A minimally conceived method for constructing dual-excitation operators in quantum computational chemistry

Abstract

This application provides a simplified construction method for dual-excitation operators in quantum computational chemistry. This simplified construction method includes the following steps: under constrained conditions, constructing an equivalent quantum circuit for the dual-excitation operator using RXY(2θ) gates, thus preparing the same output state of the dual-excitation operator as in a standard constructed quantum circuit, thereby reducing the depth of the quantum circuit for the dual-excitation operator. In the above technical solution, constructing an equivalent quantum circuit for the dual-excitation operator using RXY(2θ) gates, preparing the same output state of the dual-excitation operator as in a standard constructed quantum circuit, and reducing the depth of the quantum circuit for the dual-excitation operator reduces the construction cost of the quantum circuit for the dual-excitation operator.

Description

Technical Field

[0001] This application relates to the fields of quantum computing and quantum information technology, and in particular to a minimally simplistic method for constructing a double-excitation operator in quantum computing chemistry. Background Technology

[0002] Computational chemistry is an important component of modern chemistry. By simulating molecular behavior, it can predict crucial parameters such as the structure, properties, chemical reaction pathways, and rates of substances, finding key applications in numerous fields, including new materials development and drug discovery. However, due to the limitations of classical algorithms in effectively simulating quantum systems and constraints imposed by time and resources, traditional computational chemistry methods cannot handle large-scale molecular systems. Quantum computers, leveraging the superposition and entanglement properties provided by quantum mechanics, can naturally solve this problem, thus giving rise to quantum computational chemistry, an interdisciplinary field combining quantum computing and chemistry.

[0003] A key task in quantum computational chemistry is solving for the lower energy levels of molecules, such as the ground state. In the 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. VQE algorithms typically use the Hatree-Fock state as the initial state. The Hatree-Fock state assumes that electrons in the molecule occupy the lowest-energy orbitals. Then, based on the orbital characteristics of the molecule, VQE can construct a hypothesis composed of different excitation operators. The hypothesis will always maintain the characteristics of the initial state, such as the number of electrons and the spin number.

[0004] Commonly used UCCSD designs only include single and double excitation operators. The excitation operators are fermionic operators, and to construct them as quantum circuits for execution on quantum computers, the Jordan-Wigner model is currently the primary approach. [1] Parity basis [2] Bravyi-Kitaev [3] and Qubit-Excitation [4]The excitation operator is converted into a Pauli string by the transformation, and then converted into a quantum circuit after taking the imaginary part. Since the implementation cost of a dual-excitation operator is much higher than that of a single-excitation operator, this patent focuses on the implementation of the dual-excitation operator. The number of CNOT gates used in the Jordan-Wigner, Parity basis, and Bravyi-Kitaev transformations depends on the specific form of the excitation operator. For dual-excitation operators, the minimum number of gates used is 48, 32, and 32, respectively, with no upper limit. The Qubit-Excitation transformation explicitly uses 48 CNOT gates, and its average number is the lowest compared to the previous three transformations.

[0005] In summary, to solve for the lower energy levels of molecules, the VQE algorithm requires converting the proposed fermion excitation operators into quantum circuits. Currently used transformation methods, such as the Jordan-Wigner, Parity basis, Bravyi-Kitaev, and Qubit-Excitation transformations, use a large number of gates, which is detrimental to obtaining high-quality computational results on current NISQ equipment. Therefore, designing better transformation schemes to use fewer excitation operators is an important research direction.

[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 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] This application provides a simplified construction method for dual-excitation operators in quantum computational chemistry, which reduces the number of CNOT gates used and lowers the cost of constructing quantum circuits for dual-excitation operators.

[0012] This application provides a simplified method for constructing dual-excitation operators in quantum computational chemistry, comprising the following steps:

[0013] Under constraints, an equivalent quantum circuit for the dual-excitation operator is constructed using the RXY(2θ) gate, producing the same output state as the standard constructed quantum circuit, thus reducing the depth of the quantum circuit for the dual-excitation operator.

[0014] In the above technical solution, the equivalent quantum circuit of the dual-excitation operator is constructed by using the RXY(2θ) gate, and the same output state of the dual-excitation operator under the standard construction quantum circuit is prepared. The depth of the quantum circuit of the dual-excitation operator is reduced, thereby reducing the construction cost of the quantum circuit of the dual-excitation operator.

[0015] In one specific implementation, the limiting conditions include:

[0016] The input state is |0011>.

[0017] In one specific implementation, the standard constructed quantum circuit is an excitation operator quantum circuit constructed using the Qubit Excitation Transform.

[0018] In one specific implementation scheme, the dual-excitation operator The matrix is:

[0019]

[0020] When the input state is |0011>, the output state of the double-excitation operator under the standard constructed 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 constrained conditions, the steps for preparing the same output state of the dual-excitation operator as that of the standard constructed quantum circuit by constructing an equivalent quantum circuit using the RXY(2θ) gate are as follows:

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

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

[0026] Then, a quantum circuit equivalent to the double-excitation operator is constructed to prepare the same output state cos(θ)|0011>-sin(θ)|1100> under the standard constructed quantum circuit.

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

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

[0029] Applying an X gate to qubits r and s yields the same output state cos(θ)|0011>-sin(θ)|1100> for the dual-excitation operator under standard constructed quantum circuits.

[0030] In one specific implementation, the dual-excitation operator equivalent quantum circuit is constructed directly through the RXY(2θ) gate.

[0031] In one specific implementation, the dual-excitation operator equivalent quantum circuit includes four CNOT gates.

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

[0033] In one specific implementation scheme, the dual-excitation operator The mapping relationship between quantum states and qubits is |pqrs>. Attached Figure Description

[0034] Figure 1 The double-excitation operator for the input state |0011> provided in the embodiments of this application A diagram of a quantum circuit structure;

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

[0036] Figure 3 This is a flowchart illustrating a simplified construction method for dual-excitation operators in quantum computational chemistry provided in an embodiment of this application. Detailed Implementation

[0037] 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.

[0038] 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.

[0039] 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.

[0040] To facilitate understanding of the simplified construction method for dual-excitation operators in quantum computational chemistry provided in this application embodiment, its application scenario is first explained. The simplified construction method for dual-excitation operators in quantum computational chemistry provided in this application embodiment reduces the number of CNOT gates used and lowers the construction cost of quantum circuits for dual-excitation operators. Commonly used UCCSDs are designed to include only single and dual-excitation operators. The excitation operators are fermion operators; to construct them as quantum circuits for execution on quantum computers, the Jordan-Wigner method is currently the primary approach. [1] Parity basis [2] Bravyi-Kitaev [3] and Qubit-Excitation [4]The transformation converts the excitation operator into a Pauli string, and after taking the imaginary part, it is converted into a quantum circuit. Since the implementation cost of a dual-excitation operator is much higher than that of a single-excitation operator, this patent focuses on the implementation of dual-excitation operators. The number of CNOT gates used in the Jordan-Wigner, Parity basis, and Bravyi-Kitaev transformations depends on the specific form of the excitation operator. For dual-excitation operators, the minimum number of gates used is 48, 32, and 32 respectively, with no upper limit. The Qubit-Excitation transformation explicitly uses 48 CNOT gates, and its average number is the smallest compared to the previous three transformations. In summary, to achieve the solution of the lower molecular energy levels, the VQE algorithm needs to convert the proposed fermion excitation operator into a quantum circuit. Currently used transformation methods, such as the Jordan-Wigner, Parity basis, Bravyi-Kitaev, and Qubit-Excitation transformations, use a large number of gates, which is not conducive to obtaining high-quality computational results on current NISQ equipment. Therefore, designing better transformation schemes to use fewer implementation excitation operators is an important research direction. To this end, this application provides a simplified construction method for dual-excitation operators in quantum computational chemistry to reduce the number of CNOT gates used and lower the quantum circuit construction cost of dual-excitation operators. The following detailed description, in conjunction with specific accompanying drawings, illustrates the method.

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

[0042] exist Figure 3 This application provides a simplified method for constructing dual-excitation operators in quantum computational chemistry, comprising the following steps:

[0043] Under constraints, an equivalent quantum circuit for the dual-excitation operator is constructed using the RXY(2θ) gate, producing the same output state as the standard constructed quantum circuit, thus reducing the depth of the quantum circuit for the dual-excitation operator.

[0044] In the above technical solution, the equivalent quantum circuit of the dual-excitation operator is constructed by using the RXY(2θ) gate, and the same output state of the dual-excitation operator under the standard construction quantum circuit is prepared. The depth of the quantum circuit of the dual-excitation operator is reduced, thereby reducing the construction cost of the quantum circuit of the dual-excitation operator.

[0045] In one specific implementation, the limiting conditions include:

[0046] The input state is >0011>.

[0047] In one specific implementation, the standard constructed quantum circuit is an excitation operator quantum circuit constructed using the Qubit Excitation Transform.

[0048] In one specific implementation scheme, the dual-excitation operator The matrix is:

[0049]

[0050] When the input state is |0011>, the output state of the double-excitation operator under the standard constructed 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 constrained conditions, the steps for preparing the same output state of the dual-excitation operator as that of the standard constructed quantum circuit by constructing an equivalent quantum circuit using the RXY(2θ) gate are as follows:

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

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

[0056] Then, a quantum circuit equivalent to the double-excitation operator is constructed to prepare the same output state cos(θ)|0011>-sin(θ)|1100> under the standard constructed quantum circuit.

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

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

[0059] Applying an X gate to qubits r and s yields the same output state cos(θ)|0011>-sin(θ)|1100> for the dual-excitation operator under standard constructed quantum circuits.

[0060] In one specific implementation, the dual-excitation operator equivalent quantum circuit is constructed directly through the RXY(2θ) gate.

[0061] In one specific implementation, the dual-excitation operator equivalent quantum circuit includes four CNOT gates.

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

[0063] In one specific implementation scheme, the dual-excitation operator The mapping relationship between quantum states and qubits is |pqrs>.

[0064] Specifically, for the double excitation operators applied to qubits p, q, r, and s Its function is to adjust the population between quantum states |0011> and |1100>, while adhering to the conservation of electron number and spin number during the adjustment. The outer product of the corresponding matrices is expressed as:

[0065]

[0066] Directly implementing this matrix is ​​costly. However, considering that the initial state of the VQE algorithm is the Hatree-Fock state, all electrons occupy the lowest energy orbital, i.e., the initial state is |0011>, which is exactly a basis vector state, and the weights of other basis vector states are all 0. Therefore, when applying the double excitation operator, the initial state |0011> is simply transformed into cos(θ)|0011>-sin(θ)|1100>. Thus, 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 having to construct the complete matrix shown in formula (1), thereby greatly reducing the implementation cost.

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

[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>. Then, by applying two CNOT gates with qubits r and s as control bits and qubits p and q as control bits respectively, the quantum state cos(θ)|1111>-sin(θ)|0000> can be obtained. Finally, by applying an X gate to qubits r and s, the desired quantum state cos(θ)|0011>-sin(θ)|1100> can be obtained.

[0070] In summary, for the input state |0011>, the proposed method for implementing the dual-excitation sub-operator in this application... Quantum circuits such as Figure 1 As shown. The part within the dashed box is the decomposition circuit of the quantum gate RXY(2θ).

[0071] from Figure 1 As can be seen, the proposed scheme uses only 4 CNOT gates to implement the double excitation operator operation on the initial state |0011>. Compared with the current best-performing Qubit-Excitation transform (which uses 48 CNOT gates), it saves approximately 92% of the number of CNOT gates used.

[0072] However, the dual-excitation operator construction scheme proposed in this application is only valid under the constraint that the input state is |0011>, and is not universal. If the input state is not |0011>, some of the population will enter the non-physical space after the circuit is applied, thus causing the VQE algorithm to fail. However, even if it can only be used a limited number of times (under the constraint), 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 in this application for low-cost implementation of the double-excitation operator, let's take the double-excitation operator as an example. As an example, a specific quantum circuit is shown.

[0074] Assuming the input state is |0011>, for the double-excitation operator The specific quantum circuit implemented based on this patented method is as follows: Figure 2 As shown.

[0075] In the above technical solution, only 4 CNOT gates are used to implement the double excitation operator operation on the initial state |0011>. Compared with the current best-performing Qubit-Excitation transform (which uses 48 CNOT gates), it saves about 92% of the number of CNOT gates, reduces construction costs, and improves the quality of computational results.

[0076] Those skilled in the art will know that this application can be implemented as a system, method, or computer program product.

[0077] Therefore, this disclosure can be implemented in the following forms: it can be entirely hardware, entirely software (including firmware, resident software, microcode, etc.), or a combination of hardware and software, generally referred to herein as a "circuit," "module," or "system." Furthermore, in some embodiments, this application can also be implemented as a computer program product in one or more computer-readable media, which contains computer-readable program code.

[0078] Any combination of one or more computer-readable media may be used. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device.

[0079] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application. Based on this, various substitutions and improvements can be made to this application, all of which fall within the protection scope of this application.

Claims

1. A method for constructing a double-excitation operator in quantum computational chemistry, the method comprising: determining a first excitation operator; determining a second excitation operator; and combining the first excitation operator and the second excitation operator to form the double-excitation operator. comprising the steps of: Under the restriction condition, by The door constructs the double excitation operator equivalent quantum circuit, prepares the same output state of the double excitation operator under the standard construction quantum circuit, and reduces the depth of the quantum circuit of the double excitation operator. the standard constructed quantum circuit is an excitation operator quantum circuit constructed using the Qubit Excitation transform; The double-excitation operator The matrix of the double-excitation operator (1) The input state is The output state of the double-excitation operator under the standard construction quantum circuit is ; acting on a qubit and the matrix of the gate is: (2) Under the restriction condition, by The door constructs a double-excitation operator equivalent quantum circuit, and prepares the output state of the double-excitation operator under the standard construction quantum circuit, and the steps are as follows: In the input state , the gate transforms it into , Or, at input state the gate transforms it to ; where acts on the two qubits that follow; Then the double-excitation operator equivalent quantum circuit is constructed, and the output state of the double-excitation operator under the standard construction quantum circuit is prepared ; The double-excitation operator equivalent quantum circuit is constructed, and the output state of the double-excitation operator under the standard construction quantum circuit is prepared The steps are specifically: applying a quantum bit and as a control bit and as a control bit gate, obtaining a quantum state ; Recoiling a qubit And Applying A gate, resulting in the same output state of the double-excitation operator under the standard construction quantum circuit ; The double-excitation operator equivalent quantum circuit includes four gates.

2. The method of claim 1, wherein, the constraints include: The input state is .

3. The method of claim 1, wherein, further comprising: directly by the double-excitation operator equivalent quantum circuit is constructed.

4. The method of claim 3, wherein, The input state is State.

5. The method of claim 4, wherein, The double-excitation operator The mapping relationship between the quantum state and the quantum bit is .

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