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arXiv · 2605.16189

Quantum Solvers for Nonlinear Matrix Equations in Quantum Chemistry

Pablo Rodenas-Ruiz·Andrew Zhao·Joonho Lee
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Abstract

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.

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Pablo Rodenas-Ruiz, Andrew Zhao, Joonho Lee. 2026-05-15. Quantum Solvers for Nonlinear Matrix Equations in Quantum Chemistry. https://arxiv.org/abs/2605.16189

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