Improved Transversal Non-Clifford Gates from Cup Products

arXiv:2609.27801 · quant-ph, cs.IT, math.IT · Submitted 2026-08-17 · Read on arXiv

quant-ph, cs.IT, math.IT

Submitted: 2026-08-17

Updated: 2026-08-17

Terminology

• Sparsity — 23× in this paper · explained in 4 episodes
• Distillation — 10× in this paper · explained in 2 episodes
• CSS Codes — 5× in this paper · explained in 2 episodes
• Adam — 4× in this paper · explained in 2 episodes
• Addressability — 4× in this paper · explained in 1 episode
• Decode — 3× in this paper · explained in 2 episodes
• Annual Symposium on Foundations of Computer Science — 2× in this paper
• Hypergraph — 2× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Redundancy — 1× in this paper · explained in 2 episodes

Sources

• Cups and Gates I: Cohomology invariants and logical quantum operations
• Sparse Quantum Codes from Quantum Circuits
• Dimensional Jump in Quantum Error Correction
• Improved QLDPC Surgery: Logical Measurements and Bridging Codes
• Shor's algorithm is possible with as few as 10,000 reconfigurable atomic qubits
• Constant overhead quantum fault-tolerance with quantum expander codes
• Constant-Overhead Addressable Gates via Single-Shot Code Switching
• How to factor 2048 bit RSA integers with less than a million noisy qubits
• Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates
• Quantum Codes with Addressable and Transversal Non-Clifford Gates
• Algebraic Expander Codes
• Transversal non-Clifford gates for quantum LDPC codes on sheaves
• Transversal non-Clifford gates on almost-good quantum LDPC and quantum locally testable codes
• Poincar'e Duality and Multiplicative Structures on Quantum Codes
• Theory of (Co)homological Invariants on Quantum LDPC Codes
• Quantum Rainbow Codes: Achieving Linear Rate, Growing Distance and Transversal Non-Clifford Gates with Generalised Colour Codes
• Single-Shot Universality in Quantum LDPC Codes via Code-Switching
• Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
• Constant-Overhead Magic State Distillation
• Constant-Overhead Fault-Tolerant Quantum Computation with Reconfigurable Atom Arrays

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• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity