A new family of magic state distillation protocols based on logical Clifford error checking achieves near-linear asymptotic rate despite overhead exponent exceeding one, showing the quantities are not tightly coupled in the sublinear regime.
Constant-overhead magic state distillation
6 Pith papers cite this work, alongside 4 external citations. Polarity classification is still indexing.
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A borrowed-identity condition unifies magic-state distillation across Clifford levels and output types, recovering all known distance-2 factories in one search and enabling malleable parent circuits.
Graphical Algebraic Geometry creates universal diagrammatic languages for commutative algebras and affine varieties that also characterize the qudit ZH calculus for quantum computation.
Entanglement entropy bounds the variance of Trotter error downward, and magic drives the error kurtosis downward (Kur = α + βM, β<0 for large systems).
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.
Quantum sieving for SVP in dimension 400 needs ~10^13 physical qubits and ~10^31 years under optimistic assumptions, offering no practical speedup over classical methods.
citing papers explorer
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Asymptotic magic state distillation with almost linear rate
A new family of magic state distillation protocols based on logical Clifford error checking achieves near-linear asymptotic rate despite overhead exponent exceeding one, showing the quantities are not tightly coupled in the sublinear regime.
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Borrowed Identities: Malleable Distillation Factories and a Unified Numerical Search
A borrowed-identity condition unifies magic-state distillation across Clifford levels and output types, recovering all known distance-2 factories in one search and enabling malleable parent circuits.
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Graphical Algebraic Geometry: From Ideals and Varieties to Quantum Calculi
Graphical Algebraic Geometry creates universal diagrammatic languages for commutative algebras and affine varieties that also characterize the qudit ZH calculus for quantum computation.
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Taming Trotter Errors with Quantum Resources
Entanglement entropy bounds the variance of Trotter error downward, and magic drives the error kurtosis downward (Kur = α + βM, β<0 for large systems).
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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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On the practicality of quantum sieving algorithms for the shortest vector problem
Quantum sieving for SVP in dimension 400 needs ~10^13 physical qubits and ~10^31 years under optimistic assumptions, offering no practical speedup over classical methods.