Roads towards fault-tolerant universal quantum computation

TL;DR

This paper reviews various approaches to achieving fault-tolerant quantum computation, comparing their resource requirements and potential, with a focus on error correction techniques and high-dimensional codes.

Contribution

It provides a comprehensive comparison of leading fault-tolerance methods, highlighting their advantages, limitations, and future prospects in scalable quantum computing.

Findings

Color code techniques offer promising error correction capabilities.

High-dimensional LDPC codes could enable more efficient fault-tolerant architectures.

No-go results restrict low-dimensional topological codes for certain fault-tolerance goals.

Abstract

Current experiments are taking the first steps toward noise-resilient logical qubits. Crucially, a quantum computer must not merely store information, but also process it. A fault-tolerant computational procedure ensures that errors do not multiply and spread. This review compares the leading proposals for promoting a quantum memory to a quantum processor. We compare magic state distillation, color code techniques and other alternative ideas, paying attention to relative resource demands. We discuss the several no-go results which hold for low-dimensional topological codes and outline the potential rewards of using high-dimensional quantum (LDPC) codes in modular architectures.