Exploiting Degeneracy in Belief Propagation Decoding of Quantum Codes
arXiv:2104.13659 · doi:10.1038/s41534-022-00623-2
Abstract
Quantum information needs to be protected by quantum error-correcting codes due to imperfect physical devices and operations. One would like to have an efficient and high-performance decoding procedure for the class of quantum stabilizer codes. A potential candidate is Pearl's belief propagation (BP), but its performance suffers from the many short cycles inherent in a quantum stabilizer code, especially highly-degenerate codes. A general impression exists that BP is not effective for topological codes. In this paper, we propose a decoding algorithm for quantum codes based on quaternary BP with additional memory effects (called MBP). This MBP is like a recursive neural network with inhibitions between neurons (edges with negative weights), which enhance the perception capability of a network. Moreover, MBP exploits the degeneracy of a quantum code so that the most probable error or its degenerate errors can be found with high probability. The decoding performance is significantly improved over the conventional BP for various quantum codes, including quantum bicycle, hypergraph-product, surface and toric codes. For MBP on the surface and toric codes over depolarizing errors, we observe error thresholds of 16% and 17.5%, respectively.
arXiv comment22 pages, 25 figures, 3 tables, and 3 algorithms
References in corpus (41)
- Fault-tolerant quantum computation by anyons
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Mixed State Entanglement and Quantum Error Correction
- Topological quantum memory
- Topological Quantum Distillation
- Surface code quantum computing by lattice surgery
- Deep Learning Methods for Improved Decoding of Linear Codes
- A fault-tolerant one-way quantum computer
- Sparse Graph Codes for Quantum Error-Correction
- Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
- Single-qubit quantum memory exceeding -minute coherence time
- Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
- Fast Decoders for Topological Quantum Codes
- Degenerate Quantum LDPC Codes With Good Finite Length Performance
- Almost-linear time decoding algorithm for topological codes
- Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
- Towards practical classical processing for the surface code
- A Neural Decoder for Topological Codes
- Decoding Across the Quantum LDPC Code Landscape
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- Quantum "hyperbicycle" low-density parity check codes with finite rate
- Iterative Optimization of Quantum Error Correcting Codes
- Deep Neural Network Probabilistic Decoder for Stabilizer Codes
- High threshold error correction for the surface code
- Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes
- Universal topological phase of 2D stabilizer codes
- Decoding color codes by projection onto surface codes
- Advantages of versatile neural-network decoding for topological codes
- Trapping Sets of Quantum LDPC Codes
- Combining hard and soft decoders for hypergraph product codes
- Efficient Decoding of Topological Color Codes
- Protocols for Packet Quantum Network Intercommunication
- Multi-path Summation for Decoding 2D Topological Codes
- Refined Belief Propagation Decoding of Sparse-Graph Quantum Codes
- Comparing the Overhead of Topological and Concatenated Quantum Error Correction
- Exploiting Degeneracy in Belief Propagation Decoding of Quantum Codes
- Error threshold estimates for surface code with loss of qubits
- Log-domain decoding of quantum LDPC codes over binary finite fields
- Decoding of Quantum Data-Syndrome Codes via Belief Propagation
- Comparison of 2D topological codes and their decoding performances
- Refined Belief-Propagation Decoding of Quantum Codes with Scalar Messages
Cited by in corpus (14)
- Exploiting Degeneracy in Belief Propagation Decoding of Quantum Codes
- Bias-tailored quantum LDPC codes
- Generalized Belief Propagation Algorithms for Decoding of Surface Codes
- Hierarchical memories: Simulating quantum LDPC codes with local gates
- Actis: A Strictly Local Union-Find Decoder
- Improved Belief Propagation Decoding Algorithms for Surface Codes
- On Belief Propagation Decoding of Quantum Codes with Quaternary Reliability Statistics
- Generalized quantum data-syndrome codes and belief propagation decoding for phenomenological noise
- Progressive-Proximity Bit-Flipping for Decoding Surface Codes
- A blindness property of the Min-Sum decoding for the toric code
- Harnessing Coding Theory for Reliable Network Quantum Communication
- Syndrome decoding by quantum approximate optimization
- Union-Intersection Union-Find for Decoding Depolarizing Errors in Topological Codes
- Streaming Belief Propagation on Mixed-Alphabet Tanner Graphs for Practical Quantum Memory