Quantum Machine Learning Discovers Novel Many-Body Physics Through Circuit Optimisation.

The pursuit of novel quantum phenomena benefits from innovative approaches to utilising available computational resources, and a recent study proposes a method for actively discovering such phenomena via the interplay between quantum computation and classical machine learning. Researchers are now exploring how quantum computers, guided by algorithms designed to identify ‘interesting’ behaviours, can autonomously uncover previously unknown states of matter and dynamics within complex quantum systems. Benedikt Placke, G. J. Sreejith, Alessio Lerose, and S. L. Sondhi, collaborating across the Rudolf Peierls Centre for Theoretical Physics at the University of Oxford, the Indian Institute of Science Education and Research, and the Institute for Theoretical Physics at KU Leuven, detail their approach in the article, “Running Quantum Computers in Discovery Mode”.

Their work demonstrates that by defining a quantifiable measure of ‘interest’ and allowing a classical learning agent to adapt quantum circuits to maximise this measure, it is possible to effectively ‘search’ for specific quantum behaviours, such as discrete time crystals and dual-unitary circuits. A discrete time crystal is a phase of matter that exhibits periodic behaviour in time, even in its ground state, while dual-unitary circuits are a special class of quantum circuits with unique symmetry properties. The study highlights the importance of designing effective ‘interest functions’ as a key future direction for utilising quantum computing in fundamental physics research.
Recent research details a methodology integrating machine learning techniques with measurements of the Partial Spectrum Form Factor (pSFF) to characterise complex quantum dynamics. The pSFF, a measure of the correlations between energy levels within a quantum system, serves as a quantifiable signature of the system’s underlying behaviour. Researchers develop an approach utilising ‘interest functions’ – metrics applied to quantum circuits – which a classical learning agent optimises to actively identify circuits exhibiting specific, desirable characteristics.

The study establishes the pSFF as a robust indicator of quantum chaos, enabling effective differentiation between maximally chaotic systems, known as dual unitary circuits, and more general chaotic systems. Dual unitary circuits represent a specific class of quantum circuits exhibiting maximal sensitivity to initial conditions and are important for understanding the limits of quantum computation. The research demonstrates that the pSFF’s spectral properties provide a measurable means of identifying these circuits.

Furthermore, the methodology successfully identifies discrete time crystals (DTCs), a unique phase of matter exhibiting periodic behaviour without energy input. An interest function based on the classifiability of quantum states guides the learning agent towards circuits displaying the characteristics of DTCs. This demonstrates the potential of the approach to discover novel quantum phenomena beyond those predicted by conventional theoretical models.

The work bridges theoretical predictions concerning quantum chaos with verifiable experimental results. By linking the pSFF to observable quantities, the research makes the study of complex quantum systems more accessible to experimental investigation. This connection is crucial for validating theoretical models and advancing our understanding of many-body physics and quantum information science. The integration of machine learning with quantum measurements provides a new tool for exploring and characterising complex quantum dynamics, potentially leading to further discoveries in the field.