Composite Quantum Simulations

TL;DR

This paper introduces a framework for combining multiple quantum simulation methods, such as Trotter-Suzuki and QDrift, to optimize simulation efficiency by partitioning Hamiltonian terms.

Contribution

It presents a novel composite channel approach with rigorous bounds, enabling flexible integration of different quantum simulation techniques.

Findings

Proves bounds on the diamond distance for the composite channel

Shows asymptotic cost bounds for combined simulation methods

Discusses strategies for partitioning Hamiltonian terms effectively

Abstract

In this paper we provide a framework for combining multiple quantum simulation methods, such as Trotter-Suzuki formulas and QDrift into a single Composite channel that builds upon older coalescing ideas for reducing gate counts. The central idea behind our approach is to use a partitioning scheme that allocates a Hamiltonian term to the Trotter or QDrift part of a channel within the simulation. This allows us to simulate small but numerous terms using QDrift while simulating the larger terms using a high-order Trotter-Suzuki formula. We prove rigorous bounds on the diamond distance between the Composite channel and the ideal simulation channel and show under what conditions the cost of implementing the Composite channel is asymptotically upper bounded by the methods that comprise it for both probabilistic partitioning of terms and deterministic partitioning. Finally, we discuss strategies for determining partitioning schemes as well as methods for incorporating different simulation methods within the same framework.