Universal fault-tolerant quantum computation with only transversal gates and error correction

TL;DR

This paper demonstrates that universal fault-tolerant quantum computation can be achieved using only transversal gates and error correction, eliminating the need for complex state distillation procedures.

Contribution

It introduces a method to implement a universal set of fault-tolerant gates solely with transversal gates and error correction, improving Toffoli gate distillation.

Findings

Transversal controlled-controlled-Z gate implementation in triorthogonal codes

Universal fault-tolerant gate set without state distillation

Enhanced Toffoli gate distillation scheme

Abstract

Transversal implementations of encoded unitary gates are highly desirable for fault-tolerant quantum computation. Though transversal gates alone cannot be computationally universal, they can be combined with specially distilled resource states in order to achieve universality. We show that "triorthogonal" stabilizer codes, introduced for state distillation by Bravyi and Haah [Phys. Rev. A 86 052329 (2012)], admit transversal implementation of the controlled-controlled-Z gate. We then construct a universal set of fault-tolerant gates without state distillation by using only transversal controlled-controlled-Z, transversal Hadamard, and fault-tolerant error correction. We also adapt the distillation procedure of Bravyi and Haah to Toffoli gates, improving on existing Toffoli distillation schemes.