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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An algorithm converts topological data of 2D bulk stabilizer codes into 1D boundary subsystem codes via operator algebra and normal forms, enabling automatic generation of boundaries and defects demonstrated on toric, color, and other codes.
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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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Operator algebra and algorithmic construction of boundaries and defects in (2+1)D topological Pauli stabilizer codes
An algorithm converts topological data of 2D bulk stabilizer codes into 1D boundary subsystem codes via operator algebra and normal forms, enabling automatic generation of boundaries and defects demonstrated on toric, color, and other codes.