Very simple construction method of double-excitation operator in quantum computational chemistry

Abstract

The invention provides an extremely simple construction method for a double-excitation operator in quantum computational chemistry, and the method comprises the following steps: constructing a quantum circuit equivalent to the double-excitation operator through an RXY (2 theta) gate under a limiting condition, the same output state of the double-excitation operator under the standard structure quantum circuit is prepared, and the depth of the quantum circuit of the double-excitation operator is reduced. According to the technical scheme, the quantum circuit equivalent to the double-excitation operator is constructed through the RXY (2 theta) gate, the same output state of the double-excitation operator under the standard constructed quantum circuit is prepared, the depth of the quantum circuit of the double-excitation operator is reduced, and the construction cost of the quantum circuit of the double-excitation operator is reduced.

Description

Background Art

[0002] Computational chemistry is an important part of modern chemistry. By simulating the behavior of molecules, important parameters such as the structure, properties, chemical reaction paths, and speed of substances can be predicted, and it has key applications in many fields such as new material development and drug development. However, due to the inability of classical algorithms to effectively simulate quantum systems and the limitations of time and resources, traditional computational chemistry methods cannot handle larger-scale molecular systems. Quantum computers can naturally solve this problem with the help of superposition and entanglement provided by quantum mechanics, thus giving birth to quantum computational chemistry, an interdisciplinary subject in the fields of quantum computing and chemistry.

[0003] An important task in quantum computational chemistry is to solve the low-level energy levels of molecules, such as the ground state energy levels. In the current era of noisy intermediate-scale quantum (NISQ) devices, the most promising quantum algorithm for solving molecular energy levels is the variational quantum eigensolver (VQE) algorithm. The VQE algorithm generally uses the Hatree-Fock state as the initial state. The Hatree-Fock state assumes that the electrons in the molecule occupy several orbits with the lowest energy. After that, VQE can construct a pseudo-set composed of different excitation operators based on the orbital characteristics of the molecule. The pseudo-set will always maintain the characteristics of the initial state such as the number of electrons and the number of spins.

[0004] The commonly used UCCSD simulation only contains single and double excitation operators. The excitation operator is a fermion operator. In order to construct it into a quantum circuit for execution on a quantum computer, the Jordan-Wigner [1] , Parity basis [2] , Bravyi-Kitaev [3] and Qubit-Excitation [4] Transformations such as these convert the excitation operator into a Pauli string, and then convert it into a quantum circuit after taking the imaginary part. Since the implementation cost of the double excitation operator is much higher than that of the single excitation operator, this patent also focuses on the implementation of the double excitation operator. The number of CNOT gates used for Jordan-Wigner, Parity basis, and Bravyi-Kitaev transformations depends on the specific form of the excitation operator. For the double excitation operator, a minimum of 48, 32, and 32 are used respectively, and there is no upper limit at most. The Qubit-Excitation transformation explicitly uses 48 CNOT gates, and compared to the previous three transformations, its average number is the least.

[0005] In summary, in order to solve the molecular low-level energy levels, the VQE algorithm needs to convert the fermion excitation operators in the proposed scheme into quantum circuits. Currently commonly used transformation methods, such as Jordan-Wigner, Parity basis, Bravyi-Kitaev and Qubit-Excitation transformations, use a large number of gates, which is not conducive to obtaining high-quality calculation results on current NISQ devices. Therefore, designing a better transformation scheme to use fewer excitation operators is an important research direction.

[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 minimalist construction method for a double excitation operator in quantum computational chemistry, which is used to reduce the number of CNOT gates used and reduce the quantum circuit construction cost of the double excitation operator.

[0012] The present application provides a minimalist construction method for a double excitation operator in quantum computational chemistry, comprising the following steps:

[0013] Under restricted conditions, a double excitation operator equivalent quantum circuit is constructed through the RXY(2θ) gate, and the same output state of the double excitation operator under the standard constructed quantum circuit is prepared, thereby reducing the depth of the quantum circuit of the double excitation operator.

[0014] In the above technical scheme, the double excitation operator equivalent quantum circuit is constructed through the RXY (2θ) gate, and the same output state of the double excitation operator under the standard construction quantum circuit is prepared, the depth of the quantum circuit of the double excitation operator is reduced, and the quantum circuit construction cost of the double excitation operator is reduced.

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

[0016] The input state is |0011>.

[0017] In a specific embodiment, the standard construction quantum circuit is an excitation operator quantum circuit constructed using Qubit Excitation transformation.

[0018] In a specific embodiment, the double excitation operator The matrix is:

[0019]

[0020] When the input state is |0011>, the output state of the double excitation operator in the standard construction quantum circuit is cos(θ)|0011>-sin(θ)|1100>;

[0021] The matrix of the RXY(2θ) gate acting on qubits r and s is:

[0022]

[0023] Under restricted conditions, the steps of constructing a double excitation operator equivalent quantum circuit through the RXY(2θ) gate and preparing the same output state of the double excitation operator under the standard construction quantum circuit are as follows:

[0024] In the input state |11>, the RXY(2θ) gate transforms it into cos(θ)|11>-sin(θ)|00>,

[0025] Alternatively, when the input state is |0011>, the RXY(2θ) gate transforms it into cos(θ)|0011>-sin(θ)|0000>; wherein RXY(2θ) acts on the latter two qubits;

[0026] 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.

[0027] In a specific implementation scheme, the steps of constructing a double excitation operator equivalent quantum circuit and preparing the same output state cos(θ)|0011>-sin(θ)|1100> of the double excitation operator under the standard constructed quantum circuit are as follows:

[0028] Apply CNOT gates with qubits r and s as control bits and qubits p and q as control bits respectively, and obtain the quantum state cos(θ)|1111>-sin(θ)|0000>;

[0029] Then, applying the X gate to the quantum bits r and s, we obtain the same output state of the double excitation operator under the standard construction quantum circuit: cos(θ)|0011>-sin(θ)|1100>.

[0030] In a specific embodiment, the double excitation operator equivalent quantum circuit is constructed directly through RXY (2θ) gates.

[0031] In a specific embodiment, the dual excitation operator equivalent quantum circuit includes four CNOT gates.

[0032] In a specific implementation manner, the input state is a |0011> state.

[0033] In a specific embodiment, the double excitation operator The mapping relationship between the quantum state and the quantum bit is |pqrs>. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 The double excitation operator for the input state |0011> provided in the embodiment of the present application The quantum circuit structure diagram of

[0035] Figure 2 The double excitation operator for the input state |0011> provided in the embodiment of the present application The specific implementation quantum circuit diagram;

[0036] Figure 3 A flowchart of a simplified construction method for a double excitation operator in quantum computational chemistry provided in an embodiment of the present application. DETAILED DESCRIPTION

[0037] 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.

[0038] 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.

[0039] 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.

[0040] To facilitate understanding of the extremely simple construction method of the double excitation operator in quantum computational chemistry provided in the embodiment of the present application, its application scenario is first explained. The extremely simple construction method of the double excitation operator in quantum computational chemistry provided in the embodiment of the present application is used to reduce the number of CNOT gates used and reduce the quantum circuit construction cost of the double excitation operator. The commonly used UCCSD is assumed to include only single and double excitation operators. The excitation operator is a fermion operator. In order to construct it as a quantum circuit for execution on a quantum computer, the Jordan-Wigner method is currently mainly used. [1] , Parity basis [2] , Bravyi-Kitaev [3] and Qubit-Excitation [4]Transformations such as convert the excitation operator into a Pauli string, and then convert it into a quantum circuit after taking the imaginary part. Since the implementation cost of the double excitation operator is much higher than that of the single excitation operator, this patent also focuses on the implementation of the double excitation operator. The number of CNOT gates used for Jordan-Wigner, Parity basis and Bravyi-Kitaev transformations depends on the specific form of the excitation operator. For the double excitation operator, at least 48, 32, and 32 are used respectively, and there is no upper limit at most. The Qubit-Excitation transformation explicitly uses 48 CNOT gates, and its average number is the least compared to the previous three transformations. In summary, in order to solve the low-level energy levels of molecules, the VQE algorithm needs to convert the fermion excitation operator in the assumption into a quantum circuit. Currently commonly used transformation methods, such as Jordan-Wigner, Parity basis, Bravyi-Kitaev and Qubit-Excitation transformations, use a large number of gates, which is not conducive to obtaining high-quality calculation results on current NISQ devices. Therefore, designing a better transformation scheme to use fewer excitation operators is an important research direction. To this end, the present application embodiment provides a minimalist construction method for dual excitation operators in quantum computational chemistry to reduce the number of CNOT gates used and reduce the quantum circuit construction cost of dual excitation operators. The following is a detailed description of the embodiment in conjunction with specific drawings.

[0041] refer to Figures 1 to 3 , Figure 1 The double excitation operator for the input state |0011> provided in the embodiment of the present application The quantum circuit structure diagram of Figure 2 The double excitation operator for the input state |0011> provided in the embodiment of the present application The specific implementation quantum circuit diagram; Figure 3 A flowchart of a simplified construction method for a double excitation operator in quantum computational chemistry provided in an embodiment of the present application.

[0042] exist Figure 3 In the present application, a simplified construction method of a double excitation operator in quantum computational chemistry is provided, comprising the following steps:

[0043] Under restricted conditions, a double excitation operator equivalent quantum circuit is constructed through the RXY(2θ) gate, and the same output state of the double excitation operator under the standard constructed quantum circuit is prepared, thereby reducing the depth of the quantum circuit of the double excitation operator.

[0044] In the above technical scheme, the double excitation operator equivalent quantum circuit is constructed through the RXY (2θ) gate, and the same output state of the double excitation operator under the standard construction quantum circuit is prepared, the depth of the quantum circuit of the double excitation operator is reduced, and the quantum circuit construction cost of the double excitation operator is reduced.

[0045] In a specific implementation scheme, the restrictions include:

[0046] The input state is >0011>.

[0047] In a specific embodiment, the standard construction quantum circuit is an excitation operator quantum circuit constructed using Qubit Excitation transformation.

[0048] In a specific embodiment, the double excitation operator The matrix is:

[0049]

[0050] When the input state is |0011>, the output state of the double excitation operator in the standard construction quantum circuit is cos(θ)|0011>-sin(θ)|1100>;

[0051] The matrix of the RXY(2θ) gate acting on qubits r and s is:

[0052]

[0053] Under restricted conditions, the steps of constructing a double excitation operator equivalent quantum circuit through the RXY(2θ) gate and preparing the same output state of the double excitation operator under the standard construction quantum circuit are as follows:

[0054] In the input state |11>, the RXY(2θ) gate transforms it into cos(θ)|11>-sin(θ)|00>,

[0055] Alternatively, when the input state is |0011>, the RXY(2θ) gate transforms it into cos(θ)|0011>-sin(θ)|0000>; wherein RXY(2θ) acts on the latter two qubits;

[0056] 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.

[0057] In a specific implementation scheme, the steps of constructing a double excitation operator equivalent quantum circuit and preparing the same output state cos(θ)|0011>-sin(θ)|1100> of the double excitation operator under the standard constructed quantum circuit are as follows:

[0058] Apply CNOT gates with qubits r and s as control bits and qubits p and q as control bits respectively, and obtain the quantum state cos(θ)|1111>-sin(θ)|0000>;

[0059] Then, applying the X gate to the quantum bits r and s, we obtain the same output state of the double excitation operator under the standard construction quantum circuit: cos(θ)|0011>-sin(θ)|1100>.

[0060] In a specific embodiment, the double excitation operator equivalent quantum circuit is constructed directly through RXY (2θ) gates.

[0061] In a specific embodiment, the dual excitation operator equivalent quantum circuit includes four CNOT gates.

[0062] In a specific implementation manner, the input state is a |0011> state.

[0063] In a specific embodiment, the double excitation operator The mapping relationship between the quantum state and the quantum bit is |pqrs>.

[0064] Specifically, for the double excitation operator applied to qubits p, q, r, and s Its function is to adjust the population between the quantum states |0011> and |1100>, and the conservation of the number of electrons and spins must be followed during the adjustment. The outer product of the corresponding matrix is ​​expressed as:

[0065]

[0066] The cost of directly implementing this matrix is ​​high. However, considering that the initial state of the VQE algorithm is the Hatree-Fock state, all electrons occupy the lowest energy orbit, that is, the initial state is |0011>, which is exactly a basis state, and the weights of other basis states are all 0, so when applying the double excitation operator to it, it only transforms the initial state |0011> into cos(θ)|0011>-sin(θ)|1100>. Therefore, for the initial state |0011>, it is only necessary to design a quantum circuit to transform it into the quantum state cos(θ)|0011>-sin(θ)|1100>, without constructing the complete matrix shown in formula (1), thereby greatly reducing the implementation cost.

[0067] Since the matrix of the quantum gate RXY(2θ) acting on quantum bits r and s is expressed as:

[0068]

[0069] It can transform the input state |11> into cos(θ)|11>-sin(θ)|00>, or transform |0011> into cos(θ)|0011>-sin(θ)|0000>. After that, two CNOT gates are applied, with qubits r and s as control bits and qubits p and q as control bits, to obtain the quantum state cos(θ)|1111>-sin(θ)|0000>. Finally, it is only necessary to apply the X gate to qubits r and s to obtain the desired quantum state cos(θ)|0011>-sin(θ)|1100>.

[0070] In summary, for the input state |0011>, the biexciton operator proposed in this application is The quantum circuit is Figure 1 The part in the dashed box is the decomposition circuit of the quantum gate RXY(2θ).

[0071] from Figure 1 It can be seen that the present application scheme uses only 4 CNOT gates to implement the double excitation operator operation on the initial state |0011>. Compared with the current best Qubit-Excitation transformation (using 48 CNOT gates), the number of CNOT gates used is saved by about 92%.

[0072] However, the dual excitation operator construction scheme proposed in this application is only effective for the restricted condition: the input state is |0011>, and is not universal. If the input state is not |0011>, some population numbers will enter the non-physical space after the circuit action, causing the VQE algorithm to fail. However, even if it can only be used a limited number of times (under restricted conditions), it can significantly reduce the overall circuit depth proposed in the VQE algorithm and improve the quality of the calculation results.

[0073] To further explain the method proposed by the present application for realizing the dual excitation operator at low cost, the dual excitation operator As an example, a specific quantum circuit is shown.

[0074] Assuming the input state is |0011>, for the double excitation operator The specific quantum circuits realized based on this patent method are as follows: Figure 2 shown.

[0075] In the above technical solution, only four CNOT gates are used to implement the double excitation operator operation on the initial state |0011>. Compared with the current best Qubit-Excitation transformation (using 48 CNOT gates), it saves about 92% of the number of CNOT gates used, reduces the construction cost, and improves the quality of the calculation results.

[0076] Those skilled in the art will appreciate that the present application may be implemented as a system, method or computer program product.

[0077] 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.

[0078] 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.

[0079] 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 minimalist construction method for double excitation operators in quantum computational chemistry, characterized in that: The following steps are involved: Under restricted conditions, a double excitation operator equivalent quantum circuit is constructed through the RXY(2θ) gate, and the same output state of the double excitation operator under the standard constructed quantum circuit is prepared, thereby reducing the depth of the quantum circuit of the double excitation operator.

2. The method for constructing a double excitation operator in quantum computational chemistry according to claim 1, characterized in that: The restrictions include: The input state is |0011>.

3. The method for constructing a double excitation operator in quantum computational chemistry according to claim 2, characterized in that: The standard construction quantum circuit is an excitation operator quantum circuit constructed using Qubit Excitation transformation.

4. The method for constructing a double excitation operator in quantum computational chemistry according to claim 3, characterized in that: The double excitation operator The matrix is: When the input state is |0011>, the output state of the double excitation operator in the standard construction quantum circuit is cos(θ)0011>-sin(θ)|1100>; The matrix of the RXY(2θ) gate acting on qubits r and s is: Under restricted conditions, the steps of constructing a double excitation operator equivalent quantum circuit through the RXY(2θ) gate and preparing the same output state of the double excitation operator under the standard construction quantum circuit are as follows: In the input state |11>, the RXY(2θ) gate transforms it into cos(θ)|11>-sin(θ)|00>, Alternatively, when the input state is |0011>, the RXY(2θ) gate transforms it into Cos(θ)|0011>-sin(θ)|0000>; wherein RXY(2θ) acts on the latter two quantum bits; 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.

5. The method for constructing a double excitation operator in quantum computational chemistry according to claim 4, characterized in that: The steps of constructing a double excitation operator equivalent quantum circuit and preparing the same output state cos(θ)|0011>-sin(θ)|1100> of the double excitation operator under the standard constructed quantum circuit are as follows: Apply CNOT gates with qubits r and s as control bits and qubits p and q as control bits respectively, and obtain the quantum state cos(θ)|1111>-sin(θ)|0000>; Then, applying the X gate to the quantum bits r and s, we obtain the same output state of the double excitation operator under the standard construction quantum circuit: cos(θ)|0011>-sin(θ)|1100>.

6. The method for constructing a double excitation operator in quantum computational chemistry according to claim 5, characterized in that: Also includes: The double excitation operator equivalent quantum circuit is constructed directly through the RXY (2θ) gate.

7. The method for constructing a double excitation operator in quantum computational chemistry according to claim 6, characterized in that: The double excitation operator equivalent quantum circuit includes four CNOT gates.

8. The method for constructing a double excitation operator in quantum computational chemistry according to claim 7, characterized in that: The input state is the |0011> state.

9. The method for constructing a double excitation operator in quantum computational chemistry according to claim 8, characterized in that: The double excitation operator The mapping relationship between the quantum state and the quantum bit is |pqrs>.

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