The document discusses Grover's search algorithm, a quantum computing method that offers the fastest possible search capabilities with a complexity of O(n^1/2). It highlights advancements in quantum computing, including the ability to read 16 qubits, achievements in quantum entanglement, and the emergence of the first commercially available quantum computer. The overall message conveys that quantum computing is advancing rapidly and poses unique computational abilities that classical computing cannot match.

1. The Fastest Possible Search
Algorithm
Sep, 2011
Daniel Austin
Technical Staff
PayPal, Inc.
Surge 2011 Conference
September 28, 2011

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
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3. QUANTUM COMPUTING 101
• Describes quantum logical processes
analogous to classical computing
• Multivariate Logic
– Bits: yes|| no
– Qubits: yes||no||maybe
– Probabilistic results instead of hard answers
• Quantum “Weirdness”
– Teleportation, superdense coding, non-
causal computations, multiversal
parallelism, entanglement, cryptography
R. P. Feynman, “Quantum mechanical computers”, Optics News, February 1985, 11, p. 11
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4. CURRENT STATE OF QUANTUM
COMPUTATIONAL PLAY
• We can now read and write 16 qubits
• Transient spintronics experiments ~ 2000 ms!
• Teleportation: intercontinental, ~ 5000 KM
• IBM demonstrates true entanglement 2006
• RSA algorithm Cracked 2008
• Yale demonstrates 1st quantum chip 2009
• D-Wave Announces the first commercially
available „quantum computer‟ May 2011!
– (But does it really work??)
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5. QUANTUM LOGIC GATES
• Like classical logic
circuits, but
additional quantum
logic gates
• Hadamard, Pi/8
(phase), CNOT,
many others
Images courtesy Wikipedia.com
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6. GROVER’S SEARCH
Image courtesy Bernard Omer “Quantum Programming in QCL” 2007
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7. 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
}
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8. 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
• Proof can‟t be contained in 1 slide! 
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9. SUMMING UP
Quantum Computing is real and coming
soon to a computer near you
QC algorithms are qualitatively different
and can perform non-classical feats of
computation
Rapid progress in the field right now
– 1st commercial implementations
– Quantum cryptography, teleportation,
spintronics all featured in Nature this week!
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10. QUANTUM ADVICE
I think I can safely say that nobody understands
quantum mechanics. ... Do not keep saying to yourself,
if you can possibly avoid it, 'But how can it be like that?'
because you will get 'down the drain', into a blind alley
from which nobody has yet escaped. Nobody knows how
it can be like that.
Richard Feynman, The Character of Physical Law
Daniel Austin
PayPal, Inc.
daaustin@PayPal.com
@daniel_b_austin
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