Quantum Information and Quantum Computation
Spring 2017
Physics 680-01
Class Number 51036
Tuesday and Thursday at 8:30-9:50am
Physics building, room P128
Office Hours: Tuesday and Thursday at 10-11 am
Instructors:
Vladimir Korepin
Office: Physics D-147
Office Hours: Thursday 10am-11am
Course description
The course will be based on graduate course of quantum mechanics. It will start with advanced quantum mechanics of open systems: master equation and Lindblad operators. Measurements theory [including POVM]; trace preserving completely positive maps [of density matrices]; as well as Bell inequalities will be explained.
Entanglement theory will start with measures of entanglement: von Neumann entropy, Renyi entropy and negativity.
Application of entanglement for analysis of dynamical systems will be explained, including entanglement Hamiltonian. Holographic approach for description of entanglement entropy also will be explained.
Information theory [starting from Shannon theorems about channel capacity] will be related to statistical physics and probability theory.
Algorithm theory: Shor's and Grover's quantum algorithms. Quantum cryptography also will be explained [BB84].
Different approaches to building of quantum computers: solid state [fractional quantum Hall effect and Josephson junction] and quantum optics [including optical lattices, cold atoms, ion traps and electromagnetically induced transparency]. Different architectures of quantum computation: circuit, adiabatic, topological quantum computation [including models of anyons] and measurement based quantum computation.
Application of ideas of quantum information to condensed matter also will be explained: topological phases of matter [including conformal field theory], Kitaev model, spin chains (VBS, Takhtajan-Babujan model), topological Kondo model and Sachdev-Ye-Kitaev model. Also generalized Gibbs ensemble will be explained. Simulation of models of mathematical physics in optical lattices [massive Thirring model, XXZ spin chain and Lieb-Linger model].
Computational physics also will be mentioned: MERA (and its relation to AdS) matrix product states and relation to algebraic Bethe ansatz.
New exactly solvable spin chains, emerging from quantum information [Shor-Movassagh, Fredkin] will be mentioned. Advances material form the program
Entanglement and Dynamical Systems
will be mentioned. Guest lecturers [theorists, mathematicians and experimentalists] will be invited.
Course requirements.
Graduate course of quantum mechanics.
Only enrolled students can attend. Attendance is expected. Home work has to be turned in time.
Learning outcomes
- Understanding of foundations of quantum mechanics: measurement theory, interaction with environment and the role of entanglement
- Understanding of quantum algorithms such as Shor's and Grover's
- Understand of information theory and their relation to statistical mechanics
- Understanding of boundary degrees of freedom and topological phases of matter (including Majorana fermions)
Mid Term Exam: March 9
Final Exam: May 10
Main textbooks
Entanglement in quantum spin chains
Isotropic XY model
XY model
Renyi entropy in XY model
Entanglement in AKLT model
AKLT on arbitrary graph
Power law violation of the area law by Peter Shor and Ramis Movassagh
Feather reading
Richard Feynman On quantum physics and computer simulation .
Quantum Mechanics: Photons Corpuscles of Light by Richard Feynman
Claude Shannon Father of the Information Age
ALAN TURING
popular lecture by Michael Freedman
Trends in Quantum Computing Research Reprint volume edited by Susan Shannon
MIT
Quantum Information Processing with Superconducting Circuits
D-wave
Anyons in one dimension
Quantum algorithm for partial search
Algebraic Bethe Ansatz and Tensor networks.
Web page of professor Wei : phy680; quantum
Quantum Information Processing
For your information.
If you have a physical, psychological, medical or learning disability that
may impact your course work, please contact Disability Support Services
(631) 632-6748. They will determine with you what accommodations are
necessary and appropriate. All information and documentation is
confidential.
Students requiring emergency evacuation are encouraged to discuss their
needs with their professors and Disability Support Services. For
procedures and information, go to the following web site
http://studentaffairs.stonybrook.edu/dss/
Disability Support Services, Academic Integrity and Critical Incident Management, see
http://www.stonybrook.edu/provost/facultyinfo/index.shtml
Last updated Thursday, 02-Feb-2017 10:36:03 EST