Topological Order for Hubbard model simulation and fault-tolerance with trapped-ion quantum computers (45' + 15')

• Henrik Dreyer (Quantinuum)

**Abstract**: I will discuss two use cases of topologically ordered states: (i) When all components of a quantum circuit are local, we generically expect the Dilution of Error effect, which says that individual errors only affect intensive observables by O(1/system size). In order to simulate fermionic lattice systems with local components, (Abelian) topological order needs to be prepared quickly and with high fidelity. (ii) all known universal error correction codes in two spatial dimensions require non-Abelian topological order and those codes may come with lower overheads than Magic State Distillation protocols. I will discuss three experiments on Quantinuum ion trap quantum computers to show the current limits of the hardware (for topological states preparation and otherwise). **Short bio**: Henrik Dreyer is a theoretical physicist interested in quantum computation, tensor networks, and their application to condensed matter systems. Currently, he is working as a Scientific Lead in the Condensed Matter group at Quantinuum. Before that, he was a post-doc in the Rudolf Peierls Centre for Theoretical Physics at Oxford University and obtained his PhD at the Max-Planck Institute of Quantum Optics.