Nested Quantum Walks Andrew M. Childs Stacey Jeffery Robin Kothari Frederic Magniez QIP 2014...
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Transcript of Nested Quantum Walks Andrew M. Childs Stacey Jeffery Robin Kothari Frederic Magniez QIP 2014...
![Page 1: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/1.jpg)
Nested Quantum Walks
Andrew M. Childs
Stacey Jeffery
Robin Kothari
Frederic Magniez
arXiv:1210.1199
arXiv:1302.7316
arX
iv:1
30
2.7
31
6arX
iv:1
21
0.1
19
9
SODA 2013
With arXiv:1302.3143,ICALP 2013
![Page 2: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/2.jpg)
QuantumAlgorithmica
![Page 3: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/3.jpg)
QuantumAlgorithmica
![Page 4: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/4.jpg)
Anatomy of a Quantum Walk
Setup
Update
Checking
Quantum Walk Algorithm
![Page 5: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/5.jpg)
Our First Result: Efficient Nested Checking
Update
Setup
![Page 6: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/6.jpg)
Application to Triangle Finding
![Page 7: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/7.jpg)
Aside: Query Complexity
![Page 8: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/8.jpg)
Application to Triangle Finding
![Page 9: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/9.jpg)
Second Contribution: Nested Updates
Setup
Checking
Update
![Page 10: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/10.jpg)
Application to k-Distinctness (k>2)
(6, 2, 12, 7, 2, 4, 1, 5, 11, 4, 5, 2, 9, 7, 6)
![Page 11: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/11.jpg)
Application to k-Distinctness (k>2)
![Page 12: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/12.jpg)
arXiv:1210.1199
arXiv:1302.7316
Summary of Results
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Random Walks
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Recipe for Quantum Walk Upper Bound
![Page 15: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/15.jpg)
Example: 2-Distinctness
![Page 16: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/16.jpg)
3-Distinctness Attempt
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c c
cc
3-Distinctness Attempt
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3-Distinctness Attempt
![Page 19: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/19.jpg)
3-Distinctness Attempt
![Page 20: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/20.jpg)
3-Distinctness Attempt
![Page 21: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/21.jpg)
Recipe for Quantum Walk with Nested Update
![Page 22: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/22.jpg)
![Page 23: 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.](https://reader038.fdocuments.us/reader038/viewer/2022110321/56649cdc5503460f949a718e/html5/thumbnails/23.jpg)
Recap
arXiv:1210.1199
arXiv:1302.7316
Thanks QIP Freaks!