q-prior-chaos-forecasting

name	q-prior-chaos-forecasting
description	Quantum statistical prior (Q-Prior) methodology for chaotic system forecasting. Based on arXiv:2606.13422 — provable quantum advantage via two-copy Bell measurement for invariant measure estimation.
category	quantum
trigger_words	quantum statistical prior, Q-Prior, chaos forecasting, turbulent flow, weather forecasting, quantum advantage
arxiv_id	2606.13422v3

Quantum Statistical Priors for Chaotic System Forecasting

Overview

Theoretical foundations for practical quantum advantage in quantum-informed machine learning for chaotic dynamical systems. k-indexed quantum statistical priors (Q-Priors) store non-factorisable spatial correlations of invariant measures on nq = kq qubits.

Two-Stage Quantum Advantage

Stage 1: Representation

• Superposition and entanglement compactly store non-factorisable spatial correlations
• k-point marginal of invariant measure encoded on nq = kq qubits
• Extends single-site construction to multi-site k >= 2

Stage 2: Extraction

• Joint Bell measurements on two copies estimate any post hoc Pauli functional
• Copy-pair count independent of nq
• Provable quantum-classical separation: adaptive single-copy requires Omega(2^nq) copies
• Realized on IQM superconducting processors

Case Studies

Turbulent Channel Flow

• Two-copy read-out yields velocity-direction coherence
• Multi-site k=2 Q-Prior recovers DNS-level invariant-measure statistics
• Unregularised baseline loses these statistics

Weather Forecasting (ERA5)

• Diagonal k <= 2 Q-Prior steers Koopman rollout
• Improves anomaly correlation skill by 10% to 39%
• Lead times: 48 to 240 hours
• Stabilises long-horizon rollouts against collapse onto static mean field

Practical Advantage Definition

Mechanism + case studies satisfy practical-advantage definition, identifying a candidate route to practical quantum advantage before fault-tolerant hardware.

When to Use

• Chaotic system prediction (weather, fluid dynamics)
• Invariant measure estimation
• Quantum machine learning with provable advantage
• Koopman operator-based forecasting