Dual channel multi-product formulas

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.