Advanced Topics in Condensed Matter (450-0-1)

Instructors

Archana Kamal

Meeting Info

Technological Institute LG62: Tues, Thurs 2:00PM - 3:20PM

Overview of class

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 details a modern information-theoretic view of physical quantum systems combining ideas from open systems, quantum error correction and quantum measurement theory.

Registration Requirements

Graduate Quantum Mechanics (I and II) OR undergraduate quantum sequence (I and II)
OR special permission from the instructor. Primarily a solid grasp of time-dependent perturbation
theory and linear algebra is needed.

Evaluation Method

Homeworks - 60%
The students will typically get two weeks to submit their solutions.
- Final presentation - 20%
-Term paper - 20%
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 their review,
prepare a 15 minutes presentation (+5 minutes for questions) and submit a critique
written in standard APS journal format (please see: https://journals.aps.org/revtex ).

Class Materials (Suggested)

-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

Class Notes

List of Topics:
-Dirac notation and Hilbert spaces (finite and infinite dimensional)
-Qubits: Bloch sphere representation, classical driving and single-qubit unitaries, quantum
circuits, multi-qubit unitaries, universal quantum gates
-Quantum Electrodynamics: Jaynes-Cummings model, vacuum Rabi oscillations and
collapse and revival, dispersive readout in cavity/circuit QED.
- Open Quantum Systems (OQS): density matrix formalism, Kraus representation (quantum
channel description), quantum master equations, qubit decoherence (relaxation
and dephasing), resonance fluoroscence
-Entanglement: 2- and 3-qubit systems, loophole-free Bell tests, no-go theorems, quantum
teleportation and super-dense coding, projective measurements vs POVMs and
connections to OQS topics
-Quantum Information Theory: data compression and channel capacity theorems, entropy
and information
-Quantum Error Correction: classical vs quantum coding, Shor's 9-qubit code, stabilizer
formalism, fault tolerance, holographic codes