Improved Digital Quantum Simulation by Non-Unitary Channels

TL;DR

This paper demonstrates that averaging over a small set of non-unitary quantum simulation channels, constructed via Hamiltonian term permutation and symmetry transformations, significantly reduces Trotterization errors in noisy quantum devices.

Contribution

The study introduces a novel non-unitary channel averaging method that improves quantum simulation accuracy beyond traditional unitary approaches.

Findings

Averaging over few circuits reduces Trotterization error effectively.

Empirical results outperform analytical error bounds.

Method successfully tested on IonQ quantum hardware.

Abstract

Simulating quantum systems is one of the most promising avenues to harness the computational power of quantum computers. However, hardware errors in noisy near-term devices remain a major obstacle for applications. Ideas based on the randomization of Suzuki-Trotter product formulas have been shown to be a powerful approach to reducing the errors of quantum simulation and lowering the gate count. In this paper, we study the performance of non-unitary simulation channels and consider the error structure of channels constructed from a weighted average of unitary circuits. We show that averaging over just a few simulation circuits can significantly reduce the Trotterization error for both single-step short-time and multi-step long-time simulations. We focus our analysis on two approaches for constructing circuit ensembles for averaging: (i) permuting the order of the terms in the Hamiltonian and (ii) applying a set of global symmetry transformations. We compare our analytical error bounds to empirical performance and show that empirical error reduction surpasses our analytical estimates in most cases. Finally, we test our method on an IonQ trapped-ion quantum computer accessed via the Amazon Braket cloud platform, and benchmark the performance of the averaging approach.