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Transversal non-Clifford gates for quantum LDPC codes on sheaves
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A major goal in quantum computing is to build a fault-tolerant quantum computer. One approach involves quantum low-density parity-check (qLDPC) codes that support transversal non-Clifford gates. In this work, we provide a large family of such codes. The key insight is to interpret the logical operators of qLDPC codes as geometric surfaces and use the intersection number of these surfaces to define the non-Clifford operation. At a more abstract level, this construction is based on defining the cup product on the chain complex induced from a sheaf.
Forward citations
Cited by 6 Pith papers
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Transversal non-Clifford gates on almost-good quantum LDPC and quantum locally testable codes
Almost-good qLDPC and qLTC codes admit nontrivial transversal logical multi-controlled-Z gates via cohomological cup products and two-way product-expanding punctured Reed–Solomon local codes.
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Finding diagonal logical gates in CSS codes and circuits
Diagonal logical gates of a CSS code or circuit are exactly the kernel of a pullback map on phase functions, and that kernel can be computed in cubic time.
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Hardware-tailored logical Clifford circuits for stabilizer codes
A discrete optimization over Clifford gauges compiles hardware-tailored logical Clifford circuits for arbitrary stabilizer codes, demonstrated on iceberg, twisted toric, and color codes.
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Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom
A triple homological product of good quantum LDPC codes achieves distance N^(2/3) with transversal CCZ gates and prepares N^(1/3) magic states in a single round.
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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.
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Native Non-Clifford Gates in Quantum LDPC Codes: Conditions, Synthesis, and Scaling Limits
The main theorem claiming constant-depth logical CCZ gates exist from many 'magic-friendly triples' has mutually inconsistent hypotheses, and its key local-implementation step is unproved.
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