Hamiltonian Operator Approximation for Energy Measurement and Ground-State Preparation
Hamiltonian Operator Approximation for Energy Measurement and Ground-State Preparation
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DOI：
10.1103/prxquantum.2.030318
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发表时间：
2021-08-02
期刊：
影响因子：
9.7
通讯作者：
Kyriienko, Oleksandr
中科院分区：
文献类型：
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作者：
Bespalova, Tatiana A.;Kyriienko, Oleksandr
哈密顿算符在量子理论中起着核心作用，是幺正量子动力学的生成器。它的期望值描述了量子系统的能量。作为一个典型的非幺正算子，哈密顿算子的作用要么使用复杂的基于辅助的电路进行编码，要么有效地实现为泡利弦项的总和。在这里，我们展示了如何近似的哈密顿算子的传播使用微分表示的总和。所提出的方法称为哈密顿算符近似（HOA），旨在使模拟量子模拟器受益，其中可以直接访问量子动力学模拟，但测量单独的电路是不可能的。我们描述了如何使用这种策略的混合量子经典的工作流程进行能量测量。基准的测量方案，我们讨论的离散化步长，模板顺序，拍摄的数量和噪声的相关性。我们还使用HOA通过直接迭代和量子滤波器对角化来制备复杂材料科学模型的基态，使用11个时间演化参考态以10（-5）Hartree精度找到氢链H-6的12量子比特哈密顿量的最低能量。该方法相比，变分量子本征解，证明HOA是有益的系统在不断增加的尺寸，对应于嘈杂的大规模量子器件。我们发现，对于具有12个或更多自旋的海森堡模型，我们的方法可能优于变分方法，无论是在门深度和测量总数方面。
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 nonunitary 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 the 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 that HOA is beneficial for systems at increasing size, corresponding to noisy large-scale quantum devices. We find that, for the Heisenberg model with 12 or more spins, our approach may outperform variational methods, both in terms of the gate depth and the total number of measurements.