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!