Physics of Quantum Information

FALL 2018

Course Number: PHYS 6190

Course Description: This course aims to introduce the physical concepts behind the rapidly evolving field of quantum information processing, from a physicist's perspective. In the process, the course also conveys a modern information-theoretic view of physical quantum systems.


(3 CREDITS, 3 CONTACT HOURS/WEEK)

Instructor: ARCHANA KAMAL

Meeting Times: Tuesday/Thursday, 9:30 - 10:45 a.m.

Location: Ball 412; Office Hours: Tuesday/Thursday,11:30 a.m. - 1:00 p.m.

Prerequisites*: Undergraduate quantum mechanics I and II (or special permission from the instructor).

*Change in preqrequisites to undergraduate quantum mechanics. To aid the conceptual groundwork, hour-long extra tutorials will be arranged for the students in the first 6 weeks of the semester (in addition to regular office hours).

Grading Scheme:

  • Homeworks - 60%

  • Final presentation - 20%

  • Term paper - 10%

  • Class participation - 10%

PHYS 6190 Tutorials

Tutor: EMERY DOUCET (Office: OG 29)

Meeting Times: Friday, 11:00 a.m. - 12 p.m.

Schedule:

  • 09/13/2018: Second Quantization

  • 09/14/2018: Quantization of Electromagnetic Fields

  • 09/21/2018: Gauge Invariance of Quantum Mechanics

  • 09/28/2108: Atom-Field Interaction

  • 10/05/2018: Interaction Picture

  • 10/12/2018: Dyson series

Course Policy

Since this is an advanced graduate course with no exams, the students are expected to keep up with the homeworks and reading. Homework exercises are designed to both supplement and extend the details covered in the lecture through (i) demonstrating the applications of general concepts to specific research problems, and/or (ii) elucidating a new dimension of a given concept in question (not covered in the lecture explicitly). To facilitate this mode of learning, the students are strongly encouraged to complete the assigned reading as part of the homework, although no grade will be assigned for reading problems.

Homeworks: All problem sets (~ 5 in total) will be posted in the shared course folder located on UML one drive (http://onedrive.uml.edu/). The students will typically get 2 weeks to submit their solutions. No late homeworks will be accepted.

Final presentation and term paper: A list of contemporary journal articles will be made available to students. Each student should choose one of the research papers for in-depth study, and based on his/her review, prepare a 10-15 minutes presentation (+5 minutes for questions) and submit a critique written in standard APS journal format (please see: https://journals.aps.org/revtex ).

Academic Integrity: Collaborating with other students on homeworks is encouraged. However, the collective wisdom developed in the process should not preclude individual comprehension. Each student should hand in separate homeworks, (ideally) written independently of other group members.

All sources used in the course of term-paper research should be cited appropriately. Any suspected cheating or other instance of academic dishonesty will be dealt with as per the university policy (please read: https://www.uml.edu/Catalog/Graduate/Policies/AcademicIntegrity.aspx ).

Tentative List of Topics

  • Dirac notation and Hilbert spaces (finite and infinite dimensional)

  • Electromagnetic vacuum: Quantum harmonic oscillator, vacuum fluctuation, quantum-limited amplification, squeezing

  • Quantum electrodynamics: Jaynes-Cummings model, vacuum Rabi oscillations and collapse and revival, dispersive readout in cavity/circuit QED.

  • Qubits: Bloch sphere representation, Circuit quantization

  • Coupled qubits: Entanglement in 2- and 3-qubit systems, loophole-free Bell tests, No-go theorems

  • Quantum teleportation and Super-dense coding

  • Quantum measurements: projective measurements, POVMs

  • Open systems: Density matrix formalism and quantum master equation, damped quantum oscillator and quantum regression theorem, qubit decoherence (relaxation and dephasing), resonance fluoroscence

  • Quantum error correction: Quantum circuits, single-and multi-qubit unitaries, universal quantum gates, classical vs quantum coding, Shor's 9-qubit code.

  • Recent advances*: Different quantum information platforms, teleportation using squeezed states, quantum annealing etc.

*Specific topics will be chosen as per the availability of time.

Reference Texts

This is only a representative, not exhaustive, list of books. Given the broad span of topics covered in the course, the instructor will indicate specific texts during respective lectures.

  • Quantum Noise: C. W. Gardiner and P. Zoller

  • Quantum Statistical Properties of Radiation: W. H. Louisell

  • Quantum Optics: D. F. Walls and G. J. Milburn

  • The Theory of Open Quantum Systems: H. -P. Breuer and F. Petruccione

  • Quantum Computation and Quantum Information: M. A. Nielsen and I. L. Chuang