Syndrome Decoding for Product Codes

Zongwang Li, Youyun Xu, Wentao Song

Orhan Gazi

Hannes Bartz, Men‐Andrin Meier, Vladimir R. Sidorenko

Venkata Gandikota, Elena Grigorescu, Jha, Vatsal +1 more

Hypergraph product codes are a prototypical family of quantum codes with state-of-the-art decodability properties. In this work we consider the "noisy" syndrome decoding problem and exact recovery problem for hypergraph product codes and show a reduction to the decoding and exact recovery of classical codes in the noisy syndrome setting. Our results hold for a broad class of codes admitting efficient syndrome decoding, including Sipser-Spielman codes and Reed-Solomon codes.

Nguyen Thi Hong Nhung, Pham Xuan Nghia, The Cuong Dinh +2 more

R. Gayathri, Shobhit Bhatnagar, P. Vijay Kumar

Erasure decoding of quantum low-density paritycheck (QLDPC) codes has recently received a lot of interest as qubit erasures occur in many physical systems such as neutralatom systems, trapped-ion systems etc. However, decoding of QLDPC codes heavily relies on syndrome information, which may be unreliable as syndrome extraction circuits are prone to errors in practice. While syndrome errors are usually modeled as flipping of a binary syndrome bit, typically, measurement outcomes yield analog voltage/current values, which are then discretized to obtain the binary syndrome. Prior work on correcting qubit errors in the presence of syndrome noise shows that this soft (i.e., analog) information can be exploited to achieve performance improvement. In this paper, we consider the case of qubit erasures and present an iterative decoding algorithm, based on the hardware-friendly min-sum algorithm, that incorporates this soft information to perform check node updates. We show via simulations on hypergraph product codes and lifted product codes that our decoder achieves performance very close to that in the case of noiseless syndrome for a certain noise regime.