Comparison of 2D topological codes and their decoding performances

Abstract

Topological quantum codes are favored because they allow qubit layouts that are suitable for practical implementation. An $N$-qubit topological code can be decoded by minimum-weight perfect matching (MWPM) with complexity $O(\text{poly}(N))$ if it is of CSS-type. Recently it is shown that various quantum codes, including non-CSS codes, can be decoded by an adapted belief propagation with memory effects (denoted MBP) with complexity almost linear in $N$. In this paper, we show that various two-dimensional topological codes, CSS or non-CSS, regardless of the layout, can be decoded by MBP, including color codes and twisted XZZX codes. We will comprehensively compare these codes in terms of code efficiency and decoding performance, assuming perfect error syndromes.

References in corpus (28)

• Fault-tolerant quantum computation by anyons
• Good Quantum Error-Correcting Codes Exist
• Topological quantum memory
• Stabilizer Codes and Quantum Error Correction
• Topological Quantum Distillation
• Surface code quantum computing by lattice surgery
• A fault-tolerant one-way quantum computer
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Quantum codes on a lattice with boundary
• The XZZX Surface Code
• Towards practical classical processing for the surface code
• Tradeoffs for reliable quantum information storage in 2D systems
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
• Strong Resilience of Topological Codes to Depolarization
• Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
• High threshold error correction for the surface code
• The surface code with a twist
• Decoding color codes by projection onto surface codes
• From Majorana Fermions to Topological Order
• Fault-tolerant quantum computing with color codes
• Quantum Computing with Majorana Fermion Codes
• The boundaries and twist defects of the color code and their applications to topological quantum computation
• Topological Entanglement Entropy with a Twist
• Refined Belief Propagation Decoding of Sparse-Graph Quantum Codes
• Low-complexity quantum codes designed via codeword-stabilized framework
• Log-domain decoding of quantum LDPC codes over binary finite fields
• Decoding of Quantum Data-Syndrome Codes via Belief Propagation
• Trellis Decoding For Qudit Stabilizer Codes And Its Application To Qubit Topological Codes

Cited by in corpus (6)

• Exploiting Degeneracy in Belief Propagation Decoding of Quantum Codes
• Conservation laws and quantum error correction: towards a generalised matching decoder
• Improved Belief Propagation Decoding Algorithms for Surface Codes
• On Belief Propagation Decoding of Quantum Codes with Quaternary Reliability Statistics
• Degenerate quantum erasure decoding
• Generalized quantum data-syndrome codes and belief propagation decoding for phenomenological noise