Fast erasure decoder for hypergraph product codes
arXiv:2208.01002 · doi:10.22331/q-2024-08-27-1450
Abstract
We propose a decoder for the correction of erasures with hypergraph product codes, which form one of the most popular families of quantum LDPC codes. Our numerical simulations show that this decoder provides a close approximation of the maximum likelihood decoder that can be implemented in O(N^2) bit operations where N is the length of the quantum code. A probabilistic version of this decoder can be implemented in O(N^1.5) bit operations.
11 pages
References in corpus (17)
- Surface codes: Towards practical large-scale quantum computation
- Good Quantum Error-Correcting Codes Exist
- Topological quantum memory
- Multiple Particle Interference and Quantum Error Correction
- Sparse Graph Codes for Quantum Error-Correction
- Codes for the Quantum Erasure Channel
- Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
- Degenerate Quantum LDPC Codes With Good Finite Length Performance
- Almost-linear time decoding algorithm for topological codes
- Balanced Product Quantum Codes
- Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
- Constant overhead quantum fault-tolerance with quantum expander codes
- Linear-Time Maximum Likelihood Decoding of Surface Codes over the Quantum Erasure Channel
- Constant-overhead quantum error correction with thin planar connectivity
- Quantum Error Correction with Metastable States of Trapped Ions Using Erasure Conversion
- Erasure qubits: Overcoming the limit in superconducting circuits
- Fault-Tolerant Weighted Union-Find Decoding on the Toric Code