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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Exact repair achieves the same optimal storage-bandwidth point as functional repair in entanglement-assisted regenerating codes for d ≥ 2k-2.
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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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Simultaneously Minimizing Storage and Bandwidth Under Exact Repair With Quantum Entanglement
Exact repair achieves the same optimal storage-bandwidth point as functional repair in entanglement-assisted regenerating codes for d ≥ 2k-2.