Estimating the ground state energy of a local Hamiltonian is a central problem in quantum chemistry. In order to further investigate its complexity and the potential of quantum algorithms for quantum chemistry, Gharibian and Le Gall (STOC 2022) recently introduced the guided local Hamiltonian problem (GLH), which is a variant of the local Hamiltonian problem where an approximation of a ground state is given as an additional input. Gharibian and Le Gall showed quantum advantage (more precisely, BQP-completeness) for GLH with $6$-local Hamiltonians when the guiding vector has overlap (inverse-polynomially) close to 1/2 with a ground state. In this paper, we optimally improve both the locality and the overlap parameters: we show that this quantum advantage (BQP-completeness) persists even with 2-local Hamiltonians, and even when the guiding vector has overlap (inverse-polynomially) close to 1 with a ground state. Moreover, we show that the quantum advantage also holds for 2-local physically motivated Hamiltonians on a 2D square lattice. This makes a further step towards establishing practical quantum advantage in quantum chemistry.

翻译：估计当地汉密尔顿人的地面状态能量是量子化学的一个中心问题。为了进一步调查其复杂性和量子化学量子算法的潜力,加里比安和勒盖尔(STOC 2022)最近引入了引导的当地汉密尔顿问题(GLH),这是当地汉密尔顿问题的变体,当地汉密尔顿问题以近似地面状态作为附加投入。加里比安和勒盖尔对GLH来说量子优势(更确切地说,BQP完整性)为6美元地方汉密尔顿人,当指导矢量与地面状态相重叠(反政治上)接近1/2美元时。在本文件中,我们优化地改进了地点和重叠参数:我们表明这种量子优势(BQP完整性)即使与2个地方汉密尔密尔顿人持续在一起,甚至当引导矢量向1与地面状态相近。此外,我们还表明量子优势也有利于2个当地以物理为动力的汉密尔顿人。这在2D方方板上都意味着要进一步建立实际的量子化学优势。