The authors equip CSS codes with cup product structures to generate logical operators in the Λ-th Clifford hierarchy level on Λ code copies via constant-depth unitaries, and construct code families supporting this for any Λ.
arXiv preprint arXiv:2405.19412 (2024)
2 Pith papers cite this work. Polarity classification is still indexing.
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In variants of the 1D Ising model with power-law or all-to-all interactions for alpha less than 1, the topological ground state splitting scales as exp(-C L to the power (1+alpha)/2).
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Cups and Gates I: Cohomology invariants and logical quantum operations
The authors equip CSS codes with cup product structures to generate logical operators in the Λ-th Clifford hierarchy level on Λ code copies via constant-depth unitaries, and construct code families supporting this for any Λ.
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Effect of slowly decaying long-range interactions on topological qubits
In variants of the 1D Ising model with power-law or all-to-all interactions for alpha less than 1, the topological ground state splitting scales as exp(-C L to the power (1+alpha)/2).