Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Institution: University of British Columbia
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G3337417981, G9000156299
OpenAlex ID: W7220678057