Introduction into quantum information and quantum computation
by David Gross
1st Lecture: Introduction
- Gate model of quantum computation
- Grover search
2nd Lecture: Cryptography and Shor's algorythm
- Talking to your bank (or Snapchat): Public key crypto
- Quantum Fourier transform & order finding
- Sketch of Shor's algorithm
3rd Lecture: Outlook
- P, NP, BQP, and where we stand
- Non-universal "quantum supremacy" via sampling problems?
Literature: Nielsen and Chuang, "Quantum information and computation"
Quantum error correction
by Michael Kastoryano
1st Lecture: Quantum Error Correction (QEC) basics
- Classical error correction: repetition code, [n,k,d]
- CSS and stabilizer codes
- Concatenation and the Shor code
- Sources of Error
2nd Lecture: Topological Quantum Error correction
- The Toric code
- Decoding and the error correction threshold
- Gates and the fault-tolerant threshold (Eastin-Knill theorem)
3rd Lecture: QEC and many body theory
- QEC conditions and topological order (LTQO)
- QEC as the ground subspace of gapped topological models
- Approximate QEC, and other new directions
Quantum information for condensed matter physics
by Jens Eisert
1st Lecture: Tensor network basics
- Area laws and the "physical corner of Hilbert space"
- Matrix product states
- Projected entangled pair states
- Multi-scale entanglement renormalization
2nd Lecture: Capturing phases of matter with tensor networks
- Phases of matter
- Topological order captured in terms of tensor networks
3rd Lecture: Taming the non-equilibrium
- Equilibration and thermalization of many-body systems
- Many-body localization
- Wrap-up: Physical realizations of "quantum supremacy" and QEC