Quantum error correction (QEC) is one of the key challenges in building a fault-tolerant quantum computer and differs significantly from classical error correction coding. The latter is a well-established scientific field with decades of research, while QEC is very active, pushing forward every day.
For classica coding, there exist strong theoretical results, great codes and profound decoder implementations, making everyday digital communications robust and practically error free. Low-Density Parity-Check (LDPC) codes are capacity approaching and among the best codes for all practical use in communications engineering. They were originally discovered by Robert Gallager in the 1950s, but their potential was not understood as simulation resources were limited. With the advent of Turbo Codes in the 1990s, the community focused on iterative decoding algorithms and rediscovered LDPC codes in conjunction with iterative Belief-Propagation (BP) decoding.
Contrary, QEC is still in the early stages and bears a more difficult task. Compared to classical bits, qubits are much more delicate and literally collapse just by observing them. Moreover they suffer from amplitude errors and phase errors which both require correction. While much progress has been made, current QEC schemes suffer from low code rates and comparably low correction capabilities. We will see that we need both new channel models and new decoder optimizations.
Consequently, the success of LDPC and BP decoding does not easily carry over to quantum error correction, and in this article series on quantum LDPC (qLDPC) we will find out why. But we can transfer knowledge and experience from the field of classical error correction coding to quantum error correction (QEC) and from LDPC to qLDPC.
And that is exactly what I am aiming for: my background is on LDPC codes in tough situations, like stopping sets, trapping sets and harsh code-length constraints. I want to use this experience to support the qLDPC development to achieve higher code rates and better qubit correction capabilities.