Tailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries

TL;DR

This paper introduces an adaptive linear combination of unitaries method for quantum simulations of electronic structures, which improves accuracy by selectively truncating terms based on their magnitude, leading to more efficient quantum computations.

Contribution

It presents a novel adaptive truncation technique for LCU in quantum simulations, optimizing for Hamiltonians with varying term magnitudes, and provides bounds and numerical validation.

Findings

Adaptive truncation improves simulation accuracy by an order of magnitude.

The method reduces circuit depth needed for accurate simulations.

Bounds on simulation error are established and validated.

Abstract

A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to approximate a Taylor series by truncating after some order. Here we present an adaptation of that method, optimized for Hamiltonians with terms of widely varying magnitude, as is commonly the case in electronic structure calculations. We show that it is more efficient to apply LCU using a truncation that retains larger magnitude terms as determined by an iterative procedure. We obtain bounds on the simulation error for this generalized truncated Taylor method, and for a range of molecular simulations, we report these bounds as well as exact numerical results. We find that our adaptive method can typically improve the simulation accuracy by an order of magnitude, for a given circuit depth.