biostudies-literatureLeng JSimons FoundationDOE | Office of Science (SC)Simons Foundation (SF)Heising-Simons FoundationDOE | Office of ScienceHeising-Simons Foundation (HSF)e2512789123https://www.ebi.ac.uk/biostudies/studies/S-EPMC12933055biostudies-literatureUnknown123(8)Sampling from probability distributions of the form [Formula: see text], where [Formula: see text] is a continuous potential, is a fundamental task across physics, chemistry, biology, computer science, and statistics. However, when [Formula: see text] 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 yielProceedings of the National Academy of Sciences of the United States of AmericaOperator-level quantum acceleration of non-logconcave sampling.PMC12933055No. 825053FP00010905Quantum Systems AcceleratorQuantum Utility through Advanced Computational Quantum Algorithms No. DE-SC0025572Quantum Systems AcceleratorsChen ZDing ZLin LLeng JfalseOperator-level quantum acceleration of non-logconcave sampling.Sampling from probability distributions of the form [Formula: see text], where [Formula: see text] is a continuous potential, is a fundamental task across physics, chemistry, biology, computer science, and statistics. However, when [Formula: see text] 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 yiel2026-01-01T00:00:00Z2026 Feb2026-07-16T20:45:47.324Z2026-07-10T03:11:56.09ZS-EPMC129330554171933310.1073/pnas.2512789123