The Fastest Possible (NoSQL) Search AlgorithmThe Fastest Possible (NoSQL) Search Algorithm

Grover’s Search and the World of Quantum Computing, Part IIGrover’s Search and the World of Quantum Computing, Part II

Daniel AustinPayPal, Inc.

NoSQL Now! 2013August 20, 2013V1.6

Intro: Grover’s SearchIntro: 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

Quantum Logic GatesQuantum Logic Gates

• Like classical logic circuits, but additional quantum logic gates

• Hadamard, Pi/8 (phase), CNOT, many others

Images courtesy Wikipedia.com

Grover’s SearchGrover’s Search

Image courtesy Bernard Omer “Quantum Programming in QCL” 2007

Grover’s Code!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

}

Fastest Possible?? Prove It!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!

Summing Up 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

Quantum AdviceQuantum Advice

Daniel AustinPayPal, Inc.daaustin@PayPal.com@daniel_b_austin