Quantum Computing Semester, January–April 2024

• Quantum Computing Semester, Jan–Apr, 2024

Quantum Error Correcting Codes: 15–20 April, 2024

Faculty

• Pavithran S Iyer (Xanadu Quantum Technologies)
• Prabha Mandayam (IIT Madras)
• Pradeep Sarvepalli (IIT Madras)

Lecture plan

• Prabha Mandyam (IIT Madras)

  1. Quantum Channels [System-Bath picture, Kraus operators, Choi matrix, Pauli-Louiville representation, Examples of channels]

  2. QEC conditions [Detection vs Correction, code parameters, Hamming bound]

  3. Stabilizer formalism - I [Pauli group, Abelian subgroup, coset, normalizer, idea of stabilizer, eigenspaces of Pauli subgroups, stabilizers for 3-qubit/9-qubit, generators < … > codespace]

• Pavithran S Iyer (Xanadu, Canada)

  1. Challenges of QEC, 3-qubit code, Phase-flip Code

  2. Shor Code

  3. Stabilizer formalism - II [5-qubit code, QEC conditions in stabilizer language, Decoding: syndrome detection and error correction, syndrome measurement circuits]

  4. Logical operations and motivation for fault tolerance, Universal FT Scheme, Threshold Theorem

• Pradeep Sarvepalli (IIT Madras)

  1. Classical Coding Theory [Hamming Codes, Parity check matrix, generator matrix, dual codes, symplectic inner product]

  2. CSS Codes, Steane Code

  3. Surface codes, Toric code

Schedule

• Playlist with all recorded lectures

Course material

• Pavithran S Iyer, Lecture 2, 15 Apr 2024

• Pavithran S Iyer, Lecture 3, 16 Apr 2024

• Pavithran S Iyer, Lecture 7, 18 Apr 2024