A new in-situ scheme prepares logical magic states inside arbitrary CSS qLDPC codes using only syndrome-extraction ancillas, with simulations on the [[144,12,12]] BB code and [[225,9,4]] hypergraph-product code showing injection error rates around 10^{-3} or lower under depolarizing and asymmetric噪声
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Above a critical noise strength, operator scrambling in random circuits is suppressed leading to classical simulability; below it, simulation stays exponentially hard.
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 deterministic recursive quantum circuit prepares antisymmetric states for η fermions in N orbitals with O(η²√N) T-gates and O(√N) dirty ancillas, outperforming sorting methods for η ≲ √N.
A cut-cat state syndrome extraction protocol for CSS codes reduces simultaneous qubit count by more than half and improves two-qubit gate efficiency over flag-based approaches for larger code distances.