Quantum Simulation Reveals How Disorder Drives System Thermalisation

Faisal Alam and colleagues at Phasecraft Ltd, in a collaboration between Phasecraft Ltd, Phasecraft Inc and Virginia Tech, observed the onset of ergodicity, the property of a system exploring all accessible states, using a two-dimensional disordered Heisenberg Floquet model simulated on IBM’s Nighthawk superconducting processor. The study probes ergodicity across multiple length scales using a new measure based on collision entropy, accessing system sizes previously intractable for classical computation. By analysing how ergodic behaviour emerges at different scales, the team reveal a hierarchical transition from subergodic to ergodic behaviour as Heisenberg coupling increases, and provide a new pathway for using digital quantum processors to study thermalisation phenomena. Emergent ergodicity and spatial hierarchy in a large-scale quantum system This breakthrough utilised IBM’s Nighthawk superconducting processor, a device employing transmon qubits fabricated using superconducting materials, enabling the probing of ergodicity, a system’s tendency to explore all accessible states, across multiple length scales. The Heisenberg model, a cornerstone of quantum magnetism, was chosen to represent interacting spins, and the ‘Floquet’ aspect introduces time-periodic driving, adding complexity and potentially enhancing ergodicity. A novel measure based on ‘collision entropy’ quantified the emergence of ergodic behaviour within spatial patches of the system, revealing a hierarchy where smaller regions become ergodic before larger ones. The concept of ergodicity is crucial in statistical mechanics, as it underpins the equivalence between time averages and ensemble averages, essential for predicting macroscopic properties from microscopic dynamics. Disordered systems, where imperfections or randomness are present, pose a particular challenge to establishing ergodicity, as localisation effects can hinder the exploration of the entire state space. The 10 × 10 qubit system represents a significant step forward, allowing researchers to investigate these effects in a regime inaccessible to many classical algorithms. The collision entropy, a measure of how much information is lost when tracing out degrees of freedom within a patch, effectively gauges the degree of entanglement and mixing within that region. Higher collision entropy indicates greater ergodicity. The simulations extended to analyse spatial patches up to size 3 × 3 within the 10 × 10 qubit system, providing further insight into ergodicity at varying scales. Excellent agreement was found between the quantum simulation and classical tensor-network methods for smaller patches and lower values of J, validating the approach. This validation is important because tensor networks, while limited in scalability, provide a well-established benchmark for quantum simulations in certain regimes. Current simulations do not yet address the challenges of volume-law entanglement, which will be important for modelling larger, more complex systems relevant to materials science, and future work will focus on extending the system size and exploring the limits of this methodology. The observed smooth transition from subergodic to ergodic behaviour as the Heisenberg coupling increased is particularly noteworthy. Subergodicity implies that the system explores only a subset of its accessible states, while full ergodicity signifies complete exploration. The Heisenberg coupling, denoted by ‘J’, dictates the strength of the interaction between neighbouring spins; increasing J promotes entanglement and facilitates the spread of information throughout the system. The fact that the quantum simulation accurately matches classical results in regimes where both methods are reliable strengthens confidence in the quantum approach and provides a valuable cross-validation. The ability to probe the system at multiple length scales, from single qubits to 3 × 3 patches, allows for a detailed understanding of how ergodicity emerges and propagates throughout the system. This hierarchical behaviour, where smaller regions become ergodic before larger ones, suggests a cascading process of thermalisation, starting locally and gradually extending to the entire system. Superconducting qubits validate ergodicity in complex quantum systems Thermalization, the process by which an isolated quantum system reaches equilibrium, is fundamental to understanding materials and fundamental physics; however, accurately modelling this behaviour remains computationally challenging. Traditional modelling techniques, such as tensor networks and Monte Carlo simulations, face escalating computational demands as system size increases; their memory requirements quickly become prohibitive, scaling exponentially with the number of qubits. This approach circumvents those limitations by using the unique strengths of quantum hardware, allowing exploration of larger systems and longer timescales. Superconducting qubits, due to their inherent quantum nature, can directly represent and manipulate quantum states, offering a natural platform for simulating quantum systems. The Nighthawk processor, with its advanced control and connectivity, is particularly well-suited for this task. Ergodicity was probed across different scales, revealing a hierarchy in how quickly patches become ergodic. Achieving this with a 10 × 10 qubit system surpasses the scale of some traditional computational methods, particularly when modelling complex quantum connectedness. The quantum connectedness refers to the degree of entanglement and correlations between different parts of the system. Classical simulations often struggle to capture these correlations accurately, especially in strongly interacting systems. The approach revealed a clear hierarchy; smaller regions exhibited chaotic behaviour before larger ones, indicating a gradual transition, and this observation provides a foundation for understanding the emergence of thermalisation in larger, more realistic systems. The observation of a hierarchical transition is significant because it suggests that thermalisation does not occur instantaneously but rather proceeds through a series of stages, starting with the formation of local chaotic regions and eventually spreading throughout the entire system. The implications of this work extend beyond fundamental physics. Understanding thermalisation is crucial for designing new materials with specific properties, such as high-temperature superconductors or efficient energy storage devices. The ability to simulate complex quantum systems on quantum hardware opens up new possibilities for materials discovery and optimisation. Furthermore, this methodology could be applied to study other many-body systems, such as those found in condensed matter physics, nuclear physics, and even cosmology. The development of robust and scalable quantum simulations represents a significant step towards harnessing the power of quantum computers for solving real-world problems. 👉 More information 🗞 Onset of Ergodicity Across Scales on a Digital Quantum Processor 🧠 ArXiv: https://arxiv.org/abs/2603.12236 Tags: