Parallelizable and addressable transversal non-Clifford gates on good quantum LDPC codes

arXiv:2609.26691 · quant-ph, cs.IT, math-ph, math.IT, math.MP · Submitted 2026-09-22 · Read on arXiv

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

Submitted: 2026-09-22

Updated: 2026-10-06

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

Terminology

• Distillation — 11× in this paper · explained in 2 episodes
• Trace — 7× in this paper · explained in 2 episodes
• Sheaf Codes — 5× in this paper · explained in 2 episodes
• Addressability — 2× in this paper · explained in 1 episode
• CSS Codes — 2× in this paper · explained in 2 episodes
• Foundations of Computer Science — 2× in this paper
• Hypergraph — 2× in this paper · explained in 2 episodes
• No-Go Theorem — 2× in this paper · explained in 2 episodes
• Computational Universality — 1× in this paper · explained in 3 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Generative AI — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Transversal non-Clifford gates on almost-good quantum LDPC and quantum locally testable codes
• Asymptotically Good Quantum Locally Testable Codes
• Fault-Tolerant Quantum Computation with Constant Overhead
• Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes
• Quantum Rainbow Codes: Achieving Linear Rate, Growing Distance and Transversal Non-Clifford Gates with Generalised Colour Codes
• Transversal non-Clifford gates for quantum LDPC codes on sheaves
• Copy-cup Gates in Tensor Products of Group Algebra Codes
• A topological theory for qLDPC: non-Clifford gates and magic state fountain on homological product codes with constant rate and beyond the $N^{1/3}$ distance barrier
• Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom
• Quantum Codes with Addressable and Transversal Non-Clifford Gates
• Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates
• Good quantum codes with addressable and parallelizable transversal non-Clifford gates
• Quantum group codes for non-Clifford logic: enhanced decoding, addressability and parallelizability
• No-go theorems for logical gates on product quantum codes
• Poincar'e Duality and Multiplicative Structures on Quantum Codes
• Theory of (Co)homological Invariants on Quantum LDPC Codes
• Maximally Extendable Sheaf Codes
• Maximally Extendable Product Codes are Good Coboundary Expanders

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