论文标题
用于能量测量和基态制备的哈密顿操作员近似
Hamiltonian operator approximation for energy measurement and ground state preparation
论文作者
论文摘要
哈密顿操作员在量子理论中起着核心作用，是统一量子动力学的发生者。它的期望值描述了量子系统的能量。通常是一个非单身的操作员，哈密顿式的动作要么使用基于复杂的Ancilla电路编码，要么是作为Pauli字符串术语的有效实施的。在这里，我们展示了如何使用差分表示将汉密尔顿操作员近似为传播器的总和。所提出的方法（称为Hamiltonian操作员近似（HOA））旨在使模拟量子模拟器有益于量子动力学的模拟，但是无法测量单独的电路。我们描述了如何在混合量子古典工作流中使用此策略来执行能量测量。测量方案基准测试，我们讨论了离散的步长大小，模板顺序，射击数和噪声的相关性。我们还使用HOA来制备具有直接迭代和量子过滤对角线化的复杂材料科学模型的基态，找到了氢链12 Qubit Hamiltonian h $ _6 $的最低能量，使用$ 10^{ - 5} $ hartree Precision使用$ 11 $ time-ever-time-eper-precision。将该方法与变异量子本质量器进行了比较，该方法证明了HOA对与嘈杂大规模量子设备相对应的尺寸增加的系统有益。我们发现，对于具有十二或更多旋转的海森堡模型，我们的方法在门深度和测量总数方面都可能超过变异方法。
The Hamiltonian operator plays a central role in quantum theory being a generator of unitary quantum dynamics. Its expectation value describes the energy of a quantum system. Typically being a non-unitary operator, the action of the Hamiltonian is either encoded using complex ancilla-based circuits, or implemented effectively as a sum of Pauli string terms. Here, we show how to approximate the Hamiltonian operator as a sum of propagators using a differential representation. The proposed approach, named Hamiltonian operator approximation (HOA), is designed to benefit analog quantum simulators, where one has direct access to simulation of quantum dynamics, but measuring separate circuits is not possible. We describe how to use this strategy in the hybrid quantum-classical workflow for performing energy measurements. Benchmarking the measurement scheme, we discuss the relevance of the discretization step size, stencil order, number of shots, and noise. We also use HOA to prepare ground states of complex material science models with direct iteration and quantum filter diagonalization, finding the lowest energy for the 12-qubit Hamiltonian of hydrogen chain H$_6$ with $10^{-5}$ Hartree precision using $11$ time-evolved reference states. The approach is compared to the variational quantum eigensolver, proving HOA beneficial for systems at increasing size corresponding to noisy large scale quantum devices. We find that for Heisenberg model with twelve or more spins our approach may outperform variational methods, both in terms of the gate depth and the total number of measurements.
