Advances in decoding schemes for Surface codes*

Quantum error correction (QEC) is an invaluable ingredient in any strategy that pursues the construction of reliable quantum computers. QEC Codes define methods through which to arrange the available qubits into subsets of noise-protected qubits. Surface codes and quantum low density parity check codes (QLDPC) are promising candidates to implement QEC strategies in near future quantum computers. The aim of this presentation is to showcase the recent developments we have made (in Tecnun) on the topic of decoding schemes for the aforementioned families of codes. This includes considering independent and non-identically distributed (i.ni.d.) noise present in state-of-the-art quantum processors and tailoring the decoding algorithms to this specific type of noise [1]. In addition, we will discuss different decoders for surface codes based on the MWPM and BP algorithms for i.i.d. unbiased and biased noise (Z-noise is predominant). We will introduce and explain our modifications to these decoders and we will show how the thresholds of the surface codes improve significantly when such decoders are applied under both i.i.d. and i.ni.d. noise.

[1] de Martí i Olius et al. Performance of surface codes in realistic quantum hardware. arXiv: 2203.15695 (2022).