CMSE 890.001: Tensor Networks

Table of contents

CMSE 890.001: Tensor Networks        1

Table of contents        1

Overview        1

Prerequisites        1

Topic list        2

Reading        2

Grading        2

Academic Integrity        3

Accommodations        3

Schedule        4

Overview

Lecture: T/Th 12:40-2pm, 1225 EGR

Office hours: Th 4-5:30pm, 2507E EB or by appointment if needed (email me)

Instructor: Ryan LaRose, rmlarose@msu.edu 

Tensor networks are a powerful theoretical and computational tool for problems ranging from machine learning to condensed matter and quantum physics. This course provides a practical introduction to tensor networks to enable you to use them in your research and/or contribute to open problems in the field. After reviewing linear algebra, we’ll introduce the fundamentals of tensor networks including notation, contraction, and complexity, then cover specific tensor networks such as matrix product states which have wide-ranging applications. Lectures will focus on practical, hands-on aspects while still emphasizing the underlying theory, and homework assignments will include mathematical and programming exercises. A final project on the application or theory of tensor networks constitutes a bulk of the course.

Prerequisites

• Linear algebra (ideally with some numerical aspect)
• Programming experience in Python or a similar language

For a refresher on these prerequisites, I recommend the relevant topics from Harvard AM205 which run parallel to Trefethen and Bau, Numerical Linear Algebra.

Topics

The course will be thematically divided into three “phases” with the following main topics:

Phase 1: Tensor network fundamentals

Scientific computing, computational complexity, matrix factorizations & algorithms, tensors,  tensor networks

Phase 2: The tensor network canon

Matrix product states, matrix product operators, DMRG, TEBD

Phase 3: Additional tensor networks and applications

Applications of tensor networks in physics, machine learning, etc., & additional tensor networks such as PEPS, tree tensor networks, MERA, etc.

Reading

The two main sources we will use are:

• Jacob C. Bridgeman, Christopher T. Chubb, Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks, https://arxiv.org/abs/1603.03039  (“Chubb”)
• Mari Carmen Banuls, Tensor Network States: Basic Introduction, Notes_TNSLecture.pdf (“Mari”)

In the schedule, these are respectively referred to as “Chubb” and “Mari”. Additional online sources on a topic-by-topic basis may be linked in the schedule.

Grading

There will be four homework assignments of equal weight (4 x 10%). Announcements and due dates will be posted on the schedule.

Project evaluation is broken down into the following categories:

• Project proposal: 6%
• Project checkpoint: 6%
• Peer assessment: 6%
• Final project notebook: 20%
• Final project presentation: 12%

Attendance and participation is based on an honest effort to come to lectures and participate in class. In addition to staying up with lectures, attendance is important because some classes will be flipped and/or include individual/group work. Four absences will be excused without question. For longer absences please contact me.

Grading scale: 4.0 ≥ 90%, 3.5 ≥ 80%, 3.0 ≥ 75%, 2.5 ≥ 70%, 2.0 ≥ 65%, 1.5 ≥ 60%, 1.0 ≥ 50%, 0.0 < 50%

Academic Integrity

You are expected to adhere to the Spartan Code of Honor academic pledge, as written by the Associated Students of Michigan State University (ASMSU):

“As a Spartan, I will strive to uphold values of the highest ethical standard. I will practice honesty in my work, foster honesty in my peers, and take pride in knowing that honor is worth more than grades. I will carry these values beyond my time as a student at Michigan State University, continuing the endeavor to build personal integrity in all that I do.”

Violations of academic integrity are inexcusable and will not be tolerated.

Accommodations

If you have a university-documented learning difficulty or require other accommodations, please provide your instructor with your VISA as soon as possible and speak with them about how they can assist you in your learning. If you do not have a VISA but have been documented with a learning difficulty or other problems for which you may still require accommodation, please contact MSU’s Resource Center for People with Disabilities (355-9642) in order to acquire current documentation.

Schedule

Note: This schedule is a living document and will be updated throughout the semester.