Solving messy real-world equations on quantum computers without the usual workaround

Quantum computers naturally run unitary (reversible) operations, but equations describing open systems — like a molecule losing energy to its surroundings — are nonunitary and messy. Previous approaches required pre-computing the awkward propagator on a classical machine at every step. This algorithm handles everything on the quantum hardware by decomposing the propagator via singular value decomposition and simulating the pieces directly, demonstrated on a charge-transfer model in a solvated molecule.