Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation
Name
024106_1_online.pdf
Description
Published version
Size
5.11 MB
Format
Adobe PDF
Checksum (MD5)
3880b4c854ac478cb9c1452e2fee6f57
Author(s)
Martyn, John M
Liu, Yuan
Chin, Zachary E
Chuang, Isaac L
Date Issued
January 10, 2023
Journal
The Journal of Chemical Physics
Publisher
AIP Publishing
Citation
John M. Martyn, Yuan Liu, Zachary E. Chin, Isaac L. Chuang; Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation. J. Chem. Phys. 14 January 2023; 158 (2): 024106.
Version
Final published version
Abstract
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by the property of being fully-coherent: the algorithm succeeds with arbitrarily high success probability 1 − δ while only requiring a single copy of the initial state. We subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time t, ln(1/δ), and ln(1/ϵ) for error tolerance ϵ: Θ‖H‖|t|+ln(1/ϵ)+ln(1/δ). Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H2 molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves as a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Chemistry
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DOI of Published Version
https://doi.org/10.1063/5.0124385
