superposition Quantum Mechanics Physics Computer

Science A Presentation by Maggie Tse Quantum Computing

and

Quantum Information Algorithms Condensed Matter

Physics AMO Physics 1982 2010 1994 1997 Classical Computing bit = 1 or 0 Quantum Computing quantum bit = qubit can exist in a superposition of states n bits can represent any integer 0 to 2^n - 1 n bits can represent all integers 0 through 2^n - 1 simultaneously! |0> |1> |0> |1> measurement Richard Feynman proposes the idea of creating machines based on the laws of QM instead of classical physics http://www.nndb.com/people/584/000026506/ David Deutsch creates the "quantum Turing machine", demonstrating that quantum circuits are universal

(see: Church-Turing thesis) http://www.3quarksdaily.com/3quarksdaily/2011/11/a-brilliant-and-exhilarating-and-profoundly-eccentric-book.html Shor's Algorithm Grover's Algorithm What is a quantum computer? how do we manipulate these qubits? Classical Gates logic operators such as OR, AND, NOR, NAND, etc. take input bits, performs operation, gives output bit Quantum Gates unitary transformations quantum bits + quantum gates = ... but what's the catch? Artificial

Intelligence Quantum

Information

Theory amplitudes are not accessible! shuffle the amplitudes universal: any other logic gate can be made from just NAND gates (similarly for NOR) David Deutsch: there exists a set of universal quantum gates Hadamard gate Factoring Searching controlled-NOT gate pi/8 gate classical: quantum: general number field sieve Shor's algorithm Cryptography RSA works because factoring large numbers is hard quantum cryptography:

since measurement collapses a system,

eavesdroppers can be detected classical: quantum: quadratic speedup! quantum computers are governed by QM but can also teach us about QM

by simulating quantum systems

better than a classical computer Optical Photons Ion trapping Superconductors Topological Insulators Cavity QED N-V Centers in Diamond quantum AI? What we need to build a quantum computer: 1) a two-level quantum system = a qubit

2) a way to have the qubit evolve in a controlled way

3) a way to prepare qubits in specific initial states

4) a way to measure the output of the circuit A coin good bit: has two states

bad qubit: cannot remain in a superposition very long A nuclear spin good qubit: superpositions of being aligned/antialigned with

external magnetic field can last days

bad bit: coupling to world is small, cannot measure the

orientation of single nuclei Grover's Algorithm Qubits from hyperfine spin state of a single atom

and lowest level vibrational modes of collection of atoms use laser cooling to put atoms in motional ground state Operations - single-qubit operation done with short laser pulses

- same for swapping spin and phonon qubits - can perform controlled-gate operations similarly Drawbacks - phonon lifetimes are short

- cooling to motional ground state is hard N-V center: a point defect in diamond qubit: electron spin localized at the N-V center photoluminescence of N-V centers can be exploited qubit: photon polarization operations: phase shifters, beamsplitters, nonlinear Kerr media pros: easy to create and manipulate single photons

cons: hard to make two photons interact - materials that are insulators inside with a conducting surface

- superconductivity can be induced on surface

- potential host of Majorana fermions further reading: http://research.microsoft.com/apps/video/dl.aspx?id=154238

http://en.wikipedia.org/wiki/Topological_quantum_computer

http://en.wikipedia.org/wiki/Majorana_fermion image source:

Nielsen and Chuang, Quantum Computing and Quantum Information image source:

Nielsen and Chuang, Quantum Computing and Quantum Information further reading:

http://www.dwavesys.com/en/dw_homepage.html

http://web.physics.ucsb.edu/~martinisgroup/classnotes/finland/LesHouchesJunctionPhysics.pdf Majorana fermions obey statistics that allow them to be used as anyons for topological quantum computing charge qubits:

use superconductors coupled through Josephson Junctions flux qubits:

micrometer sized loops of superconducting material interrupted with Josephson Junctions image source:

http://upload.wikimedia.org/wikipedia/en/0/04/Flux_Qubit_-_Holloway.jpg image source:

http://upload.wikimedia.org/wikipedia/en/0/07/Cooper_pair_box_circuit.png effectively zero-resistance at certain temperatures

currents of superfluid of Cooper pairs Main reference used:

Nielsen and Chuang, Quantum Computing and Quantum Information for W3072, Spring 2013, Professor Kim

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# Introduction to Quantum Computing

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