Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session A64: Algorithms for Hamiltionian Simulations
8:00 AM–11:00 AM,
Monday, March 6, 2023
Room: Room 415
Sponsoring
Unit:
DQI
Chair: William Munizzi, Arizona State University
Abstract: A64.00001 : Simple and high-precision Hamiltonian simulation by compensating Trotter errors with linear combination of unitary operations
8:00 AM–8:12 AM
Presenter:
Pei Zeng
(University of Chicago)
Authors:
Pei Zeng
(University of Chicago)
jinzhao sun
(University of Oxford)
Liang Jiang
(University of Chicago)
Qi Zhao
(The University of Hong Kong)
Collaboration:
N/A
We study the Hamiltonian simulation algorithms which combine the Trotter and LCU method --- In each time segment, we first implement Trotter method, and then apply LCU to compensate the residue error. We provide versatile realizations based on either random-sampling or coherent implementation of LCU formulas.
We propose two types of composite algorithms with unique advantages in various regions. The first algorithm is generic, with the random-sampling implementation, we prove that with only one ancillary qubit, one can achieve a gate cost almost linear to the time and logarithmically dependent on the inversed accuracy. In our second algorithm, we consider the detailed structure of Hamiltonians and propose a modified composite algorithms with commutator scaling utilizing nested-commutator analysis in the Trotter algorithms. Consequently, for the lattice Hamiltonians, our algorithm enjoys almost linear time and system-size dependence, and achieves a higher accuracy than 2Kth-order Trotter only with Kth-order Trotter's gate complexity.
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