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Operator-level quantum acceleration of non-logconcave sampling.

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Bibliographic Details
Title: Operator-level quantum acceleration of non-logconcave sampling.
Authors: Leng, Jiaqi, Ding, Zhiyan, Chen, Zherui, Lin, Lin
Source: Proceedings of the National Academy of Sciences of the United States of America; 2/24/2026, Vol. 123 Issue 8, p1-9, 30p
Subject Terms: LANGEVIN equations, SAMPLING (Process), LAPLACIAN operator, QUANTUM computing, GIBBS' free energy, POTENTIAL energy
Abstract: Sampling from probability distributions of the form σ ∝ e-βV, where V is a continuous potential, is a fundamental task across physics, chemistry, biology, computer science, and statistics. However, when V is nonconvex, the resulting distribution becomes non-logconcave, and classical methods such as Langevin dynamics often exhibit poor performance. We introduce a quantum algorithm that provably accelerates a broad class of continuous-time sampling dynamics. For Langevin dynamics, our method encodes the target Gibbs measure into the amplitudes of a quantum state, identified as the kernel of a block matrix derived from a factorization of the Witten Laplacian operator. This connection enables Gibbs sampling via singular value thresholding and yields up to a quartic quantum speedup over best-known classical Langevin-based methods in the non-logconcave setting. Building on this framework, we further develop the first quantum algorithm that accelerates replica exchange Langevin diffusion, a widely used method for sampling from complex, rugged energy landscapes. [ABSTRACT FROM AUTHOR]
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Database: Complementary Index
Description
Abstract:Sampling from probability distributions of the form σ ∝ e-βV, where V is a continuous potential, is a fundamental task across physics, chemistry, biology, computer science, and statistics. However, when V is nonconvex, the resulting distribution becomes non-logconcave, and classical methods such as Langevin dynamics often exhibit poor performance. We introduce a quantum algorithm that provably accelerates a broad class of continuous-time sampling dynamics. For Langevin dynamics, our method encodes the target Gibbs measure into the amplitudes of a quantum state, identified as the kernel of a block matrix derived from a factorization of the Witten Laplacian operator. This connection enables Gibbs sampling via singular value thresholding and yields up to a quartic quantum speedup over best-known classical Langevin-based methods in the non-logconcave setting. Building on this framework, we further develop the first quantum algorithm that accelerates replica exchange Langevin diffusion, a widely used method for sampling from complex, rugged energy landscapes. [ABSTRACT FROM AUTHOR]
ISSN:00278424
DOI:10.1073/pnas.2512789123