Pablo Rodenas-Ruiz, Andrew Zhao, Joonho Lee (May 18 2026).
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.
