Construction method of excitation operator at leftmost end of planned line in VQE algorithm

Abstract

The invention provides a construction method of an excitation operator at the leftmost end of a simulated circuit in a VQE algorithm, and the method comprises the following steps: constructing an equivalent quantum circuit through an RY (2 theta) gate under a limiting condition, preparing the same output state of the excitation operator under a standard construction quantum circuit, and carrying out the construction of the excitation operator at the leftmost end of the simulated circuit in the VQE algorithm. And reducing the depth of the quantum circuit of the excitation operator at the leftmost end of the to-be-set circuit. According to the technical scheme, under the limiting condition, the equivalent quantum circuit is constructed through the RY (2 theta) gate, 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 to-be-set circuit is reduced, and the solving quality of the variable component sub-intrinsic solicitation algorithm is effectively improved.

Description

Background Art

[0002] The variational quantum eigensolver (VQE) algorithm can prepare different trial states by adjusting the parameters in the proposed circuit. When the energy expectation value of the Hamiltonian of a given molecule in a certain trial state reaches the 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 knowing the ground state energy of the molecule, 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, biochemistry and other fields.

[0003] The key to the VQE algorithm is the construction of the simulated circuit. Since the current noisy intermediate-scale quantum (NISQ) devices are affected by noise and operational errors, the depth of the quantum circuit that can be accurately executed is limited, so that it is temporarily unable to effectively handle the energy level solution problem of large molecules. Designing and constructing a shallower simulated circuit to improve the solution quality of the VQE algorithm is an important current research direction.

[0004] The mainstream design idea of ​​the proposed circuit is to separate the single and double excitation operators based on the second quantized molecular Hamiltonian. At this time, the excitation operator is in the form of fermions and cannot be directly constructed into a quantum circuit that can be executed by a quantum computer. It is necessary to use the Jordan-Wigner [1] 、Parity basis [2] Bravyi-Kitaev [3] or Qubit-Excitation [4] These fermion excitation operators are converted into Pauli strings by transformation methods, and finally the simulated circuits are constructed based on these Pauli strings. Among them, Qubit-Excitation transformation has the best effect. For single and double excitation operators, quantum circuits with depths of 4 and 48 are required to be implemented respectively. However, for larger molecules, even with Qubit-Excitation transformation, the depth of the simulated circuit obtained in the end still exceeds the range that current NISQ equipment can withstand. Therefore, designing an excitation operator construction scheme with a shallower circuit depth is the key to promoting the practical application of the VQE algorithm.

[0005] In summary, the implementation of the VQE algorithm requires the construction of fermion-based excitation operators as quantum circuits. The current mainstream construction schemes, such as Jordan-Wigner, Parity basis, Bravyi-Kitaev, and Qubit-Excitation, use quantum circuits that are too deep to realize the excitation operators, resulting in the overall proposed circuit being unable to be accurately executed by current NISQ devices.

[0006] References:

[0007] [1]Pascual Jordan and Eugene Paul Wigner. The Paulist Springer, 1993.

[0008] [2]Andrew Tranter, Sarah Sofia, Jake Seeley, Michael Kaicher, Jarrod McClean, Ryan Babbush, Peter V Coveney, Florian Mintert, Frank Wilhelm, and PeterJ 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 quantumcomputation. Annals of Physics, 298(1):210-226,2002.

[0010] [4]Yordan S Yordanov, Vasileios Armaos, Crispin HW Barnes, and David RMArvidsson-Shukur. Qubit-excitation-based adaptive variational quantumeigensolver. Communications Physics, 4(1):228,2021. Summary of the invention

[0011] The present application provides a method for constructing the leftmost excitation operator of a proposed circuit in a VQE algorithm, so as to reduce the depth of the quantum circuit and effectively improve the solution quality of the variational quantum eigensolution algorithm.

[0012] The present application provides a method for constructing a leftmost excitation operator of a proposed line in a VQE algorithm, comprising the following steps:

[0013] Under restricted conditions, an equivalent quantum circuit is constructed through RY(2θ) gates to prepare the same output state of the excitation operator under the standard constructed quantum circuit, and reduce the depth of the quantum circuit of the excitation operator at the leftmost end of the proposed circuit.

[0014] In the above technical scheme, under restricted conditions, an equivalent quantum circuit is constructed through the RY(2θ) gate to prepare the same output state of the excitation operator under the standard constructed quantum circuit, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced, which effectively improves the solution quality of the variational quantum eigensolution algorithm.

[0015] In a specific implementation scheme, the restrictions include:

[0016] The input of the proposed circuit is in the all-zero state;

[0017] The construction line is located at the leftmost end of the proposed line;

[0018] The construction circuit cannot repeat the operation on a quantum bit that has already been operated on.

[0019] In a specific implementation scheme, under restricted conditions, an equivalent quantum circuit is constructed by an RY(2θ) gate to prepare the same output state of the excitation operator under the standard construction quantum circuit, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced, including:

[0020] Under restricted conditions, a single excitation operator equivalent quantum circuit is constructed through RY(2θ) gates, and the same output state of the single excitation operator under the standard constructed quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced.

[0021] In a specific implementation method, an equivalent quantum circuit is constructed by an RY(2θ) gate to prepare the same output state of the excitation operator under the standard construction quantum circuit, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced, including:

[0022] Under restricted conditions, a double excitation operator equivalent quantum circuit is constructed through RY(2θ) gates, and the same output state of the double excitation operator under the standard constructed quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced.

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

[0024] In a specific embodiment, the single excitation operator The matrix is:

[0025]

[0026] 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>;

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

[0028]

[0029] Under restricted conditions, the steps of constructing a single excitation operator equivalent quantum circuit through an RY(2θ) gate and preparing the same output state of the single excitation operator under the standard construction quantum circuit 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, a single excitation operator equivalent quantum circuit is constructed, and the same output state cos(θ)|01>+sin(θ)|10> of the single excitation operator under the standard constructed quantum circuit is prepared.

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

[0033] The CNOT gate with q as the control bit, 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>.

[0034] In a specific embodiment, the double excitation operator The matrix is:

[0035]

[0036] When the double excitation operator 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>;

[0037] Under restricted conditions, the steps of constructing a double excitation operator equivalent quantum circuit through the RY(2θ) gate and preparing the same output state of the double excitation operator under the standard construction quantum circuit are as follows:

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

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

[0040] In a specific implementation scheme, the specific steps of constructing a double excitation operator equivalent quantum circuit are:

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

[0042] Then, the CNOT gate with r as the control bit and p as the controlled bit is used again to obtain the quantum state cos(θ)|0000>+sin(θ)|1111>;

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

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

[0045] In a specific embodiment, the single excitation operator The mapping relationship between the quantum state and the quantum bit is |pq>;

[0046] The double excitation operator The mapping relationship between the quantum state and the quantum bit is |pqrs>. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 For the input quantum state |00> provided in the embodiment of the present application, a single excitation operator is implemented Quantum circuit diagram of

[0048] Figure 2 For the input quantum state |0000> provided in the embodiment of the present application, a double excitation operator is implemented Quantum circuit diagram of

[0049] Figure 3 The single excitation operator provided in the embodiment of the present application The specific implementation quantum circuit diagram;

[0050] Figure 4 The double excitation operator provided in the embodiment of the present application The specific implementation quantum circuit diagram;

[0051] Figure 5 A flowchart of a method for constructing a leftmost excitation operator of a proposed line in a VQE algorithm provided in an embodiment of the present application. DETAILED DESCRIPTION

[0052] The present application is further described in detail below through the accompanying drawings and embodiments. Through these descriptions, the characteristics and advantages of the present application will become clearer and more specific.

[0053] The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise noted.

[0054] In addition, the technical features involved in different embodiments of the present 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 of the proposed circuit in the VQE algorithm provided in the embodiment of the present application, its application scenario is first explained. The construction method of the leftmost excitation operator of the proposed circuit in the VQE algorithm provided in the embodiment of the present application is used to reduce the depth of the quantum circuit and effectively improve the solution quality of the variational quantum eigensolution algorithm. The current mainstream design idea of ​​the proposed circuit is to separate the single and double excitation operators based on the second quantized molecular Hamiltonian. At this time, the excitation operator is in the form of fermions and cannot be directly constructed as a quantum circuit that can be executed by a quantum computer. It is necessary to use methods such as Jordan-Wigner [1] 、Parity basis [2] Bravyi-Kitaev [3] or Qubit-Excitation [4]Transformation methods such as Qubit-Excitation transform convert these fermion excitation operators into Pauli strings, and finally construct the simulated circuits based on these Pauli strings. Among them, the Qubit-Excitation transformation has the best effect. For single and double excitation operators, they require quantum circuits with depths of 4 and 48 respectively to achieve. However, for larger molecules, even with the Qubit-Excitation transformation, the depth of the simulated circuit finally obtained still exceeds the range that the current NISQ equipment can withstand. Therefore, designing an excitation operator construction scheme with a shallower circuit depth is the key to promoting the practical application of the VQE algorithm. To this end, the embodiment of the present application provides a method for constructing the leftmost excitation operator of the simulated circuit in a VQE algorithm to reduce the depth of the quantum circuit and effectively improve the solution quality of the variational quantum eigensolution algorithm. The following is a detailed description of the embodiments in conjunction with specific drawings.

[0056] refer to Figures 1 to 5 , Figure 1 For the input quantum state |00> provided in the embodiment of the present application, a single excitation operator is implemented Quantum circuit diagram of Figure 2 For the input quantum state |0000> provided in the embodiment of the present application, a double excitation operator is implemented Quantum circuit diagram of Figure 3 The single excitation operator provided in the embodiment of the present application The specific implementation quantum circuit diagram; Figure 4 The double excitation operator provided in the embodiment of the present application The specific implementation quantum circuit diagram; Figure 5 A flowchart of a method for constructing a leftmost excitation operator of a proposed line in a VQE algorithm provided in an embodiment of the present application.

[0057] exist Figure 5 In the embodiment of the present application, a method for constructing a leftmost excitation operator of a proposed line in a VQE algorithm is provided, comprising the following steps:

[0058] Under restricted conditions, an equivalent quantum circuit is constructed through RY(2θ) gates to prepare the same output state of the excitation operator under the standard constructed quantum circuit, and reduce the depth of the quantum circuit of the excitation operator at the leftmost end of the proposed circuit.

[0059] In the above technical scheme, under restricted conditions, an equivalent quantum circuit is constructed through the RY(2θ) gate to prepare the same output state of the excitation operator under the standard constructed quantum circuit, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced, which effectively improves the solution quality of the variational quantum eigensolution algorithm.

[0060] In a specific implementation scheme, the restrictions include:

[0061] The input of the proposed circuit is in the all-zero state;

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

[0063] The construction circuit cannot repeat the operation on a quantum bit that has already been operated on.

[0064] In a specific implementation scheme, under restricted conditions, an equivalent quantum circuit is constructed by an RY(2θ) gate to prepare the same output state of the excitation operator under the standard construction quantum circuit, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced, including:

[0065] Under restricted conditions, a single excitation operator equivalent quantum circuit is constructed through RY(2θ) gates, and the same output state of the single excitation operator under the standard constructed quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced.

[0066] In a specific implementation method, an equivalent quantum circuit is constructed by an RY(2θ) gate to prepare the same output state of the excitation operator under the standard construction quantum circuit, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced, including:

[0067] Under restricted conditions, a double excitation operator equivalent quantum circuit is constructed through RY(2θ) gates, and the same output state of the double excitation operator under the standard constructed quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced.

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

[0069] In a specific embodiment, the single excitation operator The matrix is:

[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 the quantum bit q is:

[0073]

[0074] Under restricted conditions, the steps of constructing a single excitation operator equivalent quantum circuit through an RY(2θ) gate and preparing the same output state of the single excitation operator under the standard construction 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, a single excitation operator equivalent quantum circuit is constructed, and the same output state cos(θ)|01>+sin(θ)|10> of the single excitation operator under the standard constructed quantum circuit is prepared.

[0077] In a specific implementation scheme, the specific steps of constructing a single excitation operator equivalent quantum circuit are:

[0078] The CNOT gate with q as the control bit, 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 embodiment, the double excitation operator The matrix is:

[0080]

[0081] When the double excitation operator 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>;

[0082] Under restricted conditions, the steps of constructing a double excitation operator equivalent quantum circuit through RY(2θ) gate and preparing the same output state of the double excitation operator under the standard construction 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, a double excitation operator equivalent quantum circuit is constructed, and the same output state cos(θ)|0011>-sin(θ)|1100> of the double excitation operator under the standard constructed quantum circuit is prepared.

[0085] In a specific implementation scheme, the specific steps of constructing a double excitation operator equivalent quantum circuit are:

[0086] Apply two CNOT gates with s as the control bit and r and q as the controlled bits to cos(θ)|0000>+sin(θ)|0001>, and the quantum state cos(θ)|0000>+sin(θ)|0111> is obtained;

[0087] Then, the CNOT gate with r as the control bit and p as the controlled bit is used again to obtain the quantum state cos(θ)|0000>+sin(θ)|1111>;

[0088] Then apply X gate to s and r to obtain the quantum state cos(θ)|0011>+sin(θ)|1100>;

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

[0090] In a specific embodiment, the single excitation operator The mapping relationship between the quantum state and the quantum bit is |pq>;

[0091] The double excitation operator The mapping relationship between the quantum state and the quantum bit is |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 a single excitation operator), the depth of the quantum circuit is 4 (considering that the implementation cost of the CNOT gate in the experiment is much higher than that of the single-qubit gate, the circuit depth only counts the CNOT gate). Considering that its role is to distribute the population of the 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 mapping relationship between the quantum state and the quantum bit is |pq>). In order to complete this task and minimize the depth of the quantum circuit, it is possible to only focus on this special case, without having to construct the entire matrix (1) as in the Qubit Excitation transformation. That is, it is only necessary to design the quantum circuit to prepare the same output state cos(θ)|01>+sin(θ)|10>.

[0095] Since the matrix form of RY(2θ) acting on the 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>. After that, the CNOT gate with q as the control bit, p as the target bit, and the X gate with q as the action bit can be used in sequence to prepare the quantum state cos(θ)|01>+sin(θ)|10>. The quantum circuit representation of this series of operations is as follows Figure 1 The result is similar to the single excitation operator acting on |01> The same, but the circuit depth is only 1. Therefore, when the single excitation operator is at the leftmost end of the circuit, the |00> state can be used instead of the |01> state as the input state, and Figure 1 The quantum circuit shown realizes the single excitation operator

[0098] Specifically, for the double excitation operator The outer product of its matrix is ​​expressed as:

[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 population of the quantum states |0011> and |1100> (where the mapping relationship between quantum states and 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>. In order to complete this task and minimize the depth of the quantum circuit, we can only focus on this special case, without having to construct the entire matrix (3) like the Qubit Excitation transformation. That is, we only need to design the quantum circuit to prepare the same output state cos(θ)|0011>-sin(θ)|1100>. To do this, we can use the following: Figure 2 The quantum circuit shown.

[0101] exist Figure 2In the example, for the input state |0000>, the RY(2θ) gate transforms it into cos(θ)|0000>+sin(θ)|0001>. After that, 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> can be obtained. By applying the CNOT gate with r as the control bit and p as the controlled bit again, the quantum state cos(θ)|0000>+sin(θ)|1111> can be obtained. After that, by applying the X gate to s and r, the quantum state cos(θ)|0011>+sin(θ)|1100> can be obtained. Finally, by applying the Z gate to p, the target output state cos(θ)|0011>-sin(θ)|1100> can be obtained. The output quantum state of the circuit is related to the double excitation operator acting on the input state |0011> The output state is the same as that of , but the depth of the circuit is only 2.

[0102] It should be pointed out that the above single excitation operator and double excitation operator minimalist construction method requires the input state to be |00> or |0000>, so that the output quantum state is consistent with the output quantum state of the standard construction method, otherwise it will lead to non-physical results 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 a Hatree Fock state, but should be a full zero state; second, the circuit constructed by the minimalist construction method must be located at the leftmost end of the proposed circuit, otherwise the input state is not |00> or |0000>; third, the minimalist construction method cannot be repeated on a quantum bit that has been acted on. Once the excitation operator needs to be applied again, the standard construction method needs to be used to construct the quantum circuit.

[0103] However, even with the above limitations, this method can be used to construct the starting part of the proposed circuit in almost all VQE algorithms to reduce the depth of the quantum circuit. Considering that the circuit depth (46) that can be reduced when the minimalist construction method is used to construct the double excitation operator is much greater than the single excitation operator case (1), this method should be used first to construct the double excitation operator in actual use.

[0104] Specifically, for a molecule with n 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(mn,m) and the minimum is 6*min(mn,m).

[0105] In the embodiment of the present application, for the excitation operator located at the leftmost end of the proposed circuit, the present application proposes a minimalist construction method that 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 scope are still considerable.

[0106] In order to further explain the method proposed in this application for realizing the excitation operator, the single excitation operator at the leftmost end of the proposed circuit is and the double excitation operator As an example, a specific quantum circuit is shown.

[0107] For the single excitation operator The specific implementation of quantum circuits based on the method of this application is as follows Figure 3 shown.

[0108] For the double excitation operator The specific implementation of quantum circuits based on the method of this application is as follows Figure 4 shown.

[0109] In the above technical scheme, under restricted conditions, an equivalent quantum circuit is constructed through the RY(2θ) gate to prepare the same output state of the excitation operator under the standard constructed quantum circuit, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced, which effectively improves the solution quality of the variational quantum eigensolution algorithm.

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

[0111] Therefore, the present disclosure may be specifically implemented in the following forms, namely: it may be completely hardware, it may be completely software (including firmware, resident software, microcode, etc.), or it may be a combination of hardware and software, generally referred to herein as a "circuit", "module" or "system". In addition, in some embodiments, the present application may also be implemented in the form of a computer program product in one or more computer-readable media, and the computer-readable medium may contain computer-readable program code.

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

[0113] Although the embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and cannot be understood as limiting the present application. A person of ordinary skill in the art can change, modify, replace and modify the above embodiments within the scope of the present application. On this basis, a variety of replacements and improvements can be made to the present application, all of which fall within the scope of protection of the present application.

Claims

1. A method for constructing a leftmost excitation operator of a proposed line in a VQE algorithm, characterized in that: The following steps are involved: Under restricted conditions, an equivalent quantum circuit is constructed through RY(2θ) gates to prepare the same output state of the excitation operator under the standard constructed quantum circuit, and reduce the depth of the quantum circuit of the excitation operator at the leftmost end of the proposed circuit.

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 restrictions include: The input of the proposed circuit is in the all-zero state; The construction line is located at the leftmost end of the proposed line; The construction circuit cannot repeat the operation on a quantum bit that has already been operated on.

3. The method for constructing the leftmost excitation operator of the proposed line in the VQE algorithm according to claim 2, characterized in that: Under restricted conditions, an equivalent quantum circuit is constructed by RY(2θ) gates, the same output state of the excitation operator under the standard constructed quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced, including: Under restricted conditions, a single excitation operator equivalent quantum circuit is constructed through RY(2θ) gates, and the same output state of the single excitation operator under the standard constructed quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced.

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 steps of constructing an equivalent quantum circuit through an RY(2θ) gate, preparing the same output state of the excitation operator under the standard constructed quantum circuit, and reducing the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit include: Under restricted conditions, a double excitation operator equivalent quantum circuit is constructed through RY(2θ) gates, and the same output state of the double excitation operator under the standard constructed quantum circuit is prepared, and the depth of the quantum circuit of the excitation operator located at the leftmost end of the proposed circuit is reduced.

5. The method for constructing the leftmost excitation operator of the proposed line in the VQE algorithm according to claim 4, characterized in that: The standard construction quantum circuit is an excitation operator quantum circuit constructed using Qubit Excitation transformation.

6. The method for constructing the leftmost excitation operator of the proposed line in the VQE algorithm according to claim 5, characterized in that: The single excitation operator The matrix is: 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>; The matrix of the RY(2θ) gate acting on the quantum bit q is: Under restricted conditions, the steps of constructing a single excitation operator equivalent quantum circuit through an RY(2θ) gate and preparing the same output state of the single excitation operator under the standard construction quantum circuit are as follows: When the input state is |00>, the RY(2θ) gate transforms it into cos(θ)|00>+sin(θ)|01>; Then, a single excitation operator equivalent quantum circuit is constructed, and the same output state cos(θ)|01>+sin(θ)|10> of the single excitation operator under the standard constructed quantum circuit is prepared.

7. The method for constructing the leftmost excitation operator of the proposed line in the VQE algorithm according to claim 6, characterized in that: The specific steps to construct a single excitation operator equivalent quantum circuit are: The output state cos(θ)|01>+sin(θ)|10> is prepared by sequentially acting on cos(θ)|00>+sin(θ)|01> through a CNOT gate with q as the control bit, a CNOT gate with q as the target bit, and an X gate with q as the action bit.

8. The method for constructing the leftmost excitation operator of the proposed line in the VQE algorithm according to claim 7, characterized in that: The double excitation operator The matrix is: When the double excitation operator 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>; Under restricted conditions, the steps of constructing a double excitation operator equivalent quantum circuit through the RY(2θ) gate and preparing the same output state of the double excitation operator under the standard construction quantum circuit are as follows: When the input state is |0000>, the RY(2θ) gate transforms it into cos(θ)|0000>+sin(θ)|0001>; Then, a double excitation operator equivalent quantum circuit is constructed, and the same output state cos(θ)|0011>-sin(θ)|1100> of the double excitation operator under the standard constructed quantum circuit is prepared.

9. The method for constructing the leftmost excitation operator of the proposed line in the VQE algorithm according to claim 8, characterized in that: The specific steps to construct a double excitation operator equivalent quantum circuit are: Apply two CNOT gates with s as the control bit and r and q as the controlled bits to cos(θ)|0000>+sin(θ)|0001>, and the quantum state cos(θ)|10000>+sin(θ)|0111> is obtained; Then, the CNOT gate with r as the control bit and θ as the controlled bit is used again to obtain the quantum state Cos(θ)|0000>+sin(θ)|1111>; Then apply X gate to s and r to obtain the quantum state cos(θ)|0011>+sin(θ)|1100>; Finally, by applying a Z gate to , we obtain the output state cos(θ)|0011>-sin(θ)|1100>.

10. The method for constructing the leftmost excitation operator of the proposed line in the VQE algorithm according to claim 9, characterized in that: The single excitation operator The mapping relationship between the quantum state and the quantum bit is |pq>; The double excitation operator The mapping relationship between the quantum state and the quantum bit is |pqrs>.

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