Decoders for Good Quantum LDPC Codes
1Shouzhen Gu (Caltech)
https://simons.berkeley.edu/talks/shouzhen-gu-caltech-2024-02-13
Advances in Quantum Coding Theory
The last few years have seen rapid progress in the development of quantum low-density parity-check (LDPC) codes. In particular, a series of pivotal works culminated in the discovery of asymptotically good codes--those with essentially optimal parameters. These codes allow for the possibility fault-tolerant quantum computation with very low overhead. However, for a code to be used in practice, it is necessary to efficiently identify errors from measurement outcomes to get back into the codespace. In this talk, I will present linear-time decoders for families of asymptotically good quantum LDPC codes. Furthermore, I will show that these codes support single-shot decoding, which means that one measurement round suffices to perform reliable quantum error correction even in the presence of measurement errors. I will share thoughts on the connection between the different decoders and the ingredients required for them to have the single-shot property. These results can be seen as a step toward making quantum LDPC codes more practical.