Quantum-inspired Method Enables Tracking of Complex System Resilience and Response
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Understanding the intricate behaviour of complex systems, from climate patterns to financial markets, presents a significant scientific challenge. Parsa Kafashi and Mozhgan Orujlu, both from Sharif University of Technology, now present a novel framework inspired by the principles of quantum mechanics to analyse these dynamic systems. Their method encodes the system’s state into a density matrix, allowing researchers to quantify the influence between different time series and track responses to external changes without simplifying the data. This approach captures complex relationships beyond simple pairwise comparisons, offering a more complete understanding of resilience and similarity in high-dimensional dynamics, and the team validates its effectiveness using both simulated and real-world climate data, analysing global temperature anomalies over extended periods.
Quantum Resilience Analysis of Multivariate Time Series This work introduces a new framework for analysing complex systems using multiple time series, employing a quantum-inspired approach to characterise system behaviour and resilience. Researchers encoded the state of a system into a density matrix, providing a compact representation of complex relationships without requiring data simplification. This method precisely quantifies the relative influence among time series and tracks their response to external perturbations, defining a recovery timescale without reducing the complexity of the data. Experiments utilized a 9-dimensional modified Lorenz-96 model to validate the approach on synthetic data, and then applied it to real-world climate data. Scientists analysed global temperature anomalies across nine regions, quantifying the dissimilarity of each 288-month time window relative to a baseline period of 1850-1874 up to July 2025. The core of the method involves assigning binary labels to each component of a multi-dimensional state variable, indicating whether it is increasing or not, creating a compact encoding with multiple possible configurations. This simplification ensures comparability across variables of different scales and physical meanings, mapping similar qualitative changes to the same binary value. By embedding this representation into a mathematical space analogous to quantum mechanics, scientists constructed a density matrix, a mathematical object that represents the probabilities of each configuration in a unified form.
The team employed fidelity, a measure ranging from 0 to 1, to quantify the similarity between density matrices corresponding to consecutive observation windows, capturing the temporal similarity of state distributions in the time series.
Results demonstrate that this approach intrinsically captures complex co-fluctuations and joint dependencies among all variables, offering a richer characterization of temporal dynamics than conventional methods. Specifically, the fidelity measure provides a single number that captures the collective similarity between multi-dimensional segments. This framework allows for the definition of a recovery timescale, crucial for understanding how quickly a system returns to equilibrium after a disturbance.
Density Matrix Reveals System Resilience and Similarity This research presents a novel framework for analysing complex systems using multiple time series. By representing a system’s state as a density matrix, the team developed a method to quantify the influence of individual time series and track responses to external changes, all without requiring data simplification. This approach leverages concepts from quantum information theory, specifically fidelity, to capture complex co-fluctuations beyond simple pairwise statistics, offering a more holistic understanding of resilience and similarity in complex dynamics.
The team validated this method using both synthetic data generated from a modified Lorenz-96 model and real-world climate data, analysing global temperature anomalies across nine regions relative to a historical baseline.
Results demonstrate the ability to quantify dissimilarity in time series, providing a new tool for assessing the behaviour of complex systems. 👉 More information 🗞 Quantum-Inspired Approach to Analyzing Complex System Dynamics 🧠 ArXiv: https://arxiv.org/abs/2512.14169 Tags: Rohail T. As a quantum scientist exploring the frontiers of physics and technology. My work focuses on uncovering how quantum mechanics, computing, and emerging technologies are transforming our understanding of reality. I share research-driven insights that make complex ideas in quantum science clear, engaging, and relevant to the modern world. Latest Posts by Rohail T.: Acoustic Horizons in Polariton Fluids Enable Programmable Spacetime Simulation December 18, 2025 Explainable Quantum AI Advances Encoder Selection Via Novel Visualization Tools December 18, 2025 Shadow Formulation of In-in Correlators Enables New Insights into Four Dimensional De Sitter Space December 18, 2025