Quantum-Inspired Approach to Analyzing Complex System Dynamics

TL;DR

This paper introduces a quantum-inspired framework for analyzing complex system dynamics using multivariate time series, enabling detailed insights into higher-order correlations, influence, and resilience without dimensionality reduction.

Contribution

It presents a novel quantum information-inspired method that encodes system states into density matrices for comprehensive analysis of complex dynamics and resilience.

Findings

Successfully applied to synthetic Lorenz-96 data

Effectively analyzed climate temperature anomalies

Quantified dissimilarity over time periods

Abstract

We present a quantum information-inspired framework for analyzing complex systems through multivariate time series. In this approach the system's state is encoded into a density matrix, providing a compact representation of higher-order correlations and dependencies. This formulation enables precise quantification of the relative influence among time series, tracking of their response to external perturbations and also the definition of a recovery timescale without need for dimensional reduction. By leveraging tools such as fidelity from quantum information theory, our method naturally captures higher-order co-fluctuations beyond pairwise statistics, offering a holistic characterization of resilience and similarity in high-dimensional dynamics. We validate this approach on synthetic data generated by a 9-dimensional modified Lorenz-96 model and demonstrate its utility on real-world climate data, analyzing global temperature anomalies across nine regions, quantifying the dissimilarity of each 288-month time window up to July 2025 relative to the 1850-1874 baseline period.