Compact quantum circuits from one-way quantum computation

TL;DR

This paper presents a method to convert one-way quantum computations into more compact quantum circuits by introducing circuit identities that reduce qubit count, facilitating easier implementation and analysis.

Contribution

It introduces a straightforward circuit representation for 1WQC and four circuit identities to minimize qubit usage, advancing the translation between models.

Findings

Circuit representation of 1WQC with ancilla wires

Four identities reduce qubit count in equivalent circuits

Examples demonstrate circuit simplification

Abstract

In this paper we address the problem of translating one-way quantum computation (1WQC) into the circuit model. We start by giving a straightforward circuit representation of any 1WQC, at the cost of introducing many ancilla wires. We then propose a set of four simple circuit identities that explore the relationship between the entanglement resource and correction structure of a 1WQC, allowing one to obtain equivalent circuits acting on fewer qubits. We conclude with some examples and a discussion of open problems.