发表机构
Center on Frontiers of Computing Studies, Peking University; School of Computer Science, Peking University; Tencent Quantum Laboratory, Tencent; Department of Mathematical Sciences, Tsinghua University; Yau Mathematical Sciences Center, Tsinghua University; RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS); RIKEN Center for Computational Science (R-CCS)（北京大学前沿计算研究中心; 北京大学计算机学院; 腾讯量子实验室; 清华大学数学科学系; 清华大学丘成桐数学科学中心; 理化学研究所跨学科理论数学科学中心; 理化学研究所计算科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出联合外推策略，将噪声强度与Trotter步长关联，通过单次Richardson外推同时消除物理噪声和Trotter误差，并在超导量子计算机及100比特SPD模拟中验证其高效性。
AI 中文摘要
乘积公式哈密顿模拟天然适用于近期量子处理器，但其精度受两种相互竞争的误差制约：有限步Trotter偏差和物理硬件噪声。我们提出一种联合外推策略，将可调的单层噪声强度与Trotter步长关联，对于p阶乘积公式取λ(s)=c(sT)^{p+1}。沿此一维路径，整个演化过程中领先的物理噪声和Trotter修正均进入s^p阶，可通过单次Richardson外推予以消除。基于先前建立的有限阶Baker–Campbell–Hausdorff截断界，我们为联合外推推导出可证明的交换子缩放资源保证。对于具有局域Lindblad噪声的局域哈密顿量，该协议以相对于无噪声Trotter外推仅常数渐近开销的代价，同时抑制物理噪声和Trotter误差，前提是所需噪声强度高于器件固有噪声基底。我们在超导量子计算机上利用学习噪声放大实验演示了Ising动力学中的该协议。补充的100比特稀疏泡利动力学（SPD）模拟以更少的电路设置实现了与二维Richardson外推相当的精度。
英文摘要
Product-formula Hamiltonian simulation is naturally suited to near-term quantum processors, but its accuracy is set by two competing errors: finite-step Trotter bias and physical hardware noise. We introduce a joint extrapolation strategy that ties the tunable per-layer noise strength to the Trotter step size, $λ(s)=c(sT)^{p+1}$ for a $p$-th order product formula. Along this one-dimensional path, the leading physical-noise and Trotter corrections over the full evolution both enter at order $s^p$ and can be canceled by a single Richardson extrapolation. Building on a previously established finite-order Baker--Campbell--Hausdorff truncation bound, we derive a provably commutator-scaling resource guarantee for the joint extrapolation. For local Hamiltonians with local Lindbladian noise, the protocol mitigates physical noise together with Trotter error with only a constant asymptotic overhead relative to noiseless Trotter extrapolation, provided the required noise strengths lie above the intrinsic device-noise floor. We experimentally demonstrate the protocol for Ising dynamics on a superconducting quantum computer using learned noise amplification. Complementary 100-qubit Sparse Pauli Dynamics (SPD) simulations achieve comparable accuracy to two-dimensional Richardson extrapolation with fewer circuit settings.
Comments32 Pages, 7 Figures
