Efficient higher-order matrix product operators for time evolution

TL;DR

This paper presents a systematic method for constructing higher-order matrix product operators to efficiently simulate time evolution in one-dimensional quantum systems, significantly reducing computational costs.

Contribution

The authors develop a new systematic approach for higher-order MPO approximations, enabling faster and more accurate time evolution simulations for complex Hamiltonians.

Findings

Achieved an order of magnitude speedup in simulation cost.

Demonstrated effectiveness for both short and long-range Hamiltonians.

Provided a systematic construction method for higher-order MPOs.

Abstract

We introduce a systematic construction of higher-order matrix product operator (MPO) approximations of the time evolution operator for generic (short and long range) one-dimensional Hamiltonians. We demonstrate the utility of our construction, by showing an order of magnitude speedup in simulation cost compared to conventional first-order MPO time evolution schemes.