FALL SEMESTER (2021):
QUANTUM COMPUTING FOR PHYSICISTS

Introducing basic concepts and ideas in quantum information and computation from a physically-oriented point of view.

Topics to be covered:

  1. Introduction and Motivation, Information and Computation in Physics

  2. Foundations I: Density Matrices, Mixed States, Ensembles, Schmidt Decomposition and Entanglement

  3. Foundations II: Measurements – orthogonal and generalized, Quantum Channels and operations, Decoherence

  4. Playing with Entanglement: EPR, Bell Inequalities, Teleportation, Dense Coding, Key Distribution etc.

  5. Quantum (and classical) Circuits, Complexity, Universal Gates

  6. Quantum Algorithms (basic examples, period finding, factoring, quantum search)

  7. Physical algorithms: quantum simulation, the local Hamiltonian problem, cluster states, adiabatic quantum computation

  8. Quantum error correction

 

The course material is accessible to Hebrew University Students via moodle.huji.ac.il.

Spring Semster (2020, 2021, 2022):
Quantum Information Methods
for Many-Body Physics

Quantum Many Body Physics is a very challenging research field, that requires the development of new computation methods, for handling strong interaction and non-pertubative models. The course will introduce two modern approaches to many-body physics and quantum field theory, rooted in quantum information theory: one is quantum simulation – mapping one quantum system to another one which is controllable in the laboratory, and tensor networks, which allow one to perform efficient calculations for physically relevant many body quantum states. The course will include examples from both condensed matter and particle physics (prior knowledge with the demonstrated models is not required).

Topics to be covered:

  1. Introduction to Many-Body Physics and review of Second Quantization

  2. Symmetries in Quantum Mechanics

  3. Quantum Simulation: Motivation and approaches, state preparation and the adiabatic theorem, mapping symmetries and effective Hamiltonians

  4. Cold atoms in optical lattices and their application for quantum simulation

  5. Local symmetries and quantum simulation of gauge theories

  6. Quantum entanglement, entropy, entanglement in a many body system and the area law

  7. MPS (Matrix Product States) – definition and physical relevance, fundamental properties and examples

  8. Correlation functions of MPS and the relation to Gapped Hamiltonians

  9. The AKLT model and the parent Hamiltonian theorem

  10. The fundamental theorem of MPS and symmetries

  11. PEPS (Projected Entangled Pair States) – definition and examples

  12. Symmetries in PEPS

  13. Fermionic PEPS

  14. PEPS with a local symmetry

 

The course material is accessible to Hebrew University Students via moodle.huji.ac.il