Efficient One-way Quantum Computations for Quantum Error Correction

TL;DR

This paper presents a method to construct efficient, scalable quantum circuits for encoding stabilizer codes using one-way quantum computation and cluster states, enhancing quantum algorithm design.

Contribution

It introduces a novel construction of constant-depth quantum circuits for stabilizer code encoding based on graphic descriptions and the one-way quantum computation model.

Findings

Constructed $O(nd)$ size, constant-depth circuits for stabilizer code encoding.

Demonstrated use of cluster states as scalable resources.

Improved design strategies for quantum algorithms using one-way quantum computation.

Abstract

We show how to explicitly construct an $O(nd)$ size and constant quantum depth circuit which encodes any given $n$-qubit stabilizer code with $d$ generators. Our construction is derived using the graphic description for stabilizer codes and the one-way quantum computation model. Our result demonstrates how to use cluster states as scalable resources for many multi-qubit entangled states and how to use the one-way quantum computation model to improve design of quantum algorithms.