REVIEW 7 cited by
Logical Operators and Fold-Transversal Gates of Bivariate Bicycle Codes
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of surface codes even with near-term hardware. The question of how to implement logical gates fault-tolerantly for these codes is still open. We present new examples of high-rate bivariate bicycle (BB) codes with enhanced symmetry properties. These codes feature explicit nice bases of logical operators (similar to toric codes) and support fold-transversal Clifford gates without overhead. As examples, we construct $[[98,6,12]]$ and $[[162, 8, 12]]$ BB codes which admit interesting fault-tolerant Clifford gates. Our work also lays the mathematical foundations for explicit bases of logical operators and fold-transversal gates in quantum two-block and group algebra codes, which might be of independent interest.
Forward citations
Cited by 7 Pith papers
-
Quantum Codes with Addressable and Transversal Non-Clifford Gates
The authors construct qubit CSS codes with addressable transversal CCZ gates and introduce an addressable orthogonality framework that generalizes Bravyi-Haah triorthogonality.
-
Logical computation with canonical lifted product codes
Canonical lifted-product qLDPC codes admit a row/column cyclic logical basis that enables constant-seed modular surgery, compact extractors, and parallel Clifford and magic primitives.
-
Logical Spectroscopy: Lifted-Product Codes with Addressable Bases
Logical spectroscopy decomposes Abelian lifted-product codes into Frobenius packets, builds a complete addressable conjugate logical basis by finite-field algebra plus idempotent lifts, and supplies design diagnostics...
-
Transversal Logical Clifford gates on rotated surface codes with reconfigurable neutral atom arrays
The authors complete a transversal Clifford gate set on rotated surface codes by embedding a fold-transversal S gate inside a syndrome extraction round, with detector construction and numerical support.
-
Quantum Bicycle LDPC Codes with High $kd^2/n$ from Divisor-Driven Search
A polynomial-gcd reformulation of bicycle quantum LDPC codes enables an exact-distance search that finds [[66,20,7]] with kd^2/n=14.85 and proves an n=48 exclusion result.
-
Transversal architecture for megaquop-scale quantum simulation with neutral atoms
A neutral-atom co-designed 'transversal STAR' architecture could reach megaquop-scale Hamiltonian simulation with about 10,000 physical qubits at 1e-3 error rates, corresponding to over 1e6 to 1e7 T gates.
-
Multivariate Multicycle Codes for Complete Single-Shot Decoding
Koszul complexes built from four polynomial generators over cyclic group rings yield CSS codes with both X and Z metachecks, giving small, high-confinement, single-shot-decodable quantum codes.
Discussion (0). Continue with ORCID to comment.