AI finds exotic particles in complex quantum Hall systems
Non-Abelian quantum Hall states at strong Landau level mixing: finding anyons with first-principles AI
Artificial Intelligence
Summary
Certain strange particles called non-Abelian anyons could help build super-reliable quantum computers, but identifying them in experiments is tough because the systems involved are very complex. The authors used AI, specifically a neural network, to study all the electrons and energy levels in a quantum Hall system without any assumptions. Their AI discovered patterns indicating the presence of these special particles with a specific mathematical property, confirming one leading candidate theory about their nature. This shows AI can solve difficult physics problems and help find new quantum materials.
What this means in practice
- •For quantum hardware engineers: Design quantum devices by identifying stable non-Abelian anyons under realistic conditions including Landau level mixing.
- •For computational physicists: Use neural-network wave functions to model strongly interacting electron systems without simplifying assumptions about energy levels.
Authors
Pierre-Antoine Graham, Ahmed Abouelkomsan, Liang Fu
Abstract
Non-Abelian anyons, strange particles forming the basis of fault-tolerant topological quantum computing, are predicted to emerge in fractional quantum Hall states at even-denominator filling factors. Identifying which topological order is realized has proven to be a challenging problem that requires an accurate, non-perturbative treatment of realistic Landau level mixing, which has so far been missing from theoretical studies. Here we present the first complete solution of non-Abelian quantum Hall problem that includes all electrons and all Landau levels, for spin-polarized electrons at filling factor $ν= 3/2$. We develop a momentum-resolved neural-network variational wave function, optimized solely on the microscopic Hamiltonian, which gives direct access to the topologically degenerate ground states. Without any physics input about the expected outcome, it discovers a degenerate ground-state manifold whose entanglement reveals anyons with quantum dimension $\sqrt{2}$, the hallmark of Ising-type non-Abelian order. By directly computing the overlap with trial wave functions, we further show that Landau level mixing favors the anti-Pfaffian over other candidate states. Our results demonstrate the power of neural-network wave functions in finding and characterizing non-Abelian anyons from first principles, in regimes of strong Landau level mixing, relevant to many recent experiments.