Cups and Gates II: Operads, twists, and addressable intra-code gates
quant-ph, cond-mat.str-el, math-ph, math.AT, math.MP
Submitted: 2026-10-04
Updated: 2026-10-04
Comments: 63 pages, 2 figures
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Sources
- Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
- Limitations on transversal gates for hypergraph product codes
- Logical Operators and Derived Automorphisms of Tile Codes
- Cups and Gates I: Cohomology invariants and logical quantum operations
- Quantum Low-Density Parity-Check Codes
- Magic state distillation with low overhead
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Symmetry protected topological orders and the group cohomology of their symmetry group
- Exact bosonization in two spatial dimensions and a new class of lattice gauge theories
- Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes
- No-go theorems for logical gates on product quantum codes
- Spin TQFTs and fermionic phases of matter
- Generalized Global Symmetries
- Quantum LDPC Codes with Transversal Non-Clifford Gates via Products of Algebraic Codes
- Leveraging Automorphisms of Quantum Codes for Fault-Tolerant Quantum Computation
- Improved Transversal Non-Clifford Gates from Cup Products
- Commuting Pauli Hamiltonians as maps between free modules
- Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry
- Hybrid Lattice Surgery: Non-Clifford Gates via Non-Abelian Surface Codes
- Single-Shot Decoding and Fault-tolerant Gates with Trivariate Tricycle Codes
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