Quantum computation by measurements

TL;DR

This paper explores measurement-based quantum computation, demonstrating the universality of certain multi-qubit measurements and simplifying previous constructions for implementing quantum gates.

Contribution

It introduces simplified schemes for universal quantum computation using 2-qubit and 4-qubit measurements, improving upon earlier complex methods.

Findings

Universality of 4-qubit measurements rederived with simpler schemes

Proved universality of simple 2-qubit measurement sets

Showed single 4-qubit measurement can achieve universal computation

Abstract

We first consider various methods for the indirect implementation of unitary gates. We apply these methods to rederive the universality of 4-qubit measurements based on a scheme much simpler than Nielsen's original construction [quant-ph/0108020]. Then, we prove the universality of simple discrete sets of 2-qubit measurements, again using a scheme simplifying the initial construction [quant-ph/0111122]. Finally, we show how to use a single 4-qubit measurement to achieve universal quantum computation, and outline a proof for the universality of almost all maximally entangling 4-qubit measurements.