Quantum algorithms for compact polymer thermodynamics

Quantum Physics [Submitted on 12 Mar 2026] Quantum algorithms for compact polymer thermodynamics Davide Rattacaso, Daniel Jaschke, Antonio Trovato, Ilaria Siloi, Simone Montangero Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although classical Monte Carlo methods are widely regarded as the standard approach, their efficiency is strongly limited when applied to compact polymers. In this work, we enable a quadratic speedup in the estimation of thermodynamic properties of maximally compact polymers and heteropolymers by quantum computation. To this end, we encode the target thermodynamic ensemble into the amplitudes of a quantum state, i.e., a quantum sample, which can be processed via amplitude amplification. Using quantum equational reasoning, we construct a local parent Hamiltonian whose unique ground state realizes a quantum sample of all Hamiltonian cycles. This state can be prepared on quantum hardware using ground-state preparation methods, such as quantum annealing, and subsequently manipulated to generate quantum samples of polymers and heteropolymers at a target temperature. Finally, we approximate the quantum sample as a tensor network, revealing an entanglement area law. For fixed-width rectangular lattices, we obtain a time-efficient and compact encoding of the full ensemble of Hamiltonian cycles, enabling the efficient evaluation of expectation values, partition functions, and configuration probabilities via tensor contractions, without resorting to sampling. Comments: 18 pages, 11 figures Subjects: Quantum Physics (quant-ph); Soft Condensed Matter (cond-mat.soft); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2603.12334 [quant-ph]   (or arXiv:2603.12334v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.12334 Focus to learn more Submission history From: Davide Rattacaso [view email] [v1] Thu, 12 Mar 2026 18:00:24 UTC (475 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.soft cond-mat.stat-mech References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)