[{"citation":{"mla":"Gharibian, Sevag, et al. <i>Near-Optimal Bounds on the Density of Low-Energy States of $k$-Local Hamiltonians and Faster Quantum Algorithms</i>. 2026.","bibtex":"@article{Gharibian_Le Gall_Mataraarachchi_Tamaki_2026, title={Near-Optimal Bounds on the Density of Low-Energy States of $k$-Local Hamiltonians and Faster Quantum Algorithms}, author={Gharibian, Sevag and Le Gall, Francois and Mataraarachchi, Ranitha and Tamaki, Suguru}, year={2026} }","ama":"Gharibian S, Le Gall F, Mataraarachchi R, Tamaki S. Near-Optimal Bounds on the Density of Low-Energy States of $k$-Local Hamiltonians and Faster Quantum Algorithms. Published online 2026.","ieee":"S. Gharibian, F. Le Gall, R. Mataraarachchi, and S. Tamaki, “Near-Optimal Bounds on the Density of Low-Energy States of $k$-Local Hamiltonians and Faster Quantum Algorithms.” 2026.","apa":"Gharibian, S., Le Gall, F., Mataraarachchi, R., &#38; Tamaki, S. (2026). <i>Near-Optimal Bounds on the Density of Low-Energy States of $k$-Local Hamiltonians and Faster Quantum Algorithms</i>.","short":"S. Gharibian, F. Le Gall, R. Mataraarachchi, S. Tamaki, (2026).","chicago":"Gharibian, Sevag, Francois Le Gall, Ranitha Mataraarachchi, and Suguru Tamaki. “Near-Optimal Bounds on the Density of Low-Energy States of $k$-Local Hamiltonians and Faster Quantum Algorithms,” 2026."},"abstract":[{"text":"Low-energy estimation and state preparation for general $k$-local Hamiltonians are fundamental challenges in quantum complexity theory. Buhrman et al.~ [BGLGST, PRL 2025] recently broke the natural Grover bound $O^\\ast(2^{n/2})$ for both problems, with the improvement depending on the relative accuracy $\\varepsilon$ and the locality $k$. In this work, we present faster exponential quantum algorithms for these problems, where the binary entropy function governs the runtime exponent. For sufficiently small $\\varepsilon/k$, our algorithms improve the exponent by a factor of $\\log(k/\\varepsilon)$ over [BGLGST, PRL 2025]. Our main technical result is an entropy-governed lower bound on the dimension of the Hamiltonian's low-energy subspace, obtained by depolarizing its ground state. For fixed $k$, this bound is optimal up to constant factors in the exponent. The same framework yields tighter bounds for Heisenberg, $XY$, and Ising models on arbitrary interaction graphs.","lang":"eng"}],"date_created":"2026-10-01T07:35:41Z","department":[{"_id":"7"},{"_id":"623"}],"type":"preprint","author":[{"orcid":"0000-0002-9992-3379","last_name":"Gharibian","first_name":"Sevag","full_name":"Gharibian, Sevag","id":"71541"},{"full_name":"Le Gall, Francois","first_name":"Francois","last_name":"Le Gall"},{"first_name":"Ranitha","last_name":"Mataraarachchi","full_name":"Mataraarachchi, Ranitha"},{"first_name":"Suguru","last_name":"Tamaki","full_name":"Tamaki, Suguru"}],"title":"Near-Optimal Bounds on the Density of Low-Energy States of $k$-Local Hamiltonians and Faster Quantum Algorithms","status":"public","year":"2026","date_updated":"2026-10-01T08:21:44Z","language":[{"iso":"eng"}],"_id":"67293","user_id":"71541"}]