# 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