发表机构
Technische Universität München; Freie Universität Berlin; University College London（慕尼黑工业大学; 柏林自由大学; 伦敦大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立Floquet模拟理论，证明一组相互作用可模拟其李代数中所有哈密顿量，给出Floquet-通用哈密顿量的构造性刻画，仅需O(1)局部强度，驱动频率随系统大小多项式增长，并带来复杂性理论意义。
AI 中文摘要
模拟和数字哈密顿量模拟代表了使一个量子系统复制另一个量子系统物理性质的两种不同方法，其影响从实际应用延伸到复杂性理论和量子引力。它们根植于量子动力学的两个不同领域：前者对应时间无关的哈密顿量；后者对应完全可控的时间相关量子电路。时间周期哈密顿量代表了一个中间领域。在这项工作中，我们建立了Floquet模拟的理论，其中我们使用周期驱动的哈密顿量来合成时间无关的哈密顿量。我们证明了一组相互作用$S$可以Floquet模拟李代数$\nmathrm{Lie}(S)$中的每一个哈密顿量，因此我们给出了能够产生任何目标哈密顿量的Floquet-通用哈密顿量的完整且构造性的刻画。值得注意的是，我们的构造仅使用$O(1)$的局部相互作用强度及其比值，避免了在通过时间无关哈密顿量进行模拟时通常需要的不切实际的多尺度局部相互作用强度。相反，该构造需要一系列驱动频率，对于重要类别如$k$-局部晶格哈密顿量，这些频率随系统大小多项式增长。这具有直接的复杂性理论意义，包括对Floquet物理学中研究的自然物理性质和量的众多BQP完全性和QMA困难性结果。
英文摘要
Analogue and digital Hamiltonian simulation represent two distinct approaches to making one quantum system replicate the physical properties of another, with consequences ranging from practical applications to complexity theory and quantum gravity. They are rooted in two distinct regimes of quantum dynamics: time-independent Hamiltonians for the former; fully controllable time-dependent quantum circuits in the latter. Time-periodic Hamiltonians represent an intermediate regime. In this work, we establish a theory of Floquet simulation where we use periodically driven Hamiltonians to synthesise time-independent ones. We show that a set of interactions $S$ can Floquet-simulate every Hamiltonian in the Lie algebra $\mathrm{Lie}(S)$, and consequently we give a complete and constructive characterisation of Floquet-universal Hamiltonians that are able to produce any target Hamiltonian. Notably, our construction uses only $O(1)$ local interaction strengths and ratios thereof, avoiding the impractical multi-scale local interaction strengths often required in analogue simulation via time-independent Hamiltonians. Instead, the construction requires a range of driving frequencies which scales polynomially with system size for important classes such as $k$-local lattice Hamiltonians. This has immediate complexity-theoretic implications, including numerous BQP-completeness and QMA-hardness results for natural physical properties and quantities studied in Floquet physics.
Comments60 pages
