Quantum Information and Quantum Computation

Spring 2017
Physics 680-01
Class Number 51036

Tuesday and Thursday at 8:30-9:50am

Physics building, room P128
  • Office Hours: Tuesday and Thursday at 10-11 am
  • Instructors: Vladimir Korepin
    Office: Physics D-147

    Office Hours: Thursday 10am-11am

    Course description

    The course will be based on graduate course of quantum mechanics. It will start with advanced quantum mechanics of open systems: master equation and Lindblad operators. Measurements theory [including POVM]; trace preserving completely positive maps [of density matrices]; as well as Bell inequalities will be explained. Entanglement theory will start with measures of entanglement: von Neumann entropy, Renyi entropy and negativity. Application of entanglement for analysis of dynamical systems will be explained, including entanglement Hamiltonian. Holographic approach for description of entanglement entropy also will be explained.
    Information theory [starting from Shannon theorems about channel capacity] will be related to statistical physics and probability theory.
    Algorithm theory: Shor's and Grover's quantum algorithms. Quantum cryptography also will be explained [BB84].
    Different approaches to building of quantum computers: solid state [fractional quantum Hall effect and Josephson junction] and quantum optics [including optical lattices, cold atoms, ion traps and electromagnetically induced transparency]. Different architectures of quantum computation: circuit, adiabatic, topological quantum computation [including models of anyons] and measurement based quantum computation.
    Application of ideas of quantum information to condensed matter also will be explained: topological phases of matter [including conformal field theory], Kitaev model, spin chains (VBS, Takhtajan-Babujan model), topological Kondo model and Sachdev-Ye-Kitaev model. Also generalized Gibbs ensemble will be explained. Simulation of models of mathematical physics in optical lattices [massive Thirring model, XXZ spin chain and Lieb-Linger model].
    Computational physics also will be mentioned: MERA (and its relation to AdS) matrix product states and relation to algebraic Bethe ansatz.
    New exactly solvable spin chains, emerging from quantum information [Shor-Movassagh, Fredkin] will be mentioned. Advances material form the program Entanglement and Dynamical Systems will be mentioned. Guest lecturers [theorists, mathematicians and experimentalists] will be invited.

    Course requirements.

    Graduate course of quantum mechanics. Only enrolled students can attend. Attendance is expected. Home work has to be turned in time.

    Learning outcomes

    Mid Term Exam: March 9

    Final Exam: May 10

    Main textbooks

    Entanglement in quantum spin chains

  • Isotropic XY model
  • XY model
  • Renyi entropy in XY model
  • Entanglement in AKLT model
  • AKLT on arbitrary graph
  • Power law violation of the area law by Peter Shor and Ramis Movassagh
  • Feather reading

  • Richard Feynman On quantum physics and computer simulation .
  • Quantum Mechanics: Photons Corpuscles of Light by Richard Feynman
  • Claude Shannon Father of the Information Age
  • popular lecture by Michael Freedman
  • Trends in Quantum Computing Research Reprint volume edited by Susan Shannon
  • MIT
  • Quantum Information Processing with Superconducting Circuits
  • D-wave
  • Anyons in one dimension
  • Quantum algorithm for partial search
  • Algebraic Bethe Ansatz and Tensor networks.
  • Web page of professor Wei : phy680; quantum
  • Quantum Information Processing
    For your information. If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

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    Last updated Thursday, 02-Feb-2017 10:36:03 EST