Non-Abelian sheaf quantum LDPC codes: good and magical

arXiv:2609.30159 · quant-ph, cs.IT, math-ph, math.IT, math.MP · Submitted 2026-09-24 · Read on arXiv

quant-ph, cs.IT, math-ph, math.IT, math.MP

Submitted: 2026-09-24

Updated: 2026-09-24

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

Terminology

• Sheaf Codes — 33× in this paper · explained in 2 episodes
• Hypergraph — 8× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Stabilizer States — 3× in this paper · explained in 2 episodes
• Anyons — 2× in this paper · explained in 2 episodes
• CSS Codes — 2× in this paper · explained in 2 episodes
• No-Go Theorem — 2× in this paper · explained in 2 episodes
• Topological Order — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Distillation — 1× in this paper · explained in 2 episodes
• Foundations of Computer Science — 1× in this paper
• Generative AI — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Sparsity — 1× in this paper · explained in 4 episodes

Sources

• Fault-Tolerant Quantum Computation with Constant Overhead
• Constant-Overhead Fault-Tolerant Quantum Computation with Reconfigurable Atom Arrays
• Low-density parity-check codes as stable phases of quantum matter
• LDPC stabilizer codes as gapped quantum phases: stability under graph-local perturbations
• Decodable quantum LDPC codes beyond the $\sqrt{n}$ distance barrier using high dimensional expanders
• Building manifolds from quantum codes
• Poincar'e Duality and Multiplicative Structures on Quantum Codes
• Theory of (Co)homological Invariants on Quantum LDPC Codes
• Intrinsic locality dimension of quantum codes
• Maximally Extendable Sheaf Codes
• Non-Abelian Anyons and Topological Quantum Computation
• Non-Abelian Quantum Low-Density Parity Check Codes and Non-Clifford Operations from Gauging Logical Gates via Measurements
• Non-Abelian qLDPC: TQFT Formalism, Addressable Gauging Measurement and Application to Magic State Fountain on 2D Product Codes
• Universal fault tolerant quantum computation in 2D without getting tied in knots
• Long-range nonstabilizerness and quantum codes, phases, and complexity
• The Quantum PCP Conjecture
• Asymptotically Good Quantum Locally Testable Codes
• Good Quantum Locally Testable Codes from Product Expansion
• Cubical Sheaf Complexes with Constant Expansion with Applications to Asymptotically Good qLTCs
• Transversal non-Clifford gates on almost-good quantum LDPC and quantum locally testable codes

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