Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}

Abstract

The current best asymptotic lower bound on the minimum distance of quantum LDPC codes with fixed non-zero rate is logarithmic in the blocklength. We propose a construction of quantum LDPC codes with fixed non-zero rate and prove that the minimum distance grows proportionally to the square root of the blocklength.

21 pages

References in corpus (11)

• Topological Quantum Distillation
• Degenerate Quantum Codes for Pauli Channels
• Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
• Quantum "hyperbicycle" low-density parity check codes with finite rate
• Homological Error Correction: Classical and Quantum Codes
• Quantum Quasi-Cyclic LDPC Codes
• New lower bounds on the non-zero capacity of Pauli Channels
• Asymmetric Quantum LDPC Codes
• A Class of Quantum LDPC Codes Constructed From Finite Geometries
• Improved quantum hypergraph-product LDPC codes
• Quantum Error Correction beyond the Bounded Distance Decoding Limit

Cited by in corpus (156)

• Quantum Error Correction for Quantum Memories
• Roads towards fault-tolerant universal quantum computation
• High-threshold and low-overhead fault-tolerant quantum memory
• The Future of Quantum Computing with Superconducting Qubits
• Quantum Error Correction: An Introductory Guide
• Quantum Low-Density Parity-Check Codes
• The XZZX Surface Code
• Decoding Across the Quantum LDPC Code Landscape
• Quantum LDPC Codes with Almost Linear Minimum Distance
• Focus beyond quadratic speedups for error-corrected quantum advantage
• IBM Quantum Computers: Evolution, Performance, and Future Directions
• Balanced Product Quantum Codes
• Flag fault-tolerant error correction with arbitrary distance codes
• Decoding Small Surface Codes with Feedforward Neural Networks
• Constant overhead quantum fault-tolerance with quantum expander codes
• Foliated Quantum Codes
• Low-overhead fault-tolerant quantum computing using long-range connectivity
• Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes
• A theory of single-shot error correction for adversarial noise
• Linear-Time Maximum Likelihood Decoding of Surface Codes over the Quantum Erasure Channel
• Decoding color codes by projection onto surface codes
• Quantum Expander Codes
• Constant-overhead quantum error correction with thin planar connectivity
• Fiber Bundle Codes: Breaking the $N^{1/2}\mathrm{polylog}(N)$ Barrier for Quantum LDPC Codes
• Single-shot error correction of three-dimensional homological product codes
• Quantum coding with low-depth random circuits
• A fast fault-tolerant decoder for qubit and qudit surface codes
• Logical blocks for fault-tolerant topological quantum computation
• Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation
• Quantum error-correcting codes and 4-dimensional arithmetic hyperbolic manifolds
• Local Hamiltonians Whose Ground States are Hard to Approximate
• Combining hard and soft decoders for hypergraph product codes
• Calderbank-Steane-Shor Holographic Quantum Error Correcting Codes
• Quantum Codes of Maximal Distance and Highly Entangled Subspaces
• Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
• 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
• Bias-tailored quantum LDPC codes
• Flag fault-tolerant error correction, measurement, and quantum computation for cyclic CSS codes
• Finite Rate QLDPC-GKP Coding Scheme that Surpasses the CSS Hamming Bound
• Experimental benchmarking of an automated deterministic error suppression workflow for quantum algorithms
• Fault-tolerant gates on hypergraph product codes
• Partitioning qubits in hypergraph product codes to implement logical gates
• Protecting quantum memories using coherent parity check codes
• Universal logical gates with constant overhead: instantaneous Dehn twists for hyperbolic quantum codes
• Connectivity constrains quantum codes
• Cellular automaton decoders for topological quantum codes with noisy measurements and beyond
• Beyond single-shot fault-tolerant quantum error correction
• Handling Leakage with Subsystem Codes
• Low-Overhead Transversal Fault Tolerance for Universal Quantum Computation
• Entangling four logical qubits beyond break-even in a nonlocal code
• Toward a 2D Local Implementation of Quantum LDPC Codes
• Localized statistics decoding for quantum low-density parity-check codes
• High-rate quantum LDPC codes for long-range-connected neutral atom registers
• Avoiding coherent errors with rotated concatenated stabilizer codes
• Quantum LDPC Codes for Modular Architectures
• Graphical Structures for Design and Verification of Quantum Error Correction
• Numerical and analytical bounds on threshold error rates for hypergraph-product codes
• Topological wormholes
• A Spin-Optical Quantum Computing Architecture
• Demonstration of low-overhead quantum error correction codes
• Log-domain decoding of quantum LDPC codes over binary finite fields
• Good approximate quantum LDPC codes from spacetime circuit Hamiltonians
• Constant-Overhead Fault-Tolerant Bell-Pair Distillation using High-Rate Codes
• Hierarchical memories: Simulating quantum LDPC codes with local gates
• Fault-tolerant gates via homological product codes
• Decoding of Quantum Data-Syndrome Codes via Belief Propagation
• Efficient Preparation of Large Block Code Ancilla States for Fault-tolerant Quantum Computation
• Efficient Formal Verification of Quantum Error Correcting Programs
• Long-range-enhanced surface codes
• Experiments with the 4D Surface Code on a QCCD Quantum Computer
• Quantum memory at nonzero temperature in a thermodynamically trivial system
• Fast erasure decoder for hypergraph product codes
• Quantum Pin Codes
• Low-density parity-check codes as stable phases of quantum matter
• Distance-preserving stabilizer measurements in hypergraph product codes
• Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial
• Quantum XYZ Product Codes
• Homological Quantum Rotor Codes: Logical Qubits from Torsion
• Extracting topological orders of generalized Pauli stabilizer codes in two dimensions
• Optimization of decoder priors for accurate quantum error correction
• Analog information decoding of bosonic quantum LDPC codes
• LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations
• Duality and free energy analyticity bounds for few-body Ising models with extensive homology rank
• Stabilizer Entanglement Distillation and Efficient Fault-Tolerant Encoders
• Optimal quantum subsystem codes in 2-dimensions
• Leveraging Qubit Loss Detection in Fault Tolerant Quantum Algorithms
• Deconfinement and Error Thresholds in Holography
• Minimal distances for certain quantum product codes and tensor products of chain complexes
• Fault-tolerant logical measurements via homological measurement
• Systematic Design and Optimization of Quantum Circuits for Stabilizer Codes
• Partial Syndrome Measurement for Hypergraph Product Codes
• Weight Reduced Stabilizer Codes with Lower Overhead
• Layer Codes
• Time-Efficient Logical Operations on Quantum Low-Density Parity Check Codes
• Generalized toric codes on twisted tori for quantum error correction
• Efficient Concatenated Bosonic Code for Additive Gaussian Noise
• Fault-Tolerant Stabilizer Measurements in Surface Codes with Three-Qubit Gates
• Quaternary Neural Belief Propagation Decoding of Quantum LDPC Codes with Overcomplete Check Matrices
• Spatially-Coupled QLDPC Codes
• Fault-Tolerant Preparation of Quantum Polar Codes Encoding One Logical Qubit
• Refined Belief-Propagation Decoding of Quantum Codes with Scalar Messages
• Lift-Connected Surface Codes
• Low-overhead fault-tolerant quantum computation by gauging logical operators
• Quantum codes from classical graphical models
• Efficient Frequency Allocation for Superconducting Quantum Processors Using Improved Optimization Techniques
• Adaptive Syndrome Extraction
• Letting the tiger out of its cage: bosonic coding without concatenation
• Classical product code constructions for quantum Calderbank-Shor-Steane codes
• Coprime Bivariate Bicycle Codes and Their Layouts on Cold Atoms
• Generalized quantum data-syndrome codes and belief propagation decoding for phenomenological noise
• Degenerate quantum erasure decoding
• Reliable Quantum Memories with Unreliable Components
• Single-shot and measurement-based quantum error correction via fault complexes
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• A blindness property of the Min-Sum decoding for the toric code
• Single-shot preparation of hypergraph product codes via dimension jump
• Finite-rate sparse quantum codes aplenty
• Quantum low-density parity-check codes for erasure-biased atomic quantum processors
• Multiplexed Quantum Communication with Surface and Hypergraph Product Codes
• Universal graph representation of stabilizer codes
• Low-density parity-check representation of fault-tolerant quantum circuits
• Measurement-Based Entanglement Distillation and Constant-Rate Quantum Repeaters over Arbitrary Distances
• Non-local resources for error correction in quantum LDPC codes
• Qudit low-density parity-check codes
• On the energy barrier of hypergraph product codes
• Effective Distance of Higher Dimensional HGPs and Weight-Reduced Quantum LDPC Codes
• Parallel Logical Measurements via Quantum Code Surgery
• Tailoring Fault-Tolerance to Quantum Algorithms
• QUITS: A modular Qldpc code circUIT Simulator
• Finding the disjointness of stabilizer codes is NP-complete
• Quantum LDPC codes from intersecting subsets
• Efficient decoding of random errors for quantum expander codes
• Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes
• Targeted Clifford logical gates for hypergraph product codes
• Layer codes as partially self-correcting quantum memories
• Quantum subspace verification for error correction codes
• Entanglement boosting: Low-volume logical Bell pair preparation for distributed fault-tolerant quantum computation
• Gottesman-Kitaev-Preskill codes: A lattice perspective
• Fully Parallelized BP Decoding for Quantum LDPC Codes Can Outperform BP-OSD
• Accelerating Fault-Tolerant Quantum Computation with Good qLDPC Codes
• Quantum memory based on concatenating surface codes and quantum Hamming codes
• Symmetry-enriched topological order and quasifractonic behavior in ${\mathbb{Z}}_N$ stabilizer codes
• Transversal architecture for megaquop-scale quantum simulation with neutral atoms
• Equivariant Machine Learning Decoder for 3D Toric Codes
• Fracton models from product codes
• Decoding Correlated Errors in Quantum LDPC Codes
• Hierarchical Quantum Error Correction with Hypergraph Product Code and Rotated Surface Code
• Increasing the distance of topological codes with time vortex defects
• A graph-based approach to entanglement entropy of quantum error correcting codes
• Informed Dynamic Scheduling for QLDPC Codes
• Streaming Belief Propagation on Mixed-Alphabet Tanner Graphs for Practical Quantum Memory
• Unified Framework for Quantum Code Embedding
• Color code with a logical control-$S$ gate using transversal $T$ rotations