The quantum world is tricky: sometimes particles confined to a flat layer and pierced by a strong magnetic field start behaving like a liquid made not of whole electrons but of their fractions — fractional charges. This is the fractional quantum Hall effect. The most intriguing part is that such a liquid can give birth to quasiparticles with a 'memory'—their quantum state changes when they are exchanged, as if they were braided into invisible plaits. These objects are called non-Abelian anyons (quasiparticles whose state depends on the order of exchange), and they are candidates for qubits in ultra-protected quantum computers.
The problem is that stabilizing such a phase in an experiment is like holding a complex knot made of slippery threads. Usually, this requires a three-body interaction of electrons, which is almost nonexistent in real materials. The authors of the work came up with a different path: they tasked a computer with tuning the two-body forces between electrons — the so-called Haldane pseudopotentials (parameters describing repulsion at different distances)—so that the resulting many-body state matches the desired one, known as the Moore–Read state, as closely as possible. To do this, they used an inverse design method: gradient optimization directly inside the exact diagonalization procedure — a calculation of all possible quantum states of a small system. The calculations were performed on a sphere to avoid edge effects, and the code was written in the JAX library, which can quickly compute derivatives and is convenient for optimization tasks.
The result was surprising: it turned out that a properly chosen two-body interaction gives an overlap with the Moore–Read state of more than 99% for systems up to 12 electrons. This is much better than the standard Coulomb repulsion. Moreover, the found pseudopotential profile turned out to be almost universal: it decays exponentially with distance and, apparently, effectively encodes the key features of the three-body interaction. The neutral excitation spectrum and the orbital entanglement spectrum confirmed that the system is indeed in the Pfaffian phase — one of the most coveted for quantum computing. Thus, computer-aided design of interactions opens the way to engineering non-Abelian order in quantum simulators.
The Moore–Read state is named after two physicists who described it in 1991. It is closely related to the mathematics of knots and braids — literally: its wave function contains a Pfaffian, a construct from braid theory.
The idea of quantum computers based on anyons, topological quantum computers, is actively discussed in science fiction, for example, in the novel 'The Quantum Thief' by Hannu Rajaniemi.