USCDornsife
Dana and David Dornsife
College of Letters, Arts and Sciences
Phys. 660
Quantum Information Science and Many-Body Physics,
3 Units
Term—Day—Time
Location: Physical address and/or course-related URLs, etc.
Instructor: Paolo Zanardi
Office: SSC 225
Office Hours: Any time by appointment
Contact Info: zanardi@usc.edu, phone: 740-4649
Teaching Assistant:
Office:
Office Hours:
Contact Info: Email, phone number (office, cell), Skype, etc.
IT Help: Group to contact for technological services, if applicable.
Hours of Service:
Contact Info: Email, phone number (office, cell), Skype, etc.
Course Description
Eighteen years have passed since the discovery of the fast factoring quantum algorithm by Peter
Shor triggered the spectacular explosion of the Quantum Information Science (QIS) field. The
momentum of that explosion is far from fading away and the field is still quite rapidly evolving
and it by now it comprises somewhat specialized sub-areas.
This Course will focus on the most active of those subareas: the intersection between QIS and
many-body physics. QIS taught us that information is physical e.g., processing information
quantumly might be better than doing that classically. Similarly physics is informational i.e.,
physical states always encode for some sort of information and their dynamics can be regarded as
naturally enacted algorithm. In particular this implies that several of the conceptual as well as
technical tools developed by the QIS com munity could be of big value in addressing important
questions concerning complex, interacting many body systems.
Learning Objectives
The goal of this advanced Course is to bring you right at the frontier of the exciting research field
where Quantum Information Theory meets statistical mechanics and many body physics. The
student will be also introduced to fairly advanced techniques in mathematical physics
Prerequisite(s): Quantum Mechanics 438a,b; mathematical methods of theoretical physics
Recommended Preparation: quantum computation, Statistical Mechanics, Solid State Physics
Course Notes
Will be posted on the Black Board as well as references to relevant research papers
Required Readings and Supplementary Materials
[0], Quantum Computation and Quantum Information, M. Nielsen and I. Chuang
(Cambridge Series on Information and the Natural Sciences)
[1] Quantum Simulation of Time-Dependent Hamiltonians and the Convenient Illusion of
Hilbert Space, David Poulin, Angie Qarry, Rolando Somma, and Frank Verstraete
Phys. Rev. Lett. 106, 170501 (2010)
[2] Colloquium: Area laws for the entanglement entropy J. Eisert, M. Cramer, and M. B. Plenio,
Rev. Mod. Phys. 82, 277 (2010)
[3] Entanglement in many-body systems, Luigi Amico, Rosario Fazio, Andreas Osterloh, and
Vlatko Vedral, Rev. Mod. Phys. 80, 517, (2008)
[4] Quantum Entanglement in Random Physical States
Alioscia Hamma, Siddhartha Santra, and Paolo Zanardi
Phys. Rev. Lett. 109, 040502, (2012)
[5] Information-Theoretic Differential Geometry of Quantum Phase Transitions
Paolo Zanardi, Paolo Giorda, and Marco Cozzini, Phys. Rev. Lett. 99, 100603, (2007)
[6] Quantum Critical Scaling of the Geometric Tensors, Lorenzo Campos Venuti and Paolo
Zanardi, Phys. Rev. Lett. 99, 095701, (2007)
[7] Entanglement and the foundations of statistical mechanics, S. Popescu, A. J. Short, and A.
Winter, Nat. Phys. 2 , 754 (2006).
[8] Quantum mechanical evolution towards thermal equilibrium
Noah Linden, Sandu Popescu, Anthony J. Short, and Andreas Winter
Phys. Rev. E 79, 061103, (2009)
[9] Exact Infinite-Time Statistics of the Loschmidt Echo for a Quantum Quench
Lorenzo Campos Venuti, N. Tobias Jacobson, Siddhartha Santra, and Paolo Zanardi
Phys. Rev. Lett. 107, 010403
Description and Assessment of Assignments
What kind of work is to be done and how should it be completed, i.e. how the learning outcome will be
assessed. Include any assessment and grading rubrics to be used.
Grading Breakdown
The Final Grade will be based upon:
A) Class participation. In principle I don’t plan to give regular HWs but we’ll have in-class
problem solving sessions [20%]
B) Final Exam a chalkboard/slide presentation (30’) about a class-related subject you pick [80%]
Exams will be held over the last week of the class
Assignment Submission Policy
Take home exercises will be assigned on a non-regular basis
Course Schedule: A Weekly Breakdown
Syllabus for COURSE-ID, Page 2 of 4
Provide a detailed course calendar that provides a thorough list of deliverables—readings, assignments,
examinations, etc., broken down on at least a weekly basis. The format may vary, but the content must
include:
 Subject matter (topic) or activity
 Required preparatory reading, or other assignments (i.e., viewing videos) for each class
session, including page numbers.
 Assignments or deliverables.
Week 1
Dates
Week 2
Dates
Week 3
Dates
Week 4
Dates
Week 5
Dates
Week 6
Dates
Week 7
Dates
Week 8
Dates
Week 9
Dates
Week 10
Dates
Week 11
Dates
Week 12
Dates
Week 13
Dates
Week 14
Dates
Week 15
Dates
FINAL
Date
Topics/Daily Activities
Readings and
Homework
Basics of quantum information theory:
quantum zeno effect, no cloning,
quantum teleportation
Mathematical background I:
Hilbert spaces, operators norms
Mathematical background II:
Quantum operations, CP maps
Quantum Entanglement: fundamentals
(entanglement measures)
Quantum entanglement in many body
physics: random states and the Hilbert
Space illusion
Quantum entanglement in many body
physics: physical states and area laws
Quantum entanglement in many body
physics: critical phenomena
Local Quantum Stochastic circuits
[0]
The fidelity approach to quantum criticality
I: basic examples and quasi-free systems
The fidelity approach to quantum criticality
II: general geometric theory and scaling
theorems
[5]
Equilibrium stat-mech: Mathematical
Foundations I
Equilibrium stat-mech: Mathematical
Foundations II
Equilibration dynamics I: subsystems
and thermalization
Equilibration dynamics II: statistics of
the Loschmidt Echo
[7]
Deliverable/
Due Dates
[0]
[0]
[0]
[1]
[2]
[3]
[4]
[6]
[7]
[8]
[9]
Course overview and wrap-up
Final exam: will be held over the last week
of the class (individual presentations)
Date: For the
date and time of
the final for this
class, consult the
USC Schedule of
Classes at
www.usc.edu/soc.
Syllabus for COURSE-ID, Page 3 of 4
Statement for Students with Disabilities
Any student requesting academic accommodations based on a disability is required to register with
Disability Services and Programs (DSP) each semester. A letter of verification for approved accommodations
can be obtained from DSP. Please be sure the letter is delivered to me (or to TA) as early in the semester as
possible. DSP is located in STU 301 and is open 8:30 a.m.–5:00 p.m., Monday through Friday. Website and
contact information for DSP: http://sait.usc.edu/academicsupport/centerprograms/dsp/home_index.html,
(213) 740-0776 (Phone), (213) 740-6948 (TDD only), (213) 740-8216 (FAX) ability@usc.edu.
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the concept of respect for the intellectual property of others, the expectation that individual work will be
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Emergency Preparedness/Course Continuity in a Crisis
In case of a declared emergency if travel to campus is not feasible, USC executive leadership will announce
an electronic way for instructors to teach students in their residence halls or homes using a combination of
Blackboard, teleconferencing, and other technologies.
Syllabus for COURSE-ID, Page 4 of 4