Quantum Matter Seminar- Nathanan Tantivasadakarn (California Institute of Technology)- From Wave-Function Collapse and Galois Solvability to the Realization of Non-Abelian Topological Order on a Quantum Device

Abstract: I will review our recent set of theoretical works on efficiently preparing long range quantum entanglement with adaptive quantum circuits: the combination of measurements with unitary gates whose choice can depend on previous measurement outcomes. I will show that this additional ingredient can be leveraged to prepare the long sought-after non-Abelian topological phases with a circuit depth that is independent of system size. Using this framework, we uncover a complexity hierarchy of long-range entangled states based on the minimal number of measurement layers required to create the state. Moreover, we find that certain non-Abelian states that cannot be efficiently prepared with adaptive circuits have a surprising connection to the unsolvability of the quintic polynomial.

Finally, I will describe our recent collaboration with Quantinuum where we present the first unambiguous realization of non-Abelian D4 topological order and demonstrate control of its anyons. In particular, we are able to detect a non-trivial braiding where three non-Abelian anyons trace out the Borromean rings in spacetime, a signature unique to non-Abelian topological order.