# A fault-tolerant non-Clifford gate for the surface code in two dimensions

## TL;DR

This paper presents a fault-tolerant non-Clifford gate for the 2D surface code that reduces resource overhead by eliminating the need for magic-state distillation, using local operations and code deformations.

## Contribution

It introduces a novel fault-tolerant non-Clifford gate for the surface code utilizing local gates, code deformations, and a just-in-time decoder, avoiding higher-dimensional components.

## Key findings

- Gate uses only local transversal gates and code deformations.
- Decoding algorithms enable 3D advantages with 2D qubit arrays.
- Parity checks are of weight no greater than four.

## Abstract

Fault-tolerant logic gates will consume a large proportion of the resources of a two-dimensional quantum computing architecture. Here we show how to perform a fault-tolerant non-Clifford gate with the surface code; a quantum error-correcting code now under intensive development. This alleviates the need for distillation or higher-dimensional components to complete a universal gate set. The operation uses both local transversal gates and code deformations over a time that scales with the size of the qubit array. An important component of the gate is a just-in-time decoder. These decoding algorithms allow us to draw upon the advantages of three-dimensional models using only a two-dimensional array of live qubits. Our gate is completed using parity checks of weight no greater than four. We therefore expect it to be amenable with near-future technology. As the gate circumvents the need for magic-state distillation, it may reduce the resource overhead of surface-code quantum computation considerably.