Matrix Product Operator Encodings of the Magnus Expansion and Dyson Series

TL;DR

This paper presents a novel matrix product operator encoding for the Magnus expansion and Dyson series, enabling more efficient simulation of time-dependent quantum lattice models with long-range interactions.

Contribution

It introduces an MPO construction that is accurate to arbitrary order, applicable to finite and infinite systems, and improves quantum simulation methods.

Findings

Enables accurate MPO encoding of time-dependent evolutions

Improves simulation efficiency for long-range interactions

Facilitates quantum circuit optimization for time-dependent Hamiltonians

Abstract

We introduce a matrix product operator (MPO) encoding of the Magnus expansion and the Dyson series for one-dimensional quantum lattice models with time-dependent Hamiltonians. The MPO construction can be made accurate up to arbitrary order in the time step, it can be applied to both finite and infinite systems, and it can handle long-range interactions. The resulting MPO can be combined with state-of-the-art time evolution algorithms based on matrix product states, allowing for drastic improvements in simulating evolution under time-dependent Hamiltonians. Our MPO construction can also be used for the optimization of quantum circuits in the context of quantum simulation of time-dependent Hamiltonians.