Quantum Low-Density Parity-Check Codes
Nikolas P. Breuckmann, Jens Niklas Eberhardt
TL;DR
This paper reviews low-density parity-check quantum codes as promising alternatives to surface codes for quantum error correction, highlighting recent theoretical advances and open challenges in their development.
Contribution
It introduces the zoo of LDPC quantum codes, discusses recent theoretical progress, and explores their potential for robust quantum computing.
Findings
LDPC quantum codes offer promising error correction capabilities.
Recent advances include new product constructions for LDPC codes.
Open problems remain in optimizing these codes for practical use.
Abstract
Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called low-density parity-check (LDPC) quantum codes. The codes we discuss are alternatives to the surface code, which is the currently leading candidate to implement quantum fault-tolerance. We introduce the zoo of LDPC quantum codes and discuss their potential for making quantum computers robust against noise. In particular, we explain recent advances in the theory of LDPC quantum codes related to certain product constructions and discuss open problems in the field.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum Information and Cryptography · Computability, Logic, AI Algorithms