Quantum Solvers for Nonlinear Matrix Equations in Quantum Chemistry
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913132952158208 |
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| author | Rodenas-Ruiz, Pablo Zhao, Andrew Lee, Joonho |
| author_facet | Rodenas-Ruiz, Pablo Zhao, Andrew Lee, Joonho |
| contents | We present a quantum algorithm for solving algebraic Riccati equations, with applications to quantum-chemical random-phase approximation (RPA) and higher-order RPA theories. Our method block-encodes stabilizing Riccati solutions via Riesz projectors onto invariant subspaces of an associated non-normal matrix, implemented using contour-integral resolvents and quantum singular value transformations. Applied to $m$-particle, $m$-hole RPA, our algorithm yields a block-encoding of the amplitude solution and estimates the electronic correlation-energy density with it. Under localized-orbital sparsity assumptions, the end-to-end cost scales linearly with system size and polynomially with excitation rank $m$, suggesting an exponential advantage in $m$ over plausible classical local-correlation heuristics. More broadly, this work provides a framework for quantum algorithms for nonlinear matrix equations in quantum chemistry and opens a possible route toward developing quantum algorithms for coupled-cluster theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_16189 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Solvers for Nonlinear Matrix Equations in Quantum Chemistry Rodenas-Ruiz, Pablo Zhao, Andrew Lee, Joonho Quantum Physics Chemical Physics We present a quantum algorithm for solving algebraic Riccati equations, with applications to quantum-chemical random-phase approximation (RPA) and higher-order RPA theories. Our method block-encodes stabilizing Riccati solutions via Riesz projectors onto invariant subspaces of an associated non-normal matrix, implemented using contour-integral resolvents and quantum singular value transformations. Applied to $m$-particle, $m$-hole RPA, our algorithm yields a block-encoding of the amplitude solution and estimates the electronic correlation-energy density with it. Under localized-orbital sparsity assumptions, the end-to-end cost scales linearly with system size and polynomially with excitation rank $m$, suggesting an exponential advantage in $m$ over plausible classical local-correlation heuristics. More broadly, this work provides a framework for quantum algorithms for nonlinear matrix equations in quantum chemistry and opens a possible route toward developing quantum algorithms for coupled-cluster theory. |
| title | Quantum Solvers for Nonlinear Matrix Equations in Quantum Chemistry |
| topic | Quantum Physics Chemical Physics |
| url | https://arxiv.org/abs/2605.16189 |