[Slides from NoSQL Now! 2013 Lightning Talks] Grover’s Search is a famous Quantum Computing algorithm for searching random databases. It’s the fastest possible search algorithm in this universe. This is what Google will look like when it grows up! This is the second of 2 parts, explaing the algorithm in more detail.

1. The Fastest Possible
(NoSQL) Search Algorithm
Grover’s Search and the World of Quantum Computing, Part II
Daniel Austin
PayPal, Inc.
NoSQL Now! 2013
August 20, 2013
V1.6

2. Intro: Grover’s Search
• “Grover’s Search” is the name of a Quantum
Computing algorithm for searching random
databases. It’s the fastest possible search
algorithm in this universe, running in O(N^1/2)
(as opposed to O(N) in the macroverse)
• The challenge: Quantum Computing 101 in 10
minutes

3. Quantum Logic Gates
• Like classical logic
circuits, but additional
quantum logic gates
• Hadamard, Pi/8
(phase), CNOT, many
others
Images courtesy Wikipedia.com

4. Grover’s Search
Image courtesy Bernard Omer “Quantum Programming in QCL” 2007

5. Grover’s Code!
operator diffuse (qureg q) {
H(q); // Hadamard Transform
Not(q); // Invert q
CPhase(pi, q); // Rotate if q=1111..
!Not(q); // undo inversion
!H(q); // undo Hadamard Transform
}

6. Fastest Possible?? Prove It!
• Classical v. Quantum: O(N) v O(N^1/2) (!)
• Any alternate algorithm will have to run at least
as many iterations
• Requires an oracle – black box
• Complexity Theory: IS NP in BQP? (no)
• Number of iterations is optimal: π(N/k)1/2/4
• Proof can’t be contained in 1 slide! 

7. Summing Up
• Grover’s Search is the fastest possible search
algorithm, requiring π(N/k)1/2/4 iterations for k entries
• QC algorithms are based on gates and circuits that
define operators acting on the state of qubits
• QC algorithms are qualitatively different and can
perform non-classical feats of computation
• Rapid progress in the field right now
– 1st commercial implementations
– New Q-language, Quipper, released this year

8. Quantum Advice
Daniel Austin
PayPal, Inc.
daaustin@PayPal.com
@daniel_b_austin