Quantum Walks for Chemical Reaction Networks
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917544772763648 |
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| author | Hariharan, Seenivasan Zur, Sebastian Kinge, Sachin Visscher, Lucas Schoutens, Kareljan Jeffery, Stacey |
| author_facet | Hariharan, Seenivasan Zur, Sebastian Kinge, Sachin Visscher, Lucas Schoutens, Kareljan Jeffery, Stacey |
| contents | Near a detailed-balance equilibrium, the perturbed mass-action dynamics of a chemical reaction network (CRN) map exactly onto an electrical-flow problem on the bipartite species-reaction graph: chemical potentials become electrical potentials, Onsager coefficients become conductances, and the instantaneous Gibbs free-energy consumption equals the dissipated electrical energy. We exploit this map to design quantum walk algorithms that decide species reachability, sample reachable species, approximate any individual steady-state reaction flux, and estimate the total Gibbs dissipation. The first three follow from standard electrical-flow quantum walks; the last is non-trivial because the chemical flow is not the minimum-energy electrical flow on the same graph. We resolve this via a new use of alternative neighbourhoods in multidimensional quantum walks, which forces the walker onto the mass-action flow whenever the network is $σ-M$ rigid. In an adjacency-matrix QRAM access model the algorithms achieve up to a quadratic speedup over classical methods -- for example $Ω(n^{3/2})$ vs $Ω(n^2)$ for reachability -- and dissipation-aware bounds tighten this further when the perturbation is concentrated. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_07890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Walks for Chemical Reaction Networks Hariharan, Seenivasan Zur, Sebastian Kinge, Sachin Visscher, Lucas Schoutens, Kareljan Jeffery, Stacey Quantum Physics Chemical Physics Near a detailed-balance equilibrium, the perturbed mass-action dynamics of a chemical reaction network (CRN) map exactly onto an electrical-flow problem on the bipartite species-reaction graph: chemical potentials become electrical potentials, Onsager coefficients become conductances, and the instantaneous Gibbs free-energy consumption equals the dissipated electrical energy. We exploit this map to design quantum walk algorithms that decide species reachability, sample reachable species, approximate any individual steady-state reaction flux, and estimate the total Gibbs dissipation. The first three follow from standard electrical-flow quantum walks; the last is non-trivial because the chemical flow is not the minimum-energy electrical flow on the same graph. We resolve this via a new use of alternative neighbourhoods in multidimensional quantum walks, which forces the walker onto the mass-action flow whenever the network is $σ-M$ rigid. In an adjacency-matrix QRAM access model the algorithms achieve up to a quadratic speedup over classical methods -- for example $Ω(n^{3/2})$ vs $Ω(n^2)$ for reachability -- and dissipation-aware bounds tighten this further when the perturbation is concentrated. |
| title | Quantum Walks for Chemical Reaction Networks |
| topic | Quantum Physics Chemical Physics |
| url | https://arxiv.org/abs/2509.07890 |