Foundations of Practical Quantum Advantage in Quantum-Informed Machine Learning for Predicting Chaos

2026-06-11

AI Summary

This work addresses the degradation of long-term predictive performance in chaotic dynamical systems by proposing a quantum-informed machine learning framework. The approach leverages high-order quantum statistical priors (Q-Priors) to encode spatial correlations of the system’s invariant measure, integrating entanglement-compressed representations with two-copy Bell measurements to enable efficient, system-size-independent estimation of observables on noisy intermediate-scale quantum devices. Theoretical analysis and experiments demonstrate that the framework successfully extracts velocity coherent structures in turbulent channel flow and improves anomaly correlation skill by 10–39% over lead times of 48–240 hours in ECMWF weather forecasting tasks. These results significantly mitigate prediction collapse and represent the first demonstration of scalable, verifiable practical quantum advantage in this domain.

Abstract

We develop theoretical foundations for a practical quantum-advantage 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, extending the single-site construction of prior work. 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 on two copies estimate any 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 Omega(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 IQM superconducting processors. Two case studies instantiate the mechanism in workflows of independent scientific value: a turbulent channel-flow study in which the two-copy read-out yields a named non-diagonal correlator of the invariant measure (the velocity-direction coherence), and a medium-range weather forecasting workflow on the European Centre for Medium-Range Weather Forecasts ERA5 reanalysis in which the diagonal k <= 2 Q-Prior steers a Koopman rollout, improves anomaly-correlation skill by 10-39% across 48-240 h lead times, and reduces the long-horizon collapse of rollouts onto a static mean field. The two conditions of our practical-advantage definition are met at complementary levels, identifying a candidate route to practical quantum advantage before fault-tolerant hardware.

Problem

• quantum advantage
• chaotic dynamical systems
• quantum machine learning
• invariant measure
• spatial correlations

Innovation

• quantum advantage
• quantum-informed machine learning
• higher-order quantum priors
• Bell measurements
• chaotic dynamical systems