Universal Logical Gates on Topologically Encoded Qubits via Constant-Depth Unitary Circuits

Understand

A fundamental question in the theory of quantum computation is to understand the ultimate space-time resource costs for performing a universal set of logical quantum gates to arbitrary precision.

• Here we demonstrate that non-Abelian anyons in Turaev-Viro quantum error correcting codes can be moved over a distance of order the code distance, and thus braided, by a constant depth local unitary quantum circuit followed by a permutation of qubits.
• Our gates are protected in the sense that the length of error strings do not grow by more than a constant factor.
• When applied to the Fibonacci code, our results demonstrate that a universal logical gate set can be implemented on encoded qubits through a constant depth unitary quantum circuit, and without increasing the asymptotic scaling of the space overhead.