Practical Quantum Advantage before Fault Tolerance via Quantum-Informed Machine Learning

Abstract

Early quantum devices can deliver a practical advantage before fault tolerance. The role we identify is a statistical module within a classical scientific workflow: a compressed memory with a collective two-copy readout, evaluated against a verifiable definition of practical quantum advantage. We develop this mechanism in quantum-informed machine learning for chaotic dynamical systems. A family of $k$-indexed higher-order quantum statistical priors (Q-Priors) hosts the $k$-point marginal of the invariant measure on $n_q=kq$ qubits. We prove a two-stage advantage. In the representation stage, superposition and entanglement compactly store non-factorisable spatial correlations of the invariant measure on $n_q$ qubits. In the extraction stage, joint Bell measurements estimate any \emph{post hoc} Pauli functional with a copy-pair count independent of $n_q$, whereas any adaptive single-copy protocol for the corresponding full-Pauli read-out requires $\hat{I}\text{c◯}(2^{n_q})$ copies; this is a provable quantum-classical separation in copy-measurement complexity. The two-copy read-out is realised in simulation and on superconducting processors. Two case studies instantiate the mechanism in workflows of scientific value. In a turbulent channel-flow study, the readout yields the velocity-direction coherence as a named non-diagonal correlator, and the $k=2$ Q-Prior recovers invariant-measure statistics that the unregularised baseline loses. In a medium-range weather forecasting workflow on the ECMWF ERA5 reanalysis, the diagonal $k\le 2$ Q-Prior steers a Koopman rollout, improves anomaly correlation skill and stabilises long-horizon rollouts against collapse onto a static mean field. Together, the mechanism and these two case studies satisfy our practical-advantage definition, identifying a candidate route to practical quantum advantage before fault-tolerant hardware.