逐路径随机哈密顿模拟
Pathwise Random Hamiltonian Simulation
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- Università di Pavia（帕维亚大学）
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中文总结 AI 辅助
该研究针对qDrift哈密顿模拟精度受限的问题，提出PRHS方法，通过细分时间步并优化参数，在无需辅助量子比特的情况下实现查询成本增长慢于1/ε任意次幂，且数值模拟显示其精度比qDrift高2-4个数量级。
中文摘要 AI 辅助
qDrift等随机乘积公式为哈密顿模拟提供了比确定性Trotter–Suzuki分解更具资源效率的替代方案，消除了对哈密顿项数量的多项式依赖。然而qDrift本质上受限于演化时间的一阶，其查询复杂度仍与目标精度的倒数1/ε呈线性关系。我们提出逐路径随机哈密顿模拟（PRHS），通过将每个时间步细分为M个相关子步，将qDrift扩展到任意阶，每个子步根据我们以闭式构造并证明唯一的准概率分布所采样的项演化，其偏差随M阶乘衰减。对子步数量M和独立块数量N的联合优化，在长时间下可在标准qDrift协议与高精度区间间插值，无需辅助量子比特即可使查询成本的增长慢于1/ε的任意次幂。对5个分子哈密顿量的数值模拟证实了这一优势，在相同查询成本下，PRHS实现的精度比qDrift高2至4个数量级。
英文摘要
Randomized product formulas such as qDrift offer a resource-efficient alternative to deterministic Trotter--Suzuki decompositions for Hamiltonian simulation, removing their polynomial dependence on the number of Hamiltonian terms. qDrift, however, is intrinsically limited to first order in the evolution time, so its query complexity remains linear in the inverse of the target accuracy, $1/ε$. We introduce Pathwise Random Hamiltonian Simulation (PRHS), which extends qDrift to arbitrary order by subdividing each time step into $M$ correlated slices, each evolving under a term sampled from a quasi-probability distribution that we construct in closed form and prove unique, with a bias decaying factorially in $M$. Optimizing jointly over the number of slices $M$ and the number of independent blocks $N$ interpolates between the standard qDrift protocol at long times and a high-precision regime where the query cost grows slower than any power of $1/ε$, without requiring ancillary qubits. Numerical simulations of five molecular Hamiltonians confirm this advantage, with PRHS achieving accuracies two to four orders of magnitude beyond qDrift at equal query cost.
