THEORETICAL PHYSICIST
Racah Institute of Physics, Hebrew University of Jerusalem
Erez Zohar
FALL SEMESTER (2021):
QUANTUM COMPUTING FOR PHYSICISTS
Introducing basic concepts and ideas in quantum information and computation from a physicallyoriented point of view.
Topics to be covered:

Introduction and Motivation, Information and Computation in Physics

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

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

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

Quantum (and classical) Circuits, Complexity, Universal Gates

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

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

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 ManyBody Physics
Quantum Many Body Physics is a very challenging research field, that requires the development of new computation methods, for handling strong interaction and nonpertubative models. The course will introduce two modern approaches to manybody 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:

Introduction to ManyBody Physics and review of Second Quantization

Symmetries in Quantum Mechanics

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

Cold atoms in optical lattices and their application for quantum simulation

Local symmetries and quantum simulation of gauge theories

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

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

Correlation functions of MPS and the relation to Gapped Hamiltonians

The AKLT model and the parent Hamiltonian theorem

The fundamental theorem of MPS and symmetries

PEPS (Projected Entangled Pair States) – definition and examples

Symmetries in PEPS

Fermionic PEPS

PEPS with a local symmetry
The course material is accessible to Hebrew University Students via moodle.huji.ac.il