Adaptive constant-depth circuits for manipulating non-abelian anyons

Understand

We consider Kitaev's quantum double model based on a finite group $G$ and describe quantum circuits for (a) preparation of the ground state, (b) creation of anyon pairs separated by an arbitrary distance, and (c) non-destructive topological charge measurement.

• We show that for any solvable group $G$ all above tasks can be realized by constant-depth adaptive circuits with geometrically local unitary gates and mid-circuit measurements.
• Each gate may be chosen adaptively depending on previous measurement outcomes.
• Constant-depth circuits are well suited for implementation on a noisy hardware since it may be possible to execute the entire circuit within the qubit coherence time.