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Nested Quantum Walks Andrew M. Childs Stacey Jeffery Robin Kothari Frederic Magniez QIP 2014 arXiv:1210.1199 arXiv:1302.7316 arXiv:1210.1199 SODA 2013.

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Presentation on theme: "Nested Quantum Walks Andrew M. Childs Stacey Jeffery Robin Kothari Frederic Magniez QIP 2014 arXiv:1210.1199 arXiv:1302.7316 arXiv:1210.1199 SODA 2013."— Presentation transcript:

1 Nested Quantum Walks Andrew M. Childs Stacey Jeffery Robin Kothari Frederic Magniez QIP 2014 arXiv: arXiv: arXiv: SODA 2013 With arXiv: , ICALP 2013 arXiv: arXiv:

2 Quantum Algorithmica

3 Quantum Algorithmica

4 Anatomy of a Quantum Walk Setup Update Checking Quantum Walk Algorithm

5 Our First Result: Efficient Nested Checking Update Setup

6 Application to Triangle Finding

7 Aside: Query Complexity

8 Application to Triangle Finding

9 Second Contribution: Nested Updates Setup Checking Update

10 Application to k-Distinctness (k>2) (6, 2, 12, 7, 2, 4, 1, 5, 11, 4, 5, 2, 9, 7, 6)

11 Application to k-Distinctness (k>2)

12 arXiv: arXiv: Summary of Results

13 Random Walks

14 Recipe for Quantum Walk Upper Bound

15 Example: 2-Distinctness

16 3-Distinctness Attempt

17 c c cc

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21 Recipe for Quantum Walk with Nested Update

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23 Recap arXiv: arXiv: Thanks QIP Freaks!


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