# Courses

Our quantum education program is constructed from several key principles:

Broad, deep and engaging: Our quantum center takes a broad perspective of quantum science and technology, spanning from Physics, Computer Science and Mathematics, to Chemistry, Applied Physics, Engineering and Philosophy. We find the connecting themes of coherence, entanglement and complexity to be shared among these very different approaches to the quantum world. However, we firmly believe that a deep understanding of quantum theory (along with a concurrent introduction to experimental and technological aspects) is necessary in order to accomplish top-notch research. Hence, we provide a full and deep disciplinary set of courses at the undergraduate level in each discipline. This also includes an option for excellent students to conduct undergraduate research in both theory and experiment.

Interdisciplinary: At the level of Masters and PhD education, we believe that along with a strengthening of fundamentals and disciplinary depth, the quantum curriculum must include a convergence of ideas with related fields. Thus, we are fostering a set of specialized MSc. programs in quantum science and technology that provide a broad interdisciplinary component vital for the 21st century education of a quantum scientist/engineer (available now for 4-5 years already in Physics and Applied Physics, and more planned, see below).

Lifelong and outreach: In parallel with the undergraduate and graduate programs (more detail below), we believe that our educational mission needs to span a broader age-range and reach out to additional populations. This includes highschool students and engineering forums (for quantum training). We are also building outreach material for international audiences, including a MOOC course on Quantum Sensing, and an open computational quantum simulations platform for visualizing and teaching quantum mechanics.

International: We are actively developing several international joint research and teaching programs in quantum science. Specifically, we are a member of The Alliance For Quantum Innovation, together with Ulm and Stuttgart for the past 4 years, conducting joint MSc and PhD training. We recently launched (in 2020) a joint MSc program with Vienna in quantum research and education (at the graduate level), and are working on finalizing a similar collaboration with ETH.

## Specifics of the MSc specializations:

These are Masters degrees, granted in a specific discipline (such as Physics or Chemistry – in the future), but with an added specialization in Quantum Information Science and Technology. These programs are initially approved by the University’s upper management committee (“Matmedet”), and undergo standard reviewing and reporting to the PBC as well. These programs have been running for the past 4 years in Physics and Applied Physics. They are based on a core set of mandatory courses, and a broad selection of elective courses. In addition, each student is required to conduct research with a quantum center member PI. These two specializations revolve around a core competence of the numerous QISC PI’s available to teach in these specializations. The course load requires all the students to master core concepts of quantum computing (CS) along with quantum technology (engineering), taught in rigorous and detailed dedicated courses. Aside from the specialized quantum courses, all the students in the program obviously complete the full requirements of the general MSc. programs in their departments. Details of the Physics MSc specialization (specific course list) in Quantum Science and Technology: The Study Program

## Existing courses and programs on Quantum S&T:

The quantum center of the Hebrew University QISC leads many courses on quantum S&T. The perspective of the Hebrew University regarding education of Quantum S&T includes generating a broad knowledge base in many of our undergraduates via accessible introductory courses in Chemistry, Physics, Engineering, Computer Science and Mathematics. These courses already exist (as detailed below in a table summarizing the current status of our courses). Many students choose to take these courses and are then able to decide if to pursue the topic in more advanced courses and programs.

The courses provided by the QISC include:

## 77891 Quantum Technologies

Lecturer: Dr. Itay Shomroni

Introduction(4 weeks)  The Master equation of a two level system, The $g_2$ correlation function, Introduction to quantum computing, Introduction to superconducting quantum circuits Quantum Magnetometry(2 week) General theory of magnetometry , Introduction to NV centers in diamond ,The NV center as a magnetometer Quantum gates(6 weeks) Theory of effective Hamiltonians ,Quantum computing with ions, Quantum computing with atoms, Quantum computing with NV centers, Quantum computing with suprconducting devices Atomic clocks(2 weeks) Introduction to atomic clocks

Semester:
2nd semester

## 67596 Introduction to Quantum Computation

Lecturer: Prof. Michael Ben-Or

Over the past decade a new field called "Quantum Computation" has emerged and has become one of the most revolutionary and interesting areas of science today. The essence of this field is the understanding that quantum physics based physical systems will be able to perform calculations operations and information processing at unprecedent speeds compared to existing "normal" computers. The course will go over important theoretical developments of the field, including fast quantum algorithms of factorization and finding a needle in a haystack, quantum error correction, quantum cryptography information and more. The material covered will touch some mathematics and physics subjects but no prior knowledge of these shall be needed.

Semester:
2nd semester

## 69317 Quantum Thermodynamics

Lecturer: Dr. Raam Uzdin

Semester:
1st semester

## 77324 Geometry and topology in Quantum and Classical Mechanics

Lecturer: Dr. Zohar Ringel

Semester:
1st semester

## 77541 Introduction to Open Quantum Systems

Lecturer: Prof. Nir Bar Gil

The course will untroduce the subject of open quantum systems, along with the necessary mathematical tools and fundamental models. We will describe the relation to quantum information processing, decoherence and dynamical control, as well as to current research topics including quantum measurement and quantum dissipative dynamics. The theoretical concepts will be applied to a few realistic physical systems, such as NV centers in diamond and nano-mechanical oscillators

Semester:
Offered:
2021

## 77693 Physical Optics

Lecturer: Dr . Yaron Broomberg

The course's objective is teaching in an orderly fashion the subject of linear physical optics, emphasizing the notion of coherence (spatial, polarization and quantum). Some of the material covered: Maxwell's equations, plane waves, dispersion, geometric/paraxial/scalr/semi-classical/iconal approximations, geometrical optics (rays, thin lenses, mirrors, abberations, basic microscopy/telescopy), optical coherence, polarization, Fourier optics, analog signal processing, resonators, interferometry and scattering, introduction to quantum optics and non-linear quantum optics.

Semester:
2nd semester

## 77697 Quantum information methods for many body physics

Lecturer: Dr. Erez Zohar

Quantum Many Body Physics is a very challenging research field, that requires the development of new computation methods, for handling strong interactions 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).

Semester:
2nd semester

## 77800 Advanced Quantum Theory 1

The quantum formalism, quantum dynamics, the Feynman path integral, scattering theory, quantum systems in magnetic field, second quantization, relativistic wave equation, the classical theory of fields, the quantum scalar field, the Dirac field, the quantum electromagnetic field, introduction to quantum electrodynamics

Semester:
1st semester

## 77802 Statistical Mechanics 1

Lecturer: Prof. Eytan Katzav
Semester:
1st semester

## 83836 Quantum Optics

Lecturer: Dr. Shlomi Kotler

Quantization of the EM field (short recap) , Field quadratures, connection to harmonic oscillator , Quantum vacuum, Casimir, Fock states, coherent states, thermal states, shift operator, Coherence, 2nd order coherence, Hanbury-Brown Twiss, Distribution functions (Wigner, Hussimi, P-representation), Squeezed-states, cat-states (applications to metrology, QI), Non-linear effects for creating squeezed/entangled states, Measurements, photon detection, homodyne, Hong-Ou-Mandel effect, Polarization ("internal" degree of freedom, photonic spin), Two-level system, coupling to classical field (Rabi, detuning, ...),Coupling to atoms, cavities (Jaynes-Cummings model, dressed-states)

Semester:
2nd semester