Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation

An, Dong; Fang, Di; Lin, Lin

doi:10.22331/q-2022-04-15-690

Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation

Journal Article · Fri Apr 15 00:00:00 EDT 2022 · Quantum

DOI:https://doi.org/10.22331/q-2022-04-15-690· OSTI ID:1881872

An, Dong ^[1]; Fang, Di ^[2]; Lin, Lin ^[3]

Univ. of Maryland, College Park, MD (United States)
Univ. of California, Berkeley, CA (United States)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm that is both insensitive to the rapid changes of the time-dependent Hamiltonian and exhibits commutator scaling. Our method can be used for efficient Hamiltonian simulation in the interaction picture. In particular, we demonstrate that for the simulation of the Schrödinger equation, our method exhibits superconvergence and achieves a surprising second order convergence rate, of which the proof rests on a careful application of pseudo-differential calculus. Numerical results verify the effectiveness and the superconvergence property of our method.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE

Grant/Contract Number:: AC02-05CH11231; SC0017867

OSTI ID:: 1881872

Journal Information:: Quantum, Journal Name: Quantum Vol. 6; ISSN 2521-327X

Publisher:: Quantum Science Open CommunityCopyright Statement

Country of Publication:: United States

Language:: English

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