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:2408.13130 (2024)
3 Pith papers cite this work. Polarity classification is still indexing.
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Tricycle codes generalize bicycle codes to three homological dimensions, enabling constant-depth CCZ circuits and single-shot magic state generation with circuit-level thresholds above 0.5% and low error rates at block lengths of 50-100 qubits.
A new code surgery protocol measures t logically disjoint Pauli products on any LDPC code using O(t ω (log t + log³ω)) ancillas in O(d) time while preserving LDPC property and fault distance.
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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Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes
Tricycle codes generalize bicycle codes to three homological dimensions, enabling constant-depth CCZ circuits and single-shot magic state generation with circuit-level thresholds above 0.5% and low error rates at block lengths of 50-100 qubits.
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Parallel Logical Measurements via Quantum Code Surgery
A new code surgery protocol measures t logically disjoint Pauli products on any LDPC code using O(t ω (log t + log³ω)) ancillas in O(d) time while preserving LDPC property and fault distance.