论文标题
引导的当地哈密顿问题问题的复杂性：改进的参数和扩展到激发状态
Complexity of the Guided Local Hamiltonian Problem: Improved Parameters and Extension to Excited States
论文作者
论文摘要
Recently it was shown that the so-called guided local Hamiltonian problem -- estimating the smallest eigenvalue of a $k$-local Hamiltonian when provided with a description of a quantum state ('guiding state') that is guaranteed to have substantial overlap with the true groundstate -- is BQP-complete for $k \geq 6$ when the required precision is inverse polynomial in the system size $n$, and remains hard even当引导状态与地面的重叠接近常数$ \ left（\ frac12 -ω\ left（\ frac {1} {\ mathop {poly}（poly}（n）（n）}（n）} \ right）\ right）$。我们以三种方式改进了这一结果：通过证明i）i）哈密顿量为2局部时，ii）指导状态和目标特征态之间的重叠高达$ 1-ω\ left（\ frac {\ frac {1} {\ mathop {\ mathop {poly}（poly}（n）} \ right yii时，当时是$ right Instation y Imimie y时，地面。有趣的是，仅首先证明II）才能实现III）。
Recently it was shown that the so-called guided local Hamiltonian problem -- estimating the smallest eigenvalue of a $k$-local Hamiltonian when provided with a description of a quantum state ('guiding state') that is guaranteed to have substantial overlap with the true groundstate -- is BQP-complete for $k \geq 6$ when the required precision is inverse polynomial in the system size $n$, and remains hard even when the overlap of the guiding state with the groundstate is close to a constant $\left(\frac12 - Ω\left(\frac{1}{\mathop{poly}(n)}\right)\right)$. We improve upon this result in three ways: by showing that it remains BQP-complete when i) the Hamiltonian is 2-local, ii) the overlap between the guiding state and target eigenstate is as large as $1 - Ω\left(\frac{1}{\mathop{poly}(n)}\right)$, and iii) when one is interested in estimating energies of excited states, rather than just the groundstate. Interestingly, iii) is only made possible by first showing that ii) holds.
