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Quantum low-density parity-check (LDPC) codes are a promising family of quantum error-correcting codes for fault tolerant quantum computing with low overhead. Decoding quantum LDPC codes on quantum erasure channels has received more attention recently due to advances in erasure conversion for various types of qubits including neutral atoms, trapped ions, and superconducting qubits. Belief propagation with guided decimation (BPGD) decoding of quantum LDPC codes has demonstrated good performance in bit-flip and depolarizing noise. In this work, we apply BPGD decoding to quantum erasure channels. Using a natural modification, we show that BPGD offers competitive performance on quantum erasure channels for multiple families of quantum LDPC codes. Furthermore, we show that the performance of BPGD decoding on erasure channels can sometimes be improved significantly by either adding damping or adjusting the initial channel log-likelihood ratio for bits that are not erased. More generally, our results demonstrate BPGD is an effective general-purpose solution for erasure decoding across the quantum LDPC landscape.
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Triangulation codes: a family of non-linear codes with graceful degradation
This paper introduces the notion of triangulation codes, a family of non-linear codes that 1) admit efficient encoding/decoding 2) their bit error rate deteriorates gracefully as the quality of the erasure channel degrades. Some coding theoretic properties of these codes are established. In the case of transmitting data over the erasure channel, it is shown that, even with sub-optimal decoding, they can achieve lower bit error rate than uncoded transmission for any number of received output symbols.
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- Award ID(s):
- 1717842
- PAR ID:
- 10063528
- Date Published:
- Journal Name:
- 2018 Conf. Inform. Sciences and Syst. (CISS)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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