High Dimensional qLDPC Codes for Physical Architectures

Quantum Error Correction is vital for large scale quantum computers, but there is no consensus on which error correcting code is the best for fault-tolerant quantum computing. Currently, the surface code is the most successful code due to its high error threshold, good distance scaling and simple syndrome measurement circuit. However, it suffers from an asymptotically vanishing encoding rate, resulting in a large qubit overhead for fault-tolerant applications. An alternative and promising class of codes are quantum Low-Density Parity Check (qLDPC) codes, which improve the encoding rate, but come at the price of more complex syndrome measurement circuits, and non-local interactions between qubits.

In 2022 a milestone result proved the existence of 'good' qLDPC codes which has reinvigorated research in the area. Several questions remain to be answered regarding the efficacy of these codes, such as: what codes exist in 3D, what are these codes properties, can we perform universal quantum gates and what hardware is well suited to high dimensional qLDPC codes? Over the course of the PhD I intend to answer these questions.