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The Hidden Subgroup Problem - Review and Open Problems
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The Hidden Subgroup Problem - Review and Open Problems
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An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it easier to absorb the background necessary to begin research on the Hidden Subgroup Problem. Proofs are provided which give very concrete algorithms and bounds for the finite abelian case with little outside references, and future directions are provided for the nonabelian case. This summary is current as of October 2004.
Forward citations
Cited by 3 Pith papers
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Optimal Stabilizer Testing and Learning with Limited Quantum Memory
Stabilizer testing requires Θ(n-k) copies and non-adaptive learning Θ(n²/k) copies with k-qubit memory, removing the testing-learning separation.
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Quantum algorithm for Clifford multiplication
Under amplitude encoding, Clifford geometric product reduces to cocycle-twisted convolution and is realized by a polylog-size quantum circuit with postselection on the trivial Walsh character.
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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.
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