Generalizes QFT to semisimple algebras and gives poly(n, log d, log(1/ε)) gate algorithms that approximate the transform to error (d^{-1/2} + ε) poly(|A|) on partition, Brauer, and walled Brauer algebras when d is large.
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A space-efficient quantum ECDLP algorithm uses 5n + 4⌊log₂n⌋ + O(1) logical qubits and O(n³) Toffoli gates, lowering the 256-bit estimate from 2124 to 1333 qubits.
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Efficient Quantum Fourier Transforms For Semisimple Algebras
Generalizes QFT to semisimple algebras and gives poly(n, log d, log(1/ε)) gate algorithms that approximate the transform to error (d^{-1/2} + ε) poly(|A|) on partition, Brauer, and walled Brauer algebras when d is large.
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Space-Efficient Quantum Algorithm for Elliptic Curve Discrete Logarithms with Resource Estimation
A space-efficient quantum ECDLP algorithm uses 5n + 4⌊log₂n⌋ + O(1) logical qubits and O(n³) Toffoli gates, lowering the 256-bit estimate from 2124 to 1333 qubits.