AI 中文总结
该研究提出基于影子哈密顿量模拟的算法，用于近似模拟可观测量实时动力学。通过识别相关代数元素克服效率瓶颈，提出两种剪枝方案及混合方案，用晶格自旋系统对算法进行基准测试。
AI 中文摘要
我们提出了一种基于影子哈密顿量模拟的高效算法，用于近似模拟与时间无关的哈密顿量下可观测量的实时动力学。影子哈密顿量模拟在由可观测量通过与哈密顿量的对易子生成的算子代数层面上工作。由于算子代数的指数增长，在这种情况下精确编码量子态对于相互作用系统通常效率低下。我们的算法通过系统地识别与目标可观测量最相关的代数元素来克服这一瓶颈。这种有针对性的方法是一种受控近似，产生了一种高效的量子态编码，大大减少了使用影子哈密顿量进行时间演化所需的量子比特寄存器的大小。我们提出了两种主要的剪枝方案，一种基于预定义的算子基，另一种基于构造的克里洛夫子空间基。我们还提出了一种混合方案，即在预定义基的剪枝代数内构建克里洛夫子空间基。我们使用一维和二维晶格自旋系统作为可观测量，对单点和多点关联函数进行基准测试。
英文摘要
We propose an efficient algorithm based on shadow Hamiltonian simulation to approximately simulate the real-time dynamics of observables under time-independent Hamiltonians. Shadow Hamiltonian simulation works at the level of the operator algebra generated by the observables through commutators with the Hamiltonian. Exactly encoding the quantum state in this picture is generally inefficient for interacting systems due to the exponential growth of the operator algebra. Our algorithm overcomes this bottleneck by systematically identifying the elements of the algebra most relevant to the target observables. This targeted approach is a controlled approximation that yields a highly efficient quantum state encoding that substantially reduces the size of the qubit register required to perform the time evolution using the shadow Hamiltonian. We propose two main pruning schemes, one based on a predefined operator basis and another on a constructed Krylov basis. We also present a hybrid scheme that builds a Krylov basis within a pruned algebra in the predefined basis. We benchmark our algorithm using lattice spin systems in one and two dimensions, for both one- and higher-point correlators as observables.
Comments23 pages
