|QUANTUM COMPUTING>

NOON SILK - 11/11/11

Quick overview, what is QC?Computing quantumly

Classical Quantum

Datatype binary: 1, 0, “bit”

“qubit”, measured value of 1,0

Operators AND, OR, NOT, etc.

CNot, Rotations, anything valid

Space = bits. 256 bits? 256 bits.

2^qubits, 256 qubits? 2^256 space. (complex)

“Measurement”

= space = qubits (256 bits; *collapses*)

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Okay, where are they?

Here!• CQC^2T: NV Cavity, Silicon-

Phosphorus, Superconducting Grid• Adrea Morello and Andrew Dzurak

won the 2011 Eureka Prize

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Purpose?

SpeedupEnergy reduction for large

computational tasksSimulation of systems that would

otherwise be intractable (quantum chemistry)

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Okay, research areas?

Implementation– Engineering (as discussed), nv-cavity,

others– Optics (Aaronson)

• Error control:– Threshold theorem, stabilizers, Clifford

gates.– Central idea: How to implement the

algorithms with the noisy reality of … reality?

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research areas cont …

Algorithms– Hilbert spaces, linear algebra,

(quantum) complexity theory– Factoring, Search, Systems of linear

equations (Ax = b)– Higher-dimensional models (qutrit,

qudit, interesting?)– Sampling distributions (QMC, MCMC)

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research areas cont …

Programming– Quantum programming languages,

circuit models, computation models (quantum von Neumann model, QRAM), lamba calculi

– Compilation: Solovay-Kitaev: realisation of any Unitary with some universal gate set.

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research areas cont …

Information Theory– Entanglement, How to measure it? What

affect does it have, algorithmically?– Entropy, is it a good way to look at

things?– (Black holes as QCs? Seth Lloyd)– (Energy) Teleportation, input energy at

A, get it at B.– Game Theory, solution to Byzantine

Generals problem

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research areas cont …

Cryptography– Quantum Money, can we make some?

Can it be unforgeable?– Algorithms to replace RSA? AES?

SHA? (mostly, these are not quantum).

– QKD, (requires classical channel, often broken)

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research areas cont …

“Foils”– Interesting, adjustments to quantum

theory, or other physics, then consider relevance to complexity theory and bounds, etc.

– I.e. QC w/ closed time-like curves (if exist, QC=CC)

– Lends itself to philosophy

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Summary

• Almost everything that is classical can be reconsidered under quantum

• It is fun, get involved if you like!

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