CS 294: Quantum Coding Theory

General Information

Lectures

• Lecture 1 (Jan 24): Course overview; Shor 9-qubit code (scribe notes)

• Lecture 2 (Jan 26): Shor 9-qubit code continued; quantum noise (scribe notes)

• Lecture 3 (Jan 31): More noise (scribe notes)

• Lecture 4 (Feb 2): Knill-Laflamme conditions (scribe notes)

• Lecture 5 (Feb 2): More Knill-Laflamme; linear codes (scribe notes)

• Lecture 6 (Feb 9): Linear codes and stabilizer codes (scribe notes)

• Lecture 7 (Feb 14): Properties and examples of stabilizer codes (scribe notes)

• Lecture 8 (Feb 16): CSS codes (scribe notes)

• Lecture 9 (Feb 21): More on CSS codes and qudit codes (scribe notes)

• Lecture 10 (Feb 23): Polynomial codes, bounds on codes (scribe notes)

• Lecture 11 (Feb 28): The quantum Singleton bound

• Lecture 12 (Mar 1): The toric code (scribe notes)

• Lecture 13 (Mar 6): Topological codes (scribe notes)

• Lecture 14 (Mar 8): Chain complexes (scribe notes)

• Lecture 15 (Mar 13): Product codes (scribe notes)

• Lecture 16 (Mar 15): Hypergraph product codes (scribe notes)

• Lecture 17 (Mar 20): Tanner codes (scribe notes)

• Lecture 19 (Apr 3): Quantum Tanner codes I (scribe notes)

• Lecture 20 (Apr 5): Quantum Tanner codes II (scribe notes)

• Lecture 21 (Apr 10): Quantum Tanner code distance (scribe notes)

• Lecture 22 (Apr 12): Quantum Tanner codes IV (scribe notes)

• Lecture 23 (Apr 17): The Clifford group (scribe notes)

• Lecture 24 (Apr 19): The Clifford group II

• Lecture 25 (Apr 24): Fault tolerance (scribe notes)

• Lecture 26 (Apr 26): Fault tolerance II

• Lecture 27 (May 1): Fault tolerance III

• Lecture 28 (May 3): Fault tolerance IV

List of topics

• Basics of quantum error correction
  Stabilizer and CSS codes
  Knill-Laflamme conditions
  Bounds on error correcting codes
• Quantum fault tolerance
  Model of fault tolerance
  The Clifford group and the Gottesman-Knill theorem
  Proof of the fault tolerance theorem
• Good quantum codes
  The toric code and surface codes
  LDPC codes
  Quantum Tanner codes
• Applications
  Quantum PCP and NLTS conjectures

Other courses and materials

Prerequisites

Evaluation