Error Channels and the Threshold for Fault-tolerant Quantum Computation

TL;DR

This dissertation explores error models, threshold calculations, and ancilla construction methods for fault-tolerant quantum computing, providing new estimation techniques and addressing implementation challenges.

Contribution

It introduces a simple, flexible threshold estimation method and proposes a novel ancilla construction approach for quantum error correction.

Findings

Bounds on quantum error thresholds derived from stochastic Pauli channels

A new, adaptable method for estimating fault-tolerance thresholds

Discussion of implementation challenges for advanced ancilla construction

Abstract

This dissertation treats the topics of threshold calculation, ancilla construction, and non-standard error models. Chapter 2 introduces background material ranging from quantum mechanics to classical coding to thresholds for quantum computation. In Chapter 3 numerical and analytical means are used to generate estimates of and bounds on the threshold given an error model described by a restricted stochastic Pauli channel. Chapter 4 develops a simple, flexible means of estimating the threshold and applies it to some cases of interest. Finally, a novel method of ancilla construction is proposed in Chapter 5, and the difficulties associated with implementing it are discussed.