On Universal and Fault-Tolerant Quantum Computing

TL;DR

This paper introduces a simple, universal, and fault-tolerant quantum gate set suitable for noisy environments, combining minimal single- and two-qubit gates to achieve universality.

Contribution

It proposes a new minimal universal and fault-tolerant quantum gate basis using only three gates, simplifying quantum computation in noisy settings.

Findings

The new basis includes Hadamard, ${\sigma_z}^{1/4}$, and CNOT gates.

It is potentially the simplest universal basis for fault-tolerant quantum computing.

An alternative proof of universality for existing bases is provided.

Abstract

A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates (Hadamard and ${\sigma_z}^{1/4}$), and one double-qubit gate (Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of $\pi$) single-qubit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and fault-tolerant basis proposed by Shor and by Kitaev.