双通道多产品公式
Dual channel multi-product formulas
AI总结：
本文提出双通道多产品公式，通过减少Trotter误差缩放，实现更高效的量子模拟精度。
摘要：
基于产品公式（PF）的量子模拟是近期量子计算机模拟量子系统的一种有前景的方法。通常实现所需的模拟精度需要多项式增长的Trotter步骤数，这仍然具有挑战性，因为当前量子硬件的性能有限。为缓解这一问题，引入了诸如多产品公式（MPF）之类的后处理技术，以在受限的硬件资源内抑制算法误差。在本工作中，我们提出了一种双通道多产品公式，实现了Trotter误差缩放的两倍改进。因此，我们的方法使得达到目标模拟精度所需的电路深度大约是传统MPF方案的一半。重要的是，减少的电路深度在实际量子硬件上直接转化为更低的物理误差缓解开销。我们证明，对于固定CNOT计数作为量子电路的度量，我们的提案会产生显著更小的算法误差，而采样误差基本保持不变。
英文摘要：
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.
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