AI 中文总结
本文提出动态可观测子空间方法，通过李代数分解实现多项式时间经典模拟，避免贫瘠高原，为量子相位估计等任务提供高质量引导态。
AI 中文摘要
通过将量子动力学分解到一组可观测量的李轨道上，我们发现，对于具有多项式大小的动态李代数（DLA）的量子系统生成元，可以实现多项式有界的经典模拟。为此，我们描述了如何构造动态可观测子空间（DOS），该子空间捕获了计算特定可观测量的期望值所需的所有相关动力学，适用于泡利字符串、扩散器混合器以及一般的局域生成元。高效的稀疏矩阵表示、将非线性从这种表示中解耦以及允许剪枝的基构造，使我们能够模拟具有数百个量子比特的此类系统的封闭动力学。此外，我们发现，尽管受限的DOS电路可能无法表达相关哈密顿量的空间，但由于不存在贫瘠高原，它们可以显著优于完全可表达的电路。虽然可经典模拟，但此类电路仍可通过推理展现某种形式的量子优势，可作为更具表达力电路的预热启动，并为量子振幅放大或量子相位估计找到高质量的试探态。在量子动力学模拟中，我们发现我们的受限电路可以在多项式时间内被模拟，同时为下游任务（如量子相位估计）产生高质量的引导态，其能量显著低于具有完全表达力的电路。
英文摘要
By decomposing quantum dynamics across the Lie orbits of a list of observables, we find polynomial bounded classical simulations for the dynamics of the quantum system given a polynomial sized dynamic Lie algebra (DLA) for the generators of the quantum system. To do so, we describe how to construct the Dynamic Observable Subspace (DOS) that captures all the relevant dynamics for calculating expectation values for a specific observable for Pauli strings, diffusor mixers, and general local generators. Efficient sparse matrix representation, decoupling nonlinearity from such representation and basis construction with permissible pruning allows us to simulate the closed dynamics of such systems with hundreds of qubits. Moreover, we find that while restricted DOS circuits may not express the space of an associated Hamiltonian, they can dramatically outperform a fully expressive circuit due to the absence of the Barren Plateau. While classically simulatable, such circuits can still exhibit a form of quantum advantage through inference, act as warm starting for more expressive circuits, and find high quality trial states for Quantum Amplitude Amplification or Quantum Phase Estimation. In the simulation of quantum dynamics, we find that our restricted circuit can be simulated in polynomial time while producing high quality guiding state for downstream tasks like Quantum Phase Estimation with significantly lower energy than circuits with full expressivity.
