Decoding of Quantum Data-Syndrome Codes via Belief Propagation
arXiv:2102.01984 · doi:10.1109/ISIT45174.2021.9518018
Abstract
Quantum error correction is necessary to protect logical quantum states and operations. However, no meaningful data protection can be made when the syndrome extraction is erroneous due to faulty measurement gates. Quantum data-syndrome (DS) codes are designed to protect the data qubits and syndrome bits concurrently. In this paper, we propose an efficient decoding algorithm for quantum DS codes with sparse check matrices. Based on a refined belief propagation (BP) decoding for stabilizer codes, we propose a DS-BP algorithm to handle the quaternary quantum data errors and binary syndrome bit errors. Moreover, a sparse quantum code may inherently be able to handle minor syndrome errors so that fewer redundant syndrome measurements are necessary. We demonstrate this with simulations on a quantum hypergraph-product code.
References in corpus (18)
- Fault-tolerant quantum computation by anyons
- Surface codes: Towards practical large-scale quantum computation
- Good Quantum Error-Correcting Codes Exist
- Sparse Graph Codes for Quantum Error-Correction
- Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
- Quantum Error Correction
- Scalable quantum circuit and control for a superconducting surface code
- Single-shot fault-tolerant quantum error correction
- Decoding Small Surface Codes with Feedforward Neural Networks
- Fault-tolerant error correction with the gauge color code
- Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes
- Trapping Sets of Quantum LDPC Codes
- Combining hard and soft decoders for hypergraph product codes
- Refined Belief Propagation Decoding of Sparse-Graph Quantum Codes
- Modified belief propagation decoders for quantum low-density parity-check codes
- Ability of stabilizer quantum error correction to protect itself from its own imperfection
- One way quantum repeaters with quantum Reed-Solomon codes
- Quantum convolutional data-syndrome codes