TY - JOUR

T1 - Quantum Algorithm of the Divide-And-Conquer Unitary Coupled Cluster Method with a Variational Quantum Eigensolver

AU - Yoshikawa, Takeshi

AU - Takanashi, Tomoya

AU - Nakai, Hiromi

N1 - Funding Information:
Some of the calculations were performed at the Research Center for Computational Science (RCCS), Okazaki Research Facilities, and the National Institute of Natural Sciences (NINS). This study was supported in part by a Grant-in-Aid for Scientific Research (C) (KAKENHI Grant Number JP20K05436) from the Japan Society for the Promotion of Science (JSPS).
Publisher Copyright:
©

PY - 2022

Y1 - 2022

N2 - The variational quantum eigensolver (VQE) with shallow or constant-depth quantum circuits is one of the most pursued approaches in the noisy intermediate-scale quantum (NISQ) devices with incoherent errors. In this study, the divide-And-conquer (DC) linear scaling technique, which divides the entire system into several fragments, is applied to the VQE algorithm based on the unitary coupled cluster (UCC) method, denoted as DC-qUCC/VQE, to reduce the number of required qubits. The unitarity of the UCC ansatz that enables the evaluation of the total energy as well as various molecular properties as expectation values can be easily implemented on quantum devices because the quantum gates are unitary operators themselves. Based on this feature, the present DC-qUCC/VQE algorithm is designed to conserve the total number of electrons in the entire system using the density matrix evaluated on a quantum computer. Numerical assessments clarified that the energy errors of the DC-qUCC/VQE calculations decrease by using the constraint of the total number of electrons. Furthermore, the DC-qUCC/VQE algorithm could reduce the number of quantum gates and shows the possibility of decreasing incoherent errors.

AB - The variational quantum eigensolver (VQE) with shallow or constant-depth quantum circuits is one of the most pursued approaches in the noisy intermediate-scale quantum (NISQ) devices with incoherent errors. In this study, the divide-And-conquer (DC) linear scaling technique, which divides the entire system into several fragments, is applied to the VQE algorithm based on the unitary coupled cluster (UCC) method, denoted as DC-qUCC/VQE, to reduce the number of required qubits. The unitarity of the UCC ansatz that enables the evaluation of the total energy as well as various molecular properties as expectation values can be easily implemented on quantum devices because the quantum gates are unitary operators themselves. Based on this feature, the present DC-qUCC/VQE algorithm is designed to conserve the total number of electrons in the entire system using the density matrix evaluated on a quantum computer. Numerical assessments clarified that the energy errors of the DC-qUCC/VQE calculations decrease by using the constraint of the total number of electrons. Furthermore, the DC-qUCC/VQE algorithm could reduce the number of quantum gates and shows the possibility of decreasing incoherent errors.

UR - http://www.scopus.com/inward/record.url?scp=85136039167&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85136039167&partnerID=8YFLogxK

U2 - 10.1021/acs.jctc.2c00602

DO - 10.1021/acs.jctc.2c00602

M3 - Article

C2 - 35926142

AN - SCOPUS:85136039167

JO - Journal of Chemical Theory and Computation

JF - Journal of Chemical Theory and Computation

SN - 1549-9618

ER -