Extra QLunch: Julio Magdalena

Speaker: Julio Magdalena, FU Berlin

Title: Fault tolerance in topological non-Clifford circuits and protocols for reliable universal quantum computation in 2D

Abstract: Quantum error correction (QEC) is essential to realize a scalable quantum computer. Two-dimensional topological codes are amongst the most promising candidates for practically-relevant QEC codes due to their geometrically local structure, high thresholds and rich set of logic gates constructed from the underlying anyon theory.

However, 2D Pauli stabilizer codes suffer the fundamental limitation that they can only implement logic Clifford gates fault-tolerantly and have to be supplemented with some magic resource. While many schemes have been explored to circumvent this obstruction, they are not native to the 2D structure and require significant resource overheads.

In my talk I want to present a new scheme to realize non-Clifford logic gates on 2D topological codes only using 2D connectivity.

It is based code-switching between topological Pauli codes and topological codes stabilized by a non-Abelian group of Clifford operators.

I will present the derivation of protocols to implement various logic gates in the third level of the Clifford hierarchy based on an interpretation in terms of the topological phases realized by the respective codes and topological domain walls between them.

Fault tolerance is achieved using a just-in-time decoding strategy and we prove a fault-tolerance threshold. If time allows, I will explain the workings of such a decoder and comment on practical considerations and further research directions.