Qubit CSS codes with Universal Transversal Gates
quant-ph
Submitted: 2026-10-05
Updated: 2026-10-05
Comments: 25 pages, 5 figures, 6 tables. The ancillary file depth_one_universal_codes.json lists all 110 codes with their stabilizers, logical operators, depth-one generators, seed and kernel codes, and coupling circuits
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
- Restrictions on Transversal Encoded Quantum Gate Sets
- Transversality versus Universality for Additive Quantum Codes
- Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit
- The disjointness of stabilizer codes and limitations on fault-tolerant logical gates
- No-Go Theorem on Fault Tolerant Gadgets for Multiple Logical Qubits
- Achieving the limits of automorphism gates
- On the Addressability Problem on CSS Codes
- Roads towards fault-tolerant universal quantum computation
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Magic State Distillation: Not as Costly as You Think
- Magic state cultivation: growing T states as cheap as CNOT gates
- A magic state's fidelity can be superior to the operations that created it
- Surface code quantum computing by lattice surgery
- Low-overhead fault-tolerant quantum computing using long-range connectivity
- Universal fault-tolerant quantum computation with only transversal gates and error correction
- Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
- Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes
- Measurement-free, scalable and fault-tolerant universal quantum computing
- Universal quantum computation via scalable measurement-free error correction
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