发表机构
Department of Computer Science and Engineering, Pennsylvania State University（宾夕法尼亚州立大学计算机科学与工程系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种在块编码模型中具有最优加性查询复杂度的Lindblad演化模拟算法，利用换能器框架和重用电路线性组合，解决了乘性依赖是否必要的问题。
AI 中文摘要
针对在时间$t$内以精度$\epsilon$模拟Lindblad演化的问题，哈密顿模拟提供了一个加性的查询下界，非正式地表示为$\Omega(t + \mathrm{polylog}(1/\epsilon))$。然而，此前已知的用于一般Lindblad模拟的最佳算法在门复杂度上实现了乘性的上界，非正式地表示为$\mathcal{O}(t\\,\mathrm{polylog}(1/\epsilon))$。这种乘性依赖是否必要一直是一个悬而未决的问题。在本文中，我们通过给出一个在块编码模型中关于演化时间和精度具有最优加性依赖的算法，弥合了查询复杂度上的差距。我们的方法使用换能器框架来降低组合演化通道的一阶近似时的查询成本，并结合不同长度的重用电路的线性组合来抑制催化剂移除误差。尽管我们的额外门复杂度高于现有算法，但我们最优的查询复杂度解决了根本需要多少预言机访问的问题，并指出了实现最优门复杂度的剩余挑战。
英文摘要
For the problem of simulating Lindblad evolution for time $t$ to precision $ε$, Hamiltonian simulation provides an additive query lower bound, informally, $Ω(t + \mathrm{polylog}(1/ε))$. However, the best previously known algorithms for general Lindblad simulation achieve a multiplicative upper bound, informally, $\mathcal{O}(t\,\mathrm{polylog}(1/ε))$, in query complexity. It has remained open whether this multiplicative dependence is necessary. In this paper, we close the gap in query complexity by giving an algorithm with optimal additive dependence on evolution time and precision in the block-encoding model. Our approach uses the transducer framework to reduce the query cost of composing first-order approximations to the evolution channel, together with linear combinations of reuse circuits of different lengths to suppress catalyst-removal error. We further achieve nearly optimal gate complexity in evolution time and precision through history compression and an efficient implementation of the query-free part of the transducer using operation reordering and linear combinations of unitaries, while preserving the optimal query complexity.
Comments43 pages, no figures. Improved gate complexity
