Syllabus: Quantum computing - phys. yepez/Spring2013/Phys... · This course is aimed at graduate students…

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  • PHYS 711 Topics in Particles & Fields

    Syllabus: Quantum computing

    Jeffrey Yepez

    Department of Physics and AstronomyUniversity of Hawaii at ManoaWatanabe Hall, 2505 Correa RoadHonolulu, Hawaii 96822yepez@hawaii.edu

    (Dated: December 31, 2012)

    I. COURSE DESCRIPTION

    Topics in current theoretical research; e.g., quantum informational representations of field theories.

    This course is an introduction to quantum information theory (qubits, quantum gates, and qubit systems). It covers afew selected quantum algorithms, yet the emphasis of the course is on quantum simulation (i.e. quantum informationalrepresentations of quantum systems and quantum algorithms for computational physics).

    This course is aimed at graduate students in physics and astronomy, but is not restricted to particle physics. Auditingis permitted, and faculty members are welcome. There will be some weekly homework (just one problem per week),and students will be expected to give one lecture per semester (towards the end of the semester), on a quantum infor-mational topic of their choosing (such as reporting on a new development in the field, presenting a novel application,or reviewing a quantum algorithm not covered in the course). Each student will summarize her lecture in writtenjournal article form for turning in as a final project.

    Course material will involve analytical derivations predicting the behavior of engineered quantum systems. Selectedsystems will be treated numerically. Students should have facility with mathematical physics, as well as an interestin learning a symbolic mathematics language (such as Mathematica, Maple, or Sage).

    The class meets twice per week, Thursdays (1:30-2:45pm) and Fridays (10:00-11:15am).

    Prerequisites: TBA

    A. Prospectus

    1. Course overview

    2. Introduction to quantum information

    quantum bit (qubit) representations

    quantum gates as unitary matrices

    conservative quantum logic gates

    classical reversible computing

    quantum measurement

    3. Analytical quantum logic

    joint ladder operators

    joint number operators

    representations of strongly-correlated Fermi condensed matter

    pseudo-spin operators

    4. Archetypical quantum algorithms (quantum circuit model of quantum computation)

    Deutsch-Jozsa oracular algorithm

    Grovers search oracular algorithm

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    5. Path integral representation of relativistic quantum mechanics

    Feynman chessboard in 1+1 dimensions

    extension to 3+1 dimensions

    representation of covariant Lagrangian

    6. Quantum simulation (quantum lattice gas model of quantum computation)

    Dirac equation

    Schroedinger equation

    many-body simulations

    7. Nonlinear quantum systems for modeling nonlinear physics and soliton dynamics

    nonlinear Schroedinger equation

    Korteg de Vries equation

    Manakov equations

    Gross-Pitaevskii equation

    8. Introduction to ultracold quantum gases in optical lattices

    trapped BEC interferometry

    condensed matter simulation by analog

    9. Measurement-based, or one-way, model of quantum computation

    nonlinear simulation

    10. Introduction to quantum control theory

    quantum signal processing

    nonabelian Fourier transform

    11. Introduction to topological quantum computing

    introduction to knot theory

    quantum generalization of knot theory

    quantum algorithm for the Jones polynomial knot invariant

    topological quantum error correction

    12. Student presentations

    novel demonstration of quantum simulation

    review of a quantum algorithm

    B. Student learning outcomes

    We would like the students to acquire a working knowledge of quantum information theory, with a focus on quantumsimulation. The course is designed to bring graduate students and others to the level of professional understandingsuch that they may begin research at the forefront of quantum computing.

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    II. COURSE REQUIREMENTS AND EVALUATION

    Written problems and computational notebooks (assigned Thursday and due the following Thursday)

    III. METHOD OF INSTRUCTION

    In-class lectures (and internet-based video teleconferences, if needed)

    Mathematica demonstrations

    Class discussions

    Office hours (a 30 minute session per student) can be scheduled on a weekly basis by request

    IV. RESOURCES

    Lecture notes, additional resources, and weekly updates available online at:PHYS 711 Quantum computing website TBA

    In class demonstrations: Mathematica notebooks

    Additional reference textbooks:Eleanor G. Rieffel and Wolfgang H. Polak, Quantum Computing: A Gentle Introduction

    Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information

    http://www.phys.hawaii.edu/~yepez/PHYS711.html

    Course descriptionProspectusStudent learning outcomes

    Course requirements and evaluationMethod of instructionResources

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