One-way Quantum Computation - a tutorial introduction

TL;DR

This tutorial introduces one-way quantum computation, covering theoretical techniques, implementation proposals, and recent advances, including new methods for simplifying and constructing measurement patterns.

Contribution

It presents new methods and observations, such as a compact stabilizer formalism, novel implementation techniques, and strategies for constructing efficient measurement patterns.

Findings

A simplified stabilizer formalism for one-way quantum computation

New methods for implementing diagonal unitaries

Strategies for decomposing unitaries into measurement patterns

Abstract

In this book chapter, we provide a tutorial introduction to one-way quantum computation and many of the techniques one can use to understand it. The techniques which are described include the stabilizer formalism and the logical Heisenberg picture. We highlight ways in which it is useful to understand one-way computation beyond simple equivalence with the quantum circuit model. We briefly review current proposals of implementations and experimental progress and summarize some recent related theoretical developments. Although the chapter is primarily didactic in focus, we include a number of new methods and observations. These include: a simpler and more compact formulation of one-way quantum computation in the stabilizer formalism; A new way of implementing unitaries diagonal in the computational basis; New results on the family of operations which may be implemented in a single round of measurements; A method for constructing compact one-way patterns by decomposing unitaries in terms of diagonal unitaries and Clifford group transformations.