Quantum "hyperbicycle" low-density parity check codes with finite rate
arXiv:1212.6703 · doi:10.1103/PhysRevA.88.012311
Abstract
We introduce a "hyperbicycle" ansatz for quantum codes which gives the hypergraph-product (generalized toric) codes by Tillich and Zémor and generalized bicycle codes by MacKay et al. as limiting cases. The construction allows for both the lower and the upper bounds on the minimum distance; they scale as a square root of the block length. Many of thus defined codes have finite rate and a limited-weight stabilizer generators, an analog of classical low-density parity check (LDPC) codes. Compared to the hypergraph-product codes, hyperbicycle codes generally have wider range of parameters; in particular, they can have higher rate while preserving the (estimated) error threshold.
13 pages, 4 figures
References in corpus (7)
- Fault-tolerant quantum computation with high threshold in two dimensions
- Local stabilizer codes in three dimensions without string logical operators
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
- Quantum Error Correction on Linear Nearest Neighbor Qubit Arrays
- Low-complexity quantum codes designed via codeword-stabilized framework
- Universal set of scalable dynamically corrected gates for quantum error correction with always-on qubit couplings
Cited by in corpus (58)
- Demonstration of the trapped-ion quantum-CCD computer architecture
- High-threshold and low-overhead fault-tolerant quantum memory
- Quantum Error Correction: An Introductory Guide
- Quantum Computer Systems for Scientific Discovery
- Degenerate Quantum LDPC Codes With Good Finite Length Performance
- Quantum LDPC Codes with Almost Linear Minimum Distance
- IBM Quantum Computers: Evolution, Performance, and Future Directions
- Low-overhead fault-tolerant quantum computing using long-range connectivity
- Decoding color codes by projection onto surface codes
- Trapping Sets of Quantum LDPC Codes
- Refined Belief Propagation Decoding of Sparse-Graph Quantum Codes
- Higher-dimensional quantum hypergraph-product codes
- Exploiting Degeneracy in Belief Propagation Decoding of Quantum Codes
- The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
- Partitioning qubits in hypergraph product codes to implement logical gates
- Thresholds for correcting errors, erasures, and faulty syndrome measurements in degenerate quantum codes
- Localized statistics decoding for quantum low-density parity-check codes
- Toward a 2D Local Implementation of Quantum LDPC Codes
- High-rate quantum LDPC codes for long-range-connected neutral atom registers
- Numerical and analytical bounds on threshold error rates for hypergraph-product codes
- Demonstration of Shor encoding on a trapped-ion quantum computer
- A decoding algorithm for CSS codes using the X/Z correlations
- Log-domain decoding of quantum LDPC codes over binary finite fields
- Many-hypercube codes: High-rate quantum error-correcting codes for high-performance fault-tolerant quantum computing
- QDistRnd: A GAP package for computing the distance of quantum error-correcting codes
- Quantum Pin Codes
- Distance-preserving stabilizer measurements in hypergraph product codes
- Lowering Connectivity Requirements For Bivariate Bicycle Codes Using Morphing Circuits
- Quantum XYZ Product Codes
- Homological Quantum Rotor Codes: Logical Qubits from Torsion
- Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank
- Minimal distances for certain quantum product codes and tensor products of chain complexes
- Linear-optical quantum computation with arbitrary error-correcting codes
- Partial Syndrome Measurement for Hypergraph Product Codes
- Parafermion stabilizer codes
- Generalized toric codes on twisted tori for quantum error correction
- Quantum error correction for long chains of trapped ions
- Adaptive Syndrome Extraction
- Generalized quantum data-syndrome codes and belief propagation decoding for phenomenological noise
- Subsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat's Lemma
- Degenerate quantum erasure decoding
- Quantum low-density parity-check codes for erasure-biased atomic quantum processors
- Low-density parity-check representation of fault-tolerant quantum circuits
- Non-local resources for error correction in quantum LDPC codes
- Qudit low-density parity-check codes
- On the energy barrier of hypergraph product codes
- Lattice Surgery Compilation Beyond the Surface Code
- Quantum LDPC codes from intersecting subsets
- Towards self-correcting quantum codes for neutral atom arrays
- Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes
- Symmetry-enriched topological order and quasifractonic behavior in stabilizer codes
- Dihedral Quantum Codes
- Transversal architecture for megaquop-scale quantum simulation with neutral atoms
- qSIEVE: Efficient qLDPC Memory via Systolic Movement in Atom Arrays
- A graph-based approach to entanglement entropy of quantum error correcting codes
- Quantum memory based on concatenating surface codes and quantum Hamming codes
- Decoding Correlated Errors in Quantum LDPC Codes
- Streaming Belief Propagation on Mixed-Alphabet Tanner Graphs for Practical Quantum Memory