057] In Figure 5 , the embodiment of the present application provides a construction method of the leftmost excitation operator of the ansatz circuit in the VQE algorithm, comprising the following steps:

[0058] Under the constraint condition, an equivalent quantum circuit is constructed by RY(2θ) gate, and the same output state of the excitation operator under the standard construction quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the ansatz circuit is reduced.

[0059] In the above technical solution, under the constraint condition, an equivalent quantum circuit is constructed by RY(2θ) gate, and the same output state of the excitation operator under the standard construction quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the ansatz circuit is reduced, effectively improving the solving quality of the variational quantum eigenvalue solving algorithm.

[0060] In one specific implementable scheme, the constraint condition comprises:

[0061] The input to the proposed circuit is an all zero state;

[0062] The construction circuit is located at the leftmost end of the proposed circuit;

[0063] The construction circuit cannot act on a qubit that has already been acted upon.

[0064] In one specific implementation, under the constraint that the equivalent quantum circuit is constructed by RY(2θ) gates to produce the same output state of the excitation operator as the standard construction quantum circuit, the step of reducing the depth of the quantum circuit for the excitation operator located at the leftmost end of the proposed circuit comprises:

[0065] In one specific implementation, under the constraint that the equivalent quantum circuit is constructed by RY(2θ) gates to produce the same output state of the single excitation operator as the standard construction quantum circuit, the step of reducing the depth of the quantum circuit for the excitation operator located at the leftmost end of the proposed circuit comprises:

[0066] In one specific implementation, under the constraint that the equivalent quantum circuit is constructed by RY(2θ) gates to produce the same output state of the excitation operator as the standard construction quantum circuit, the step of reducing the depth of the quantum circuit for the excitation operator located at the leftmost end of the proposed circuit comprises:

[0067] In one specific implementation, under the constraint that the equivalent quantum circuit is constructed by RY(2θ) gates to produce the same output state of the double excitation operator as the standard construction quantum circuit, the step of reducing the depth of the quantum circuit for the excitation operator located at the leftmost end of the proposed circuit comprises:

[0068] In one specific implementation, the standard construction quantum circuit is an excitation operator quantum circuit constructed using the Qubit Excitation transformation.

[0069] In one specific implementation, the single excitation operator has a matrix of:

[0070]

[0071] When the single excitation operator is located at the leftmost end of the proposed circuit, the input state is |01> and the output state is cos(θ)|01>+sin(θ)|10>;

[0072] The matrix of the RY(2θ) gate acting on qubit q is:

[0073]

[0074] Under the restriction, the steps of preparing the same output state of the single-excitation operator under the standard construction quantum circuit by constructing the single-excitation operator equivalent quantum circuit are as follows:

[0075] When the input state is |00>, the RY(2θ) gate transforms it into cos(θ)|00>+sin(θ)|01>;

[0076] Then the single-excitation operator equivalent quantum circuit is constructed to prepare the same output state cos(θ)|01>+sin(θ)|10> of the single-excitation operator under the standard construction quantum circuit.

[0077] In a specific implementable embodiment, the specific steps of constructing the single-excitation operator equivalent quantum circuit are as follows:

[0078] The CNOT gate with q as the control bit and p as the target bit and the X gate with q as the action bit are sequentially applied to cos(θ)|00>+sin(θ)|01> to prepare the output state cos(θ)|01>+sin(θ)|10>.

[0079] In a specific implementable embodiment, the matrix of the double-excitation operator is as follows:

[0080]

[0081] When the double-excitation operator is located at the leftmost end of the pseudo-circuit, the input state is |0011> and the output state is cos(θ)|0011>-sin(θ)|1100>;

[0082] Under the restriction, the steps of preparing the same output state of the double-excitation operator under the standard construction quantum circuit by constructing the double-excitation operator equivalent quantum circuit are as follows:

[0083] When the input state is |0000>, the RY(2θ) gate transforms it into cos(θ)|0000>+sin(θ)|0001>;

[0084] Then the double-excitation operator equivalent quantum circuit is constructed to prepare the same output state cos(θ)|0011>-sin(θ)|1100> of the double-excitation operator under the standard construction quantum circuit.

[0085] In a specific implementable embodiment, the specific steps of constructing the double-excitation operator equivalent quantum circuit are as follows:

[0086] cos(θ)|0000>+sin(θ)|0111> is obtained by applying two CNOT gates with s as the control bit and r and q as the controlled bits on cos(θ)|0000>+sin(θ)|0001>;

[0087] cos(θ)|0000>+sin(θ)|1111> is obtained by applying again a CNOT gate with r as the control bit and p as the controlled bit;

[0088] cos(θ)|0011>+sin(θ)|1100> is obtained by applying X gates on s and r again;

[0089] Finally, the output state cos(θ)|0011>-sin(θ)|1100> is obtained by applying a Z gate on p.

[0090] In one specific embodiment, the quantum state of the single-excitation operator is mapped to the quantum bits as |pq>;

[0091] The quantum state of the double-excitation operator is mapped to the quantum bits as |pqrs>.

[0092] Specifically, for the single-excitation operator its matrix representation is:

[0093]

[0094] If the Qubit Excitation transformation is used to construct the matrix (here we call it the standard construction of the single-excitation operator), the depth of the quantum circuit is 4 (considering that the implementation cost of CNOT gates is much higher than that of single-qubit gates in experiments, so the depth of the circuit only counts CNOT gates). Considering that its role is to distribute the population of quantum states |01> and |10>, especially when it is located at the leftmost end of the proposed circuit, the input state is |01>, and the output state is cos(θ)|01>+sin(θ)|10> (where the quantum state is mapped to the quantum bits as |pq>). To complete this task and minimize the depth of the quantum circuit, only this special case needs to be considered, and the entire matrix (1) does not need to be constructed as in the Qubit Excitation transformation. That is, only the quantum circuit needs to be designed to prepare the same output state cos(θ)|01>+sin(θ)|10>.

[0095] Since the matrix form of RY(2θ) acting on quantum bit q is:

[0096]

[0097] If the input state is |00>, the RY(2θ) quantum gate can transform it into cos(θ)|00>+sin(θ)|01>. Then, by applying a CNOT gate with q as the control bit and p as the target bit, and an X gate with q as the action bit, the quantum state cos(θ)|01>+sin(θ)|10> can be prepared. The quantum circuit representation of this series of operations is shown in FIG. 4. The result is the same as the single-excitation operator acting on |01>, but the circuit depth is only 1. Therefore, when the single-excitation operator is located at the leftmost end of the circuit, the state |00> can be used instead of |01> as the input state, and the single-excitation operator can be implemented by the quantum circuit shown in FIG. 5. Figure 1 Figure 1

[0098] Specifically, for the double-excitation operator The matrix outer product representation is:

[0099]

[0100] If the Qubit Excitation transformation is used to construct this matrix (here we call it the standard construction of the double-excitation operator), a quantum circuit with a depth of 48 is required. Considering that its role is to distribute the populations of the quantum states |0011> and |1100> (where the mapping relationship between the quantum states and the quantum bits is |pqrs>), especially when it is located at the leftmost end of the proposed circuit, the input state is |0011>, and the output state is cos(θ)|0011>-sin(θ)|1100>. To complete this task and minimize the depth of the quantum circuit, we can only focus on this special case and do not need to construct the entire matrix (3) as in the Qubit Excitation transformation. That is, only the quantum circuit needs to be designed to prepare the same output state cos(θ)|0011>-sin(θ)|1100>. To do this, the quantum circuit shown in FIG. 6 can be used. Figure 2

[0101] In Figure 2 ​​​​For the input state |0000>, the RY(2θ) gate transforms it into cos(θ)|0000>+sin(θ)|0001>. Then, by applying two CNOT gates with s as the control bit and r and q as the controlled bits, the quantum state cos(θ)|0000>+sin(θ)|0111> is obtained. Again, by applying a CNOT gate with r as the control bit and p as the controlled bit, the quantum state cos(θ)|0000>+sin(θ)|1111> is obtained. Then, by applying X gates on s and r, the quantum state cos(θ)|0011>+sin(θ)|1100> is obtained. Finally, by applying a Z gate on p, the target output state cos(θ)|0011>-sin(θ)|1100> is obtained. The output quantum state of this circuit is the same as the output state of the two-excitation operator acting on the input state |0011>, but the depth of this circuit is only 2.

[0102] It should be noted that the above simple construction method of single-excitation operators and double-excitation operators requires the input state to be |00> or |0000>, and only in this case is the output quantum state consistent with the output quantum state of the standard construction method. Otherwise, non-physical results will occur in the output quantum state, causing the VQE algorithm to fail. This will impose three restrictions on the application of this construction method: first, the input of the proposed circuit is no longer the Hatree Fock state, but should be the all-zero state; second, the circuit constructed by the simple construction method must be located at the leftmost end of the proposed circuit, otherwise the input state is not |00> or |0000>; third, the simple construction method cannot be repeatedly applied to quantum bits that have already been acted on. If the excitation operator needs to be applied again, the standard construction method must be used to construct the quantum circuit.

[0103] However, even with the above limitations, this method can be used to construct the initial part of the proposed circuit in almost all VQE algorithms to reduce the depth of the quantum circuit. Considering that the simple construction method can reduce the circuit depth (46) by a much larger margin when used to construct double-excitation operators (1) than when used to construct single-excitation operators, this method should be used to construct double-excitation operators in actual use.

[0104] Specifically, for a molecule with n spatial orbitals and m electron pairs, the maximum circuit depth reduced by this method is 46, and the minimum is 3. The maximum number of CNOT gates reduced is 46*min(m-n, m), and the minimum is 6*min(m-n, m).

[0105] In the embodiments of the present application, for the excitation operator located at the leftmost end of the proposed circuit, a simple construction method is proposed, which can be used to reduce the depth of the proposed circuit of the VQE algorithm. For single-excitation operators and double-excitation operators, the depth of the constructed quantum circuit is only 1 and 2. Although this method has obvious limitations, the application effect and application range are still considerable.

[0106] To further explain the method proposed in the application for implementing the excitation operator, a single excitation operator located at the left end of the assumed circuit and a double excitation operator As an example, a specific quantum circuit is shown.

[0107] For the single excitation operator A specific implementation of the quantum circuit based on the method of the application is shown in Figure 3 .

[0108] For the double excitation operator A specific implementation of the quantum circuit based on the method of the application is shown in Figure 4 .

[0109] In the above technical solution, under the constraint condition, the RY(2θ) gate is used to construct an equivalent quantum circuit, and the output state of the excitation operator under the standard construction quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator located at the left end of the assumed circuit is reduced, thereby effectively improving the solution quality of the variational quantum eigenvalue solving algorithm.

[0110] Those skilled in the art know that the present application can be implemented as a system, a method or a computer program product.

[0111] Therefore, the present disclosure can be embodied in the form of a complete hardware, a complete software (including firmware, resident software, microcode, etc.), or a combination of hardware and software, which is generally referred to as "circuit", "module" or "system" herein. In addition, in some embodiments, the present application can also be implemented in the form of a computer program product in one or more computer readable media, which contains computer readable program code.

[0112] Any combination of one or more computer readable medium can be used. The computer readable medium can be a computer readable signal medium or a computer readable storage medium. The computer readable storage medium can be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or apparatus, or any combination of the above. More specific examples (non-exhaustive list) of the computer readable storage medium include: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read only memory (ROM), erasable programmable read only memory (EPROM or flash memory), optical fibers, portable compact disk read only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the above. In this document, the computer readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, device or apparatus.

[0113] Although the embodiments of the present application have been shown and described above, it is to be understood that the above-described embodiments are merely exemplary, and are not to be understood as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above-described embodiments within the scope of the present application. On this basis, various replacements and improvements can be made to the present application, and these all fall within the protection scope of the present application.

Claims

1. A method for constructing the leftmost excitation operator of a line in a VQE algorithm, characterized in that, Includes the following steps: Under constraints, through The gate construction is equivalent to a quantum circuit, and the same output state of the excitation operator under the standard constructed quantum circuit is prepared. The depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced. The limiting conditions include: The input to the proposed circuit is assumed to be all zeros. The constructed route is located at the leftmost end of the proposed route; The circuit cannot be used repeatedly on a qubit that has already been used; Under constraints, through The steps of constructing a gate equivalent to a quantum circuit, preparing an excitation operator with the same output state as a standard constructed quantum circuit, and reducing the depth of the quantum circuit for the excitation operator located at the leftmost end of the proposed circuit include: Under constraints, through The gate constructs a single excitation operator that is equivalent to a quantum circuit, and prepares the same output state of the single excitation operator under the standard constructed quantum circuit. The depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced. pass The steps of constructing a gate equivalent to a quantum circuit, preparing an excitation operator with the same output state as a standard constructed quantum circuit, and reducing the depth of the quantum circuit for the excitation operator located at the leftmost end of the proposed circuit include: Under constraints, through The gate constructs a double excitation operator equivalent to a quantum circuit, and prepares the same output state of the double excitation operator under the standard constructed quantum circuit, thereby reducing the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit. The standard constructed quantum circuit is an excitation operator quantum circuit constructed using the Qubit Excitation transformation; The single-excitation operator The matrix is: ；(1) When the single-excitation operator is located at the leftmost end of the proposed line, the input state is: The output state is ; Action on qubits On The gate matrix is: ；(2) Under constraints, through The steps for preparing a single-excitation operator with the same output state as a standard constructed quantum circuit are as follows: (This section is incomplete and requires further context.) In the input state At that time, the The door transformed it into ; Then, an equivalent quantum circuit for a single-excitation operator was constructed, and the same output state of the single-excitation operator under the standard constructed quantum circuit was prepared. ; The specific steps for constructing a single-excitation operator equivalent quantum circuit are as follows: right Acting in sequence To control bits, CNOT gate for target bit, and with The output state is prepared for the X gate, which is the active bit. .

2. The method for constructing the leftmost excitation operator of the proposed line in the VQE algorithm according to claim 1, characterized in that, The dual-excitation operator The matrix is: ；(3) When the dual-excitation operator is located at the leftmost end of the proposed line, the input state is: The output state is ; Under constraints, through The steps for preparing the same output state of the gate-constructed double-excitation operator as that of the standard constructed quantum circuit are as follows: In input state At that time, the The door transformed it into ; Then, an equivalent quantum circuit for the double-excitation operator was constructed to prepare the same output state of the double-excitation operator under the standard constructed quantum circuit. .

3. The method for constructing the leftmost excitation operator of the proposed line in the VQE algorithm according to claim 2, characterized in that, The specific steps for constructing a quantum circuit equivalent to a dual-excitation operator are as follows: right function to To control bits, and Two CNOT gates for the controlled qubits yield the quantum state. ; Acting again To control bits, A CNOT gate for controlled qubits yields a quantum state. ; Again and Applying the X gate yields a quantum state. ; Finally, through the analysis of Applying a Z-gate yields the output state. .

4. The method for constructing the leftmost excitation operator of the proposed line in the VQE algorithm according to claim 3, characterized in that, The single-excitation operator The mapping relationship between quantum states and qubits is as follows: ; The dual-excitation operator The mapping relationship between quantum states and qubits is as follows: .

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