Tensor Network Methods

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Description automatically generatedUNM Physics and Astronomy, Summer 2022 course (PHYS 500.001 Adv. Sem.)

Organized by the Center for Quantum Information and Control


Course coordinator:
Philip Blocher
Email: blocher@unm.edu
Office: PAIS 2526

Course duration:

Wed June 1st to Wed August 3rd, 2022. The course consists of 10 sessions to be held weekly on Wednesdays from 4.00PM to 5.15PM Mountain Daylight Time.

Course prerequisites:

This course assumes familiarity with quantum mechanics at the level of Physics 521-522.


Participants are required to read the materials assigned for each session in advance, and to participate in the group discussions during each session. Additionally, participants should be willing to present the assigned material.


General course information:

This course is a 10-week self-study program in which topics related to tensor network methods are explored. The first half of the course (sessions 1-6) will focus specifically on the matrix product states (MPS) tensor network formalism, while the second half (sessions 7-10) will survey topics related to tensor network methods in general. The first session will introduce the participants to the basics of tensor networks, while also highlighting examples of applications for tensor networks. An overview of the topics of this course will also be given in this session. In the remaining nine sessions, the course participants will take turns presenting topics based on reading material, which will be assigned every week. The presenters will also facilitate group discussions of their topics.

The 10 course sessions will be held on Wednesday from 4.00pm to 5.15pm Mountain Daylight Time and will follow the usual ‘hybrid’ format with both in-person attendance at PAIS room 2540 and virtual attendance using Zoom.

In parallel with the above sessions, the course will also include an optional “code-along” track in which participants will build their own numerical matrix product states library based on the literature presented during the course sessions. The code-along track is intended to provide the participants with intuition and hand-on experience on the numerical implementation of the matrix product states formalism. Following the completion of the course, the participants can then use their own MPS library or one of the freely available tensor networks libraries for numerical simulations. Code-along track information, goals, and suggested code tests can be found here.

Code-along track office hours with Philip Blocher will be held in person on Wednesdays 10am-12pm MDT at PAIS room 2210 and virtually on Wednesdays 1pm-2.30pm MDT using Zoom (ID: 976 1820 8213, PW: Tensor@UNM). For those participating in the code-along track, Philip will be available for help/discussion upon arrangement via email (blocher@unm.edu), via the CQuIC Slack, or in person at PAIS 2526.


Schedule of course sessions:







June 1st

Course overview and introduction to tensor networks

Philip Blocher



June 8th

Matrix product states (MPS)

Julia Kwok and
Namitha Pradeep



June 15th

Matrix product operators (MPOs) and Hamiltonians

Ivan Gunther and
Evan Borras



June 22nd

MPS bond dimensions, area law, and bond dimension compression

Jalan Ziyad and
Spencer Dimitroff



June 29th

Time evolution of MPS 

Andrew Forbes



July 6th

Open quantum system dynamics using tensor networks

Tyler Thurtell and
 Anupam Mitra



July 13th

The Density Matrix Renormalization Group (DMRG)

Ben Corbett and
Vikas Buchemmavari



July 20th

Projected Entangled Pair States (PEPS)

Juan Gonzales De Mendoza and Conor Smith



July 27th

Machine learning using tensor networks

Benjamin Anker and
Leeseok Kim



August 3rd

Quantum error correction using tensor networks

Sivaprasad Omanakuttan,
Mohsin Raza and
Cole Maurer



Syllabus and bibliography:

The course syllabus, together with a list of references, can be found here.


UNM participants: via Stream (netID required)

Non-UNM participants: via OneDrive (password required, see email)



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