Building codes with transversal CCZ using projective geometry and SAT solvers

arXiv:2610.09341 · quant-ph, cs.IT, math.IT · Submitted 2026-10-07 · Read on arXiv

quant-ph, cs.IT, math.IT

Submitted: 2026-10-07

Updated: 2026-10-07

Code: https://github.com/jerrylvx/gate2code-public

Terminology

• Distillation — 10× in this paper · explained in 2 episodes
• CSS Codes — 6× in this paper · explained in 2 episodes
• Additivity — 4× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Ambient Dimension — 1× in this paper · explained in 1 episode
• National Science Foundation — 1× in this paper
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Magic state cultivation: growing T states as cheap as CNOT gates
• Entangling logical qubits without physical operations
• Divisible Codes for Quantum Computation
• Magic State Distillation via Codes over Binary Extension Fields
• A Class of Quantum LDPC Codes Constructed From Finite Geometries
• Exploring the landscape of compact magic-state distillation factories
• Projective divisible binary codes
• The Smallest Code with Transversal T

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