Realizing Topological States on Quantum Hardware

Quantum computers have matured to the point where multipartite entanglement can reliably be created on 30+ qubits. One important capability is the creation of long-range entangled states, both as initial states for quantum simulation and for error correction within the same devices. Unfortunately, by definition, long-range entangled states require extensive unitary circuit depths for their preparation, which places constraints on the coherence times of near-term devices. I will talk about how constant-depth protocols based on measurement and feed-forward have recently been used to prepare both Abelian and non-Abelian topological order on Quantinuum's H-series trapped-ion computers. I will also cover some recent work on qutrit topological orders as well as an application of the same techniques to improve the efficiency of digital quantum simulations of the Hubbard model.