发表机构
Tsinghua University; Institute of Software, Chinese Academy of Sciences; University of Chinese Academy of Sciences; Center on Frontiers of Computing Studies, Peking University; School of Computer Science, Peking University（清华大学; 中国科学院软件研究所; 中国科学院大学; 北京大学前沿计算研究中心; 北京大学计算机学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种查询最优且门高效的林德布拉德演化模拟量子算法，通过单查询转导器和催化剂实现，匹配哈密顿量模拟的查询下界，并扩展到时间相关情形。
AI 中文摘要
我们给出一个量子算法，用于在给定哈密顿量 $H$ 的块编码和堆叠跳跃算子 $B=\sum_{k=1}^m \lvert k\rangle\otimes L_k$ 的投影酉编码的情况下进行林德布拉德演化模拟，归一化因子分别为 $\alpha_H$ 和 $\alpha_B$。对于演化时间 $t$，设 $\tau=(\alpha_H+\alpha_B^2)t$。该算法以金刚石范数误差 $\varepsilon$ 逼近演化通道，使用 $O\\!\left(\tau+\frac{\log(1/\varepsilon)}{\log\\!\left(e+\log(1/\varepsilon)/\tau\right)}\right)$ 次预言机查询，匹配哈密顿量模拟的查询下界。额外的一比特和两比特门数量与查询复杂度呈线性关系，直至多对数因子。查询和门复杂度界可扩展到在相干时间索引预言机访问下的利普希茨连续时间相关林德布拉德算子。我们的构造使用一个单查询转导器，在提供催化剂时实现短时演化的有理逼近的乘积。我们通过利用不同克劳斯标签序列之间的正交性来界定省略催化剂所产生的误差。门实现结合了压缩克劳斯标签表示（仅存储非零标签的位置和值）与Chen等人的旋转分解。
英文摘要
We give a quantum algorithm for Lindbladian simulation given a block encoding of the Hamiltonian $H$ and a projected unitary encoding of the stacked jump operator $B=\sum_{k=1}^m \lvert k\rangle\otimes L_k$, with normalization factors $α_H$ and $α_B$, respectively. For evolution time $t$, set $τ=(α_H+α_B^2)t$. The algorithm approximates the evolution channel to diamond-norm error $\varepsilon$ using $O\!\left(τ+\frac{\log(1/\varepsilon)}{\log\!\left(e+\log(1/\varepsilon)/τ\right)}\right)$ oracle queries, matching the query lower bound for Hamiltonian simulation. The number of additional one- and two-qubit gates is linear in the query complexity up to polylogarithmic factors. The query- and gate-complexity bounds extend to Lipschitz-continuous time-dependent Lindbladians under coherent time-indexed oracle access. Our construction uses a one-query transducer that implements a product of rational approximations to short-time evolution when supplied with a catalyst. We bound the error from omitting the catalyst by exploiting orthogonality between different sequences of Kraus labels. The gate implementation combines a compressed Kraus-label representation, which stores only the positions and values of the nonzero labels, with the rotation factorization of Chen et al.
Comments62 pages, 5 figures
