A 2 rebit gate universal for quantum computing

TL;DR

This paper demonstrates that a specific 2-rebit gate can perform universal quantum computation within the circuit model using only real amplitudes, highlighting a new approach to quantum universality.

Contribution

It introduces a 2-rebit gate that is universal for quantum computing with real amplitudes, expanding understanding of quantum gate universality.

Findings

Any quantum computation can be performed with real amplitude states.

A specific 2-rebit gate is universal for quantum computing.

The gate cannot perform arbitrary unitary transformations.

Abstract

We show, within the circuit model, how any quantum computation can be efficiently performed using states with only real amplitudes (a result known within the Quantum Turing Machine model). This allows us to identify a 2-qubit (in fact 2-rebit) gate which is universal for quantum computing, although it cannot be used to perform arbitrary unitary transformations.