查询最优时变哈密顿量模拟的门高效实现
Gate-Efficient Implementation of the Query-Optimal Time-Dependent Hamiltonian Simulation
- Tsinghua University（清华大学）
- Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）
- University of Chinese Academy of Sciences（中国科学院大学）
- Peking University（北京大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文针对查询最优时变哈密顿量模拟算法，提出一种保留最优查询复杂度且门开销更低的实现方案，核心为有序更新乘积的精确二进分解。
中文摘要 AI 辅助
对于区间[0,T]上满足‖H(t)‖≤α的利普希茨连续时变哈密顿量H(t)，文献[CGWZ26]提出的通用时变哈密顿量模拟的查询最优算法，使用q=O(αT + log(1/ε)/log(e + log(1/ε)/(αT)))次HAM-T查询可实现ε误差。但其直接电路实现会产生大幅更高的门开销。本文给出该算法的一种实现，在保留最优查询复杂度的同时，使用O[q(a + log(1 + T(α + βT)/ε))]个单量子比特和双量子比特门，其中a是块编码辅助量子比特的数量，β是H的利普希茨常数。核心要素是基础单查询换能器中有序更新乘积的精确二进分解。
英文摘要
The query-optimal algorithm of [CGWZ26] for general time-dependent Hamiltonian simulation uses $$ q = O\left( αT + \frac{\log(1/\varepsilon)}{\log\left(e + \log(1/\varepsilon)/(αT) \right)} \right) $$ queries to $\mathrm{HAM\mbox{-}T}$ within $\varepsilon$ error for a Lipschitz-continuous time-dependent Hamiltonian $H(t)$ on $[0,T]$ satisfying $\left\lVert H(t)\right\rVert\leqα$. However, its direct circuit implementation incurs a substantially larger gate overhead. In this note, we give an implementation of the same algorithm that retains its optimal query complexity and uses $$ O\left[ q \left( a + \log\left(1 + \frac{T(α+ βT)}{\varepsilon} \right) \right) \right] $$ one- and two-qubit gates, where $a$ is the number of block-encoding ancilla qubits and $β$ is the Lipschitz constant of $H$. The main ingredient is an exact dyadic factorization of the ordered update product in the underlying one-query transducer.
