PHYS 711 — Topics in Particles & Fields
Syllabus: Quantum computing
Jeffrey Yepez
Department of Physics and AstronomyUniversity of Hawai’i at ManoaWatanabe Hall, 2505 Correa RoadHonolulu, Hawaii [email protected]
(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
Grover’s 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 Jone’s 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”
