HP-1 circuits achieve O(n) depth while preserving shift invariance and exponentially growing Fisher information, enabling numerical replacement of the QFT in Shor's algorithm with neural net classical post-processing.
Jozsa, Quantum factoring, discrete logarithms, and the hidden subgroup problem, Computing in Science & Engineering3, 34 (2001)
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$\mathcal{O}(n)$ alternative to Quantum Fourier Transform with efficient neural net classical post-processing
HP-1 circuits achieve O(n) depth while preserving shift invariance and exponentially growing Fisher information, enabling numerical replacement of the QFT in Shor's algorithm with neural net classical post-processing.