nested quantum walks andrew m. childs stacey jeffery robin kothari frederic magniez qip 2014...
TRANSCRIPT
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
QuantumAlgorithmica
QuantumAlgorithmica
Anatomy of a Quantum Walk
Setup
Update
Checking
Quantum Walk Algorithm
Our First Result: Efficient Nested Checking
Update
Setup
Application to Triangle Finding
Aside: Query Complexity
Application to Triangle Finding
Second Contribution: Nested Updates
Setup
Checking
Update
Application to k-Distinctness (k>2)
(6, 2, 12, 7, 2, 4, 1, 5, 11, 4, 5, 2, 9, 7, 6)
Application to k-Distinctness (k>2)
arXiv:1210.1199
arXiv:1302.7316
Summary of Results
Random Walks
Recipe for Quantum Walk Upper Bound
Example: 2-Distinctness
3-Distinctness Attempt
c c
cc
3-Distinctness Attempt
3-Distinctness Attempt
3-Distinctness Attempt
3-Distinctness Attempt
Recipe for Quantum Walk with Nested Update
Recap
arXiv:1210.1199
arXiv:1302.7316
Thanks QIP Freaks!