论文标题
无偏见的随机电路编译器，用于时间依赖的哈密顿模拟
Unbiased random circuit compiler for time-dependent Hamiltonian simulation
论文作者
论文摘要
时间依赖性的汉密尔顿模拟（TDHS）是量子计算中的关键任务。对于基于产品公式的方法，现有的算法通常会偏向小算法错误$ \ varepsilon $，而门复杂度则为$ O（\ text {poly}（1/\ varepsilon）$）$，可以改进具有复杂电路结构的pologarithmic。在这里，我们通过结合Dyson扩展，一种无偏的连续采样方法来为TDHS开发一个无偏的随机编译器，用于量子演变和领先阶旋转，并且没有算法误差。我们的方法具有带有恒定抽样开销的单Qubit Gate复杂性$ O（λ^2）$，其中$λ$是哈密顿强度的时间集成。我们在相互作用图片和分子系统的绝热基态制备下对自旋模型进行数值模拟。在这两个示例中，我们都可以观察到我们的方法对现有方法的改进。我们的工作为TDHS的有效实现铺平了道路。
Time-dependent Hamiltonian simulation (TDHS) is a critical task in quantum computing. Existing algorithms are generally biased with a small algorithmic error $\varepsilon$, and the gate complexity scales as $O(\text{poly}(1/\varepsilon))$ for product formula-based methods and could be improved to be polylogarithmic with complicated circuit constructions. Here, we develop an unbiased random compiler for TDHS by combining Dyson expansion, an unbiased continuous sampling method for quantum evolution, and leading order rotations, and it is free from algorithmic errors. Our method has the single- and two-qubit gate complexity $O(Λ^2)$ with a constant sampling overhead, where $Λ$ is the time integration of the Hamiltonian strength. We perform numerical simulations for a spin model under the interaction picture and the adiabatic ground state preparation for molecular systems. In both examples, we observe notable improvements of our method over existing ones. Our work paves the way to efficient realizations of TDHS.
