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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3 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 3representative citing papers
Mutual information between non-contractible regions on the torus fully classifies long-range nonstabilizerness for toric-code states but leaves a finite subset undetected in the doubled-Fibonacci string-net model.
Ancilla-mediated protocols enable deterministic universal logical gates on any stabilizer code without ancilla consumption or code modification.
citing papers explorer
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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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Long-range nonstabilizerness of topologically encoded states from mutual information
Mutual information between non-contractible regions on the torus fully classifies long-range nonstabilizerness for toric-code states but leaves a finite subset undetected in the doubled-Fibonacci string-net model.
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Stabilizer Code-Generic Universal Fault-Tolerant Quantum Computation
Ancilla-mediated protocols enable deterministic universal logical gates on any stabilizer code without ancilla consumption or code modification.