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General Issues• Constructing initial su<strong>per</strong>position may be nontrivial• Efficient FT over group may not be known• Group may not be known (e.g., factoring)

Reducing quantum computations To elementary unitary operations ...

Chapter 3 â Chip Planning VLSI Physical Design: From Graph ...

McKay's Canonical Graph Labeling Algorithm - Department of ...

Decision diagram method for calculation of pruned ... - IEEE Xplore

Chapter 6 â Detailed Routing VLSI Physical Design: From Graph ...

General Issues• Constructing initial su<strong>per</strong>position may be nontrivial• Efficient FT over group may not be known• Group may not be known (e.g., factoring)

Issues for Non-Abelian case:Non-Abelian Groups• Non-unique Fourier Transform• Efficient implementation of FT• Determining subgroup from sampling of FT• In general no shift-invariant basis

Page 1 and 2: The Hidden Subgroup ProblemKetan Pa
Page 3 and 4: Groups• Group (G,+): closure, ass
Page 5 and 6: Quantum Fourier Transformn-qubit Qu
Page 7 and 8: Simon’s AlgorithmStep 0) Prepare
Page 9 and 10: Integer FactoringInteger factoring
Page 11 and 12: Order Finding Algorithm (cont.)Step
Page 13 and 14: More Group TheoryRepresentation ρ(
Page 15: General HSP AlgorithmStep 1) Create
Page 19 and 20: Results for Non-Abelian Case• Sol

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