Qubit CSS codes with Universal Transversal Gates
Abstract
The Eastin-Knill theorem rules out a universal set of transversal logical gates on any code that detects single-qubit errors. The theorem constrains one partition of the qubits at a time. We show that depth-one layers of few-qubit gates, each respecting its own partition, can together generate a universal logical gate set on an error-correcting code. Each logical gate generator is then a single depth-one layer followed by error correction of the same stabilizer code, with no magic-state distillation, code switching, gauge fixing, lattice surgery, or other gadgets. We show that such codes can be found by applying an entangling circuit to a lower-distance "seed" code admitting a depth-one non-Clifford gate and an appropriate "kernel" code. We construct 47 codes with depth-one generating sets that tolerate at least one faulty gate per layer, including a [[37,1,7]] and a [[59,1,9]] code, both of check weight at most eight.
Related
- Asymptotically Good Quantum Codes with Addressable Transversal T Gates
- Asymptotically good binary triorthogonal codes and higher-level transversal gates
- Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates
- Parallelizable and addressable transversal non-Clifford gates on good quantum LDPC codes
- Transversal Gates and Magic State Distillation in an Optimally Synthesized Spin-Qubit Shuttling Bus
BibTeX
@misc{dua2026qubit,
title = {{Qubit CSS codes with Universal Transversal Gates}},
author = {Arpit Dua and Adam Holmes and Michael J. Gullans and Victor V. Albert},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06730},
eprint = {2610.06730},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06730},
}
RIS
TY - UNPB
TI - Qubit CSS codes with Universal Transversal Gates
AU - Arpit Dua
AU - Adam Holmes
AU - Michael J. Gullans
AU - Victor V. Albert
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06730
UR - https://arxiv.org/abs/2610.06730
AB - The Eastin-Knill theorem rules out a universal set of transversal logical gates on any code that detects single-qubit errors. The theorem constrains one partition of the qubits at a time. We show that depth-one layers of few-qubit gates, each respecting its own partition, can together generate a universal logical gate set on an error-correcting code. Each logical gate generator is then a single depth-one layer followed by error correction of the same stabilizer code, with no magic-state distillation, code switching, gauge fixing, lattice surgery, or other gadgets. We show that such codes can be found by applying an entangling circuit to a lower-distance "seed" code admitting a depth-one non-Clifford gate and an appropriate "kernel" code. We construct 47 codes with depth-one generating sets that tolerate at least one faulty gate per layer, including a [[37,1,7]] and a [[59,1,9]] code, both of check weight at most eight.
ER -