Overview
In this course, we will discuss the theory of quantum error-correcting codes and their relevance to one of the most mysterious conjectured dualities in theoretical physics - the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence (also called holography).
Broadly, this course will describe: quantum error-correcting codes based on finite fields, the AdS/CFT correspondence, and the connection between quantum error-correction and toy models of the AdS/CFT correspondence.
More specifically, topics to be covered include: finite dimensional quantum mechanics, density matrices, spectral theorem, Heisenberg group, Stone-von Neumann theorem, von Neumann entropy, entropy inequalities, bulk-boundary correspondence, subregion duality, bulk reconstruction, Ryu-Takayanagi formula, error-correction, tensor networks. If time permits, we’ll discuss stabilizer codes, CRSS algorithm, p-adic AdS/CFT, von Neumann algebras on finite dimensional Hilbert spaces.
Course prerequisites
- linear algebra
- abstract algebra
- introductory quantum mechanics (Ph 12b)
- elementary knowledge of finite fields (towards the end of the course)
- No knowledge of quantum field theory or conformal field theory or holography is required
Course meeting time and location
- Tuesday and Thursday 10:30 - 11:55 am
- Offered online via Zoom
Course instructor
- Sarthak Parikh
- Pronouns: he, him, his
- Office hours: Online meetings via Zoom by appointment
Grading
- Final presentation (30 minutes): 50%
- Final write-up: 30%
- Class participation: 20%
Offered
- Spring 2021 (Caltech/Ma 191b)