Long-range Entanglement and Topological States in Quantum Devices: from Hamilton to Galois

Abstract: One of the most remarkable discoveries in quantum physics is that long-range entangled qubits can give rise to emergent gauge fields and collective excitations exhibiting generalized ('anyonic') exchange statistics. Despite the importance of such 'topological' states for quantum information processing, they are extremely challenging to find in materials. In this talk, we explore how novel 'bottom-up' quantum devices---built atom by atom, qubit by qubit---challenge this status quo. For instance, topological states can emerge as the low-energy description of a many-body Hamiltonian, with experimental data on Rydberg atom tweezer arrays. Alternatively, such long-range entanglement can be obtained from shallow circuits with measurements and feedforward, with experimental data on cold ions. Only the latter route is able to avoid fundamental constraints imposed by locality and unitarity, leading to a surprising connection to the unsolvability of the quintic.