Constructing Functional Braids for Low-Leakage Topological Quantum Computing

Understand

We discuss how to significantly reduce leakage errors in topological quantum computation by introducing an irrelevant error in phase, using the construction of a CNOT gate in the Fibonacci anyon model as a concrete example.

• To be specific, we construct a functional braid in a six-anyon Hilbert space that exchanges two neighboring anyons while conserving the encoded quantum information.
• The leakage error is $\sim$$10^{-10}$ for a braid of $\sim$100 interchanges of anyons.
• Applying the braid greatly reduces the leakage error in the construction of generic controlled-rotation gates.