Low-Depth Hamiltonian Simulation by an Adaptive Product Formula

Zhang, Zi-Jian1,2,3; Sun, Jinzhao4; Yuan, Xiao3; Yung, Man-Hong1,2,5

2023-01-27

10.1103/PhysRevLett.130.040601

PHYSICAL REVIEW LETTERS   Impact Factor & Quartile

0031-9007

1079-7114

Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep quantum circuit that is beyond the capability of near-term noisy quantum devices. Here, focusing on the time evolution of a fixed input quantum state, we propose an adaptive approach to construct a low-depth time evolution circuit. By introducing a measurable quantifier that characterizes the simulation error, we use an adaptive strategy to learn the shallow quantum circuit that minimizes that error. We numerically test the adaptive method with electronic Hamiltonians of the H2O and H-4 molecules, and the transverse field Ising model with random coefficients. Compared to the first-order Suzuki-Trotter product formula, our method can significantly reduce the circuit depth (specifically the number of two-qubit gates) by around two orders while maintaining the simulation accuracy. We show applications of the method in simulating many-body dynamics and solving energy spectra with the quantum Krylov algorithm. Our work sheds light on practical Hamiltonian simulation with noisy -intermediate-scale-quantum devices.

SCI

English

NI Journal Papers

First ; Corresponding

Natural Science Foundation of Guangdong Province[2017B030308003] ; Key R&D Program of Guangdong province[2018B030326001] ; Science, Technology and Innovation Commission of Shenzhen Municipality["JCYJ20170412152620376","JCYJ20170817105046702","KYTDPT-20181011104202253"] ; National Natural Science Foundation of China["11875160","U1801661"] ; Economy, Trade and Information Commission of Shenzhen Municipality[201901161512] ; Guangdong Provincial Key Laboratory[2019B121203002] ; Open Project of Shenzhen Institute of Quantum Science and Engineering[SIQSE202008] ; National Natural Science Foundation of China[12175003]

Physics

Physics, Multidisciplinary

WOS:000929471900003

AMER PHYSICAL SOC

PHYSICS

Web of Science

1.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
2.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
3.Peking Univ, Ctr Frontiers Comp Studies, Beijing 100871, Peoples R China
4.Univ Oxford, Clarendon Lab, Parks Rd, Oxford OX1 3PU, England
5.Southern Univ Sci & Technol, Shenzhen Key Lab Quantum Sci & Engn, Shenzhen 518055, Peoples R China

Zhang, Zi-Jian,Sun, Jinzhao,Yuan, Xiao,et al. Low-Depth Hamiltonian Simulation by an Adaptive Product Formula[J]. PHYSICAL REVIEW LETTERS,2023,130(4).

Zhang, Zi-Jian,Sun, Jinzhao,Yuan, Xiao,&Yung, Man-Hong.(2023).Low-Depth Hamiltonian Simulation by an Adaptive Product Formula.PHYSICAL REVIEW LETTERS,130(4).

Zhang, Zi-Jian,et al."Low-Depth Hamiltonian Simulation by an Adaptive Product Formula".PHYSICAL REVIEW LETTERS 130.4(2023).