Dual channel multi-product formulas

TL;DR

This paper introduces a dual-channel multi-product formula that halves the circuit depth needed for quantum simulation, significantly reducing errors and hardware overhead on near-term quantum computers.

Contribution

The paper proposes a novel dual-channel multi-product formula that improves Trotter error scaling and reduces circuit depth compared to existing methods.

Findings

Achieves two-fold improvement in Trotter error scaling.

Halves the circuit depth required for target simulation precision.

Results in significantly smaller algorithmic errors with unchanged sampling error.

Abstract

Product-formula (PF) based quantum simulation is a promising approach for simulating quantum systems on near-term quantum computers. Achieving a desired simulation precision typically requires a polynomially increasing number of Trotter steps, which remains challenging due to the limited performance of current quantum hardware. To alleviate this issue, post-processing techniques such as the multi-product formula (MPF) have been introduced to suppress algorithmic errors within restricted hardware resources. In this work, we propose a dual-channel multi-product formula that achieves a two-fold improvement in Trotter error scaling. As a result, our method enables the target simulation precision to be reached with approximately half the circuit depth compared to conventional MPF schemes. Importantly, the reduced circuit depth directly translates into lower physical error mitigation overhead when implemented on real quantum hardware. We demonstrate that, for a fixed CNOT count as a measure of quantum circuit, our proposal yields significantly smaller algorithmic errors, while the sampling error remains essentially unchanged.