Simple and high-precision Hamiltonian simulation by compensating Trotter error with linear combination of unitary operations

• URL: http://arxiv.org/abs/2212.04566v1
• Date: Thu, 8 Dec 2022 21:14:12 GMT
• Title: Simple and high-precision Hamiltonian simulation by compensating Trotter error with linear combination of unitary operations
• Authors: Pei Zeng, Jinzhao Sun, Liang Jiang and Qi Zhao
• Abstract summary: We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error. Our first algorithm exponentially improves the accuracy scaling of the Kth-order Trotter formula. For lattice Hamiltonians, the algorithm enjoys almost linear system-size dependence.
• Score: 17.908408323643915
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Trotter and linear-combination-of-unitary (LCU) are two popular Hamiltonian simulation methods. We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error, which enjoy both of their advantages. By adding few gates after the Kth-order Trotter, we realize a better time scaling than 2Kth-order Trotter. Our first algorithm exponentially improves the accuracy scaling of the Kth-order Trotter formula. In the second algorithm, we consider the detailed structure of Hamiltonians and construct LCU for Trotter errors with commutator scaling. Consequently, for lattice Hamiltonians, the algorithm enjoys almost linear system-size dependence and quadratically improves the accuracy of the Kth-order Trotter.

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