Universality of single quantum gates

TL;DR

This paper proves that almost all 2-qubit gates, when used with simple swap operations, are sufficient to achieve universal quantum computation, highlighting the robustness of quantum universality.

Contribution

It provides a rigorous proof that an open dense set of 2-qubit gates ensures universal quantum computation with minimal gate sets.

Findings

Almost all 2-qubit gates are universal when combined with swaps.

The set of such gates is open and dense in the space of all 2-qubit gates.

Universal quantum computation can be achieved with a restricted gate set.

Abstract

We supply a rigorous proof that an open dense set of all possible 2-qubit gates G has the property that if the quantum circuit model is restricted to only permit swap of qubits lines and the application of G to pairs of lines, then the model is still computationally universal.