发表机构
University of British Columbia（不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明截断幂方法在基态ℓ1范数多项式有界时，能以与量子算法多项式可比的经典运行时间解决引导局部哈密顿问题，实现去量子化。
AI 中文摘要
引导局部哈密顿问题（GLHP）是在给定与真实基态具有良好重叠的引导态的情况下，进行基态能量估计和制备的问题。已知该问题在小误差下是BQP完全的，但在较大误差下经典可解。在本工作中，我们识别了一个正交的经典可解区域，即真实基态ψ具有多项式有界的ℓ1范数。特别地，我们证明截断幂方法（TPM），一种由Kirby等人在量子背景下引入的经典算法，其运行时间在所有相关参数上与GLHP的量子算法多项式可比，除了额外的因子‖ψ‖₁²。换言之，如果‖ψ‖₁²是多项式有界的，则TPM使GLHP的量子算法去量子化。
英文摘要
The Guided Local Hamiltonian Problem (GLHP) is the problem of ground state energy estimation and preparation given a guiding state having good overlap with the true ground state. The problem is known to be BQP-complete for small error but is classically tractable for larger error. In this work, we identify an orthogonal regime in which the problem is classically tractable, namely when the true ground state $ψ$ has polynomially bounded $\ell_1$-norm. In particular, we show that the Truncated Power Method (TPM), a classical algorithm introduced by Kirby et al. in the quantum context, has a runtime that is polynomially comparable to quantum algorithms for GLHP in all relevant parameters, except for an extra factor of $\|ψ\|_1^2$. In other words, if $\|ψ\|_1^2$ is polynomially bounded, then TPM dequantizes quantum algorithms for GLHP.
Comments23 pages
