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This research presents a novel architectural approach to quantum error correction by constructing codes that achieve universal transversal gate sets through depth-one layers, effectively bypassing the Eastin-Knill theorem's limitations without relying on magic-state distillation or code switching. By generating 47 specific codes with robust fault tolerance and low check weights, the study offers a significant pathway toward practical, scalable quantum computation architectures.
Qubit CSS codes with Universal Transversal Gates
arXiv:2610.06730v1 Announce Type: new 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.
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.
25 pages, 5 figures, 6 tables. The ancillary file this http URL lists all 110 codes with their stabilizers, logical operators, depth-one generators, seed and kernel codes, and coupling circuits
arXiv:2610.06730 [quant-ph]
(or arXiv:2610.06730v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.06730 arXiv-issued DOI via DataCite (pending registration)
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