Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.
You can change this under Settings & Account at any time.

No, thanks

Introduction to Quantum Computing

No description
by

Maggie Tse

on 7 May 2013

Comments (0)

Please log in to add your comment.

Report abuse

Transcript of Introduction to Quantum Computing

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
Full transcript