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.
Magic-state distillation with low overhead
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Hermitian weighted graphs enable universal exact realization of arbitrary complex QL-bits as real-spectrum eigenstates, with discrete {0, ±1, ±i} couplings dense in the state space.
pygridsynth provides O(log(1/ε)) ancilla-free Clifford+T synthesis with a new partial-decomposition technique for n≥3 reducing T-count constants to (21/8·4^n - 9/2·2^n + 9)log₂(1/ε) + o(log(1/ε)) and a mixed-synthesis approach empirically lowering error to ε²/(2n).
O3LS reduces space overhead by up to 46.7% and time overhead by up to 36% in lattice surgery while suppressing logical error rates by up to an order of magnitude compared with prior layout and scheduling approaches.
Constructions for universal quantum computation in the [[n,n-2,2]] error-detecting code detect single-gate errors at computation end, providing weak fault tolerance with reduced overhead versus full error correction.
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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Universal Complex Quantum-Like Bits from Hermitian Weighted Graphs
Hermitian weighted graphs enable universal exact realization of arbitrary complex QL-bits as real-spectrum eigenstates, with discrete {0, ±1, ±i} couplings dense in the state space.
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pygridsynth: A fast numerical tool for ancilla-free Clifford+T synthesis
pygridsynth provides O(log(1/ε)) ancilla-free Clifford+T synthesis with a new partial-decomposition technique for n≥3 reducing T-count constants to (21/8·4^n - 9/2·2^n + 9)log₂(1/ε) + o(log(1/ε)) and a mixed-synthesis approach empirically lowering error to ε²/(2n).
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O3LS: Optimizing Lattice Surgery via Automatic Layout Searching and Loose Scheduling
O3LS reduces space overhead by up to 46.7% and time overhead by up to 36% in lattice surgery while suppressing logical error rates by up to an order of magnitude compared with prior layout and scheduling approaches.
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Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code
Constructions for universal quantum computation in the [[n,n-2,2]] error-detecting code detect single-gate errors at computation end, providing weak fault tolerance with reduced overhead versus full error correction.