AI 中文总结
研究多体动力学数字量子模拟中算法Trotter误差与物理噪声问题，提出恒定深度多乘积公式，通过确定辅助参数\(\alpha\)，抑制Trotter误差，结合物理噪声缓解，为近期硬件长时间量子动力学模拟提供关键方法。
AI 中文摘要
多体动力学的数字量子模拟面临算法Trotter误差与随电路深度累积的物理噪声之间的矛盾。典型的高阶乘积公式以更深的电路为代价减轻算法误差。我们的基准测试表明，在有限的物理误差预算内，可行优势仅限于远低于\(10^{-2}\)量级的绝对误差，在当前量子硬件的噪声水平下该优势消失。与之前的Trotter误差缓解方法形成鲜明对比，我们引入了恒定深度多乘积公式（cd-MPF），通过在固定电路深度组合多个电路来抑制Trotter误差。我们确定了一个辅助参数\(\alpha\)，它重塑了Trotter误差项，同时保持目标演化不变。测量期望值的经典线性组合消除了领先的\((\Delta t)^{2}\)算法贡献，并使Trotter误差与双量子比特电路深度\(d\)的缩放比例从\(d^{-2}\)变陡到\(d^{-4}\)。结合物理噪声缓解，我们的方法可作为在近期硬件上实现长时间量子动力学模拟的关键要素。
英文摘要
Digital quantum simulation of many-body dynamics faces a tension between algorithmic Trotter error and physical noise that accumulates with circuit depth. Typical higher-order product formulas mitigate the algorithmic error at the cost of deeper circuits. Our benchmark shows that, within the limited physical error budget, the feasible advantage is confined to absolute errors well below the $10^{-2}$ scale, which vanishes under noise levels of current quantum hardware. In sharp contrast to the previous Trotter error mitigation methods, we introduce a constant-depth multi-product formula (cd-MPF) that suppresses the Trotter error by combining multiple circuits at fixed circuit depth. We identify an auxiliary parameter $α$, which reshapes the Trotter error terms while leaving the target evolution invariant. The classical linear combination of the measured expectation values cancels the leading $(Δt)^{2}$ algorithmic contribution and steepens the Trotter-error scaling with the two-qubit circuit depth $d$ from $d^{-2}$ to $d^{-4}$. Combined with physical-noise mitigation, our method can serve as a key ingredient for realizing long-time quantum dynamics simulation on near-term hardware.
Comments10 pages, 5 figures, 1 table; with Supplementary Material (6 pages, 5 figures)
