Design Principles for Ultra-High-Rate Quantum Codes

arXiv:2609.30069 · quant-ph · Submitted 2026-09-24 · Read on arXiv

quant-ph

Submitted: 2026-09-24

Updated: 2026-09-24

Comments: 20 + 16 pages. This work also subsumes the earlier results of arXiv preprint 2607.14091

Code: https://github.com/ultra-high-rate-qec/design-principles-data

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• CSS Codes — 16× in this paper · explained in 2 episodes
• Hypergraph — 6× in this paper · explained in 2 episodes
• Low-Density Parity-Check — 5× in this paper
• Verification — 4× in this paper · explained in 2 episodes
• Pruning — 3× in this paper · explained in 4 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Hamming Distance — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Decode — 1× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 3 episodes
• Gauge Freedom — 1× in this paper · explained in 2 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Towards Ultra-High-Rate Quantum Error Correction with Reconfigurable Atom Arrays
• Shor's algorithm is possible with as few as 10,000 reconfigurable atomic qubits
• Logical Spectroscopy: Lifted-Product Codes with Addressable Bases
• Designer Codes from GALA: Compact, Self-Dual, and Rate-1/2 QEC on Reconfigurable Atom Arrays
• Quantum error correction at ultra-low overhead
• High-rate qLDPC processors
• Spatially-Coupled QLDPC Codes
• Genons, Double Covers and Fault-tolerant Clifford Gates
• Quantum LDPC codes with design rate 1/5 and good performance below 1000 physical qubits
• Distance-Finding Algorithms for Quantum Codes and Circuits
• Mirror codes: High-threshold quantum LDPC codes beyond the CSS regime
• Subsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat's Lemma
• Self-dual bivariate bicycle codes with transversal Clifford gates
• Improved belief propagation is sufficient for real-time decoding of quantum memory
• Hierarchical decoding to reduce hardware requirements for quantum computing
• Low-overhead fault-tolerant quantum computation by gauging logical operators
• Universal adapters between quantum LDPC codes
• Parsimonious Quantum Low-Density Parity-Check Code Surgery
• Trapping Sets of Detector Error Models
• Generalized toric codes on twisted tori for quantum error correction

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• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
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• A quasiparticle-protected superconducting qubit
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians