Dual channel multi-product formulas

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.

💡 Research Summary

The paper addresses a fundamental bottleneck in product‑formula (PF) based quantum simulation: achieving high precision requires a large number of Trotter steps, which leads to deep circuits that are vulnerable to hardware noise on near‑term devices. Multi‑product formulas (MPFs) have been proposed as a post‑processing technique that linearly combines several folded PF circuits to suppress algorithmic (Trotter) errors without increasing circuit depth dramatically. However, conventional MPFs suffer from a “conditioning problem”: to obtain well‑conditioned linear coefficients, one must use large folding numbers, which in turn increase the circuit depth and amplify physical errors.

The authors introduce the Dual‑Channel Multi‑Product Formula (DCMPF) protocol, which simultaneously employs a regular PF (T_{\alpha}(t)) and its reversed‑order counterpart (\bar T_{\alpha}(t)) (the same elementary exponentials applied in opposite sequence). The key observation is that the sum (T_{\alpha}(t)+\bar T_{\alpha}(t)) satisfies the same symmetry condition as a symmetric PF, allowing the error terms to cancel across different foldings. By forming the linear combination

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