* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Syllabus: Quantum computing - University of Hawaii Physics and
Quantum chromodynamics wikipedia , lookup
Quantum dot cellular automaton wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Double-slit experiment wikipedia , lookup
Wave–particle duality wikipedia , lookup
Bell test experiments wikipedia , lookup
Bohr–Einstein debates wikipedia , lookup
Quantum decoherence wikipedia , lookup
Probability amplitude wikipedia , lookup
Delayed choice quantum eraser wikipedia , lookup
Basil Hiley wikipedia , lookup
Renormalization wikipedia , lookup
Measurement in quantum mechanics wikipedia , lookup
Particle in a box wikipedia , lookup
Density matrix wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Topological quantum field theory wikipedia , lookup
Renormalization group wikipedia , lookup
Path integral formulation wikipedia , lookup
Copenhagen interpretation wikipedia , lookup
Quantum electrodynamics wikipedia , lookup
Coherent states wikipedia , lookup
Scalar field theory wikipedia , lookup
Quantum entanglement wikipedia , lookup
Quantum field theory wikipedia , lookup
Bell's theorem wikipedia , lookup
Quantum dot wikipedia , lookup
Hydrogen atom wikipedia , lookup
Quantum fiction wikipedia , lookup
Many-worlds interpretation wikipedia , lookup
Orchestrated objective reduction wikipedia , lookup
EPR paradox wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Quantum computing wikipedia , lookup
Interpretations of quantum mechanics wikipedia , lookup
Quantum teleportation wikipedia , lookup
Quantum key distribution wikipedia , lookup
Quantum group wikipedia , lookup
Quantum machine learning wikipedia , lookup
Quantum state wikipedia , lookup
History of quantum field theory wikipedia , lookup
Canonical quantization wikipedia , lookup
PHYS 711 — Topics in Particles & Fields Syllabus: Quantum computing Jeffrey Yepez Department of Physics and Astronomy University of Hawai’i at Manoa Watanabe Hall, 2505 Correa Road Honolulu, Hawaii 96822 [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 a few selected quantum algorithms, yet the emphasis of the course is on quantum simulation (i.e. quantum informational representations 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. Auditing is 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 informational 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 written journal article form for turning in as a final project. Course material will involve analytical derivations predicting the behavior of engineered quantum systems. Selected systems will be treated numerically. Students should have facility with mathematical physics, as well as an interest in 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 2 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 quantum simulation. The course is designed to bring graduate students and others to the level of professional understanding such that they may begin research at the forefront of quantum computing. 3 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”