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Efficient quantum algorithm for linear matrix differential equations and applications to open quantum systems

Sophia Simon, Dominic W. Berry, Rolando D. Somma · arXiv:2605.16195 · submitted 15 May 2026 · Quantum Physics

Abstract. We present an efficient, nearly optimal quantum algorithm for solving linear matrix differential equations, with applications to the simulation of open quantum systems and beyond. For unitary or dissipative dynamics, the algorithm computes an entry of the solution matrix with query complexity that scales nearly optimally with the relevant problem parameters, evolution time, and target error. The work contrasts earlier quantum approaches for differential equations, which can require exponential time because the solution is encoded in a quantum state with very small amplitudes. The authors demonstrate the method through the simulation of dissipative dynamics for non-interacting fermions, compare it with classical algorithms, and give evidence for polynomial quantum speedups in lattice systems.

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External source: arXiv quant-ph. This is a preprint and is not necessarily peer reviewed.