*Please note that not all courses are offered every semester.*

## Fall 2024 - Click to expand

(Organized alphabetically by course title)

*CSC 2332* **Introduction to Quantum Algorithms**

Provides an introduction to modern algorithmic techniques in quantum computing as well as an introduction to the quantum formalism appropriate for computer scientists or mathematicians. Topics covered include: universality of quantum computation, quantum query complexity, block encoding and linear combinations of unitaries, quantum simulation, quantum phase estimation, quantum walks and amplitude amplification and finally the quantum singular value transformation.

*PHY2321H F SPECIALIZED* **Many Body Physics I**

Denis Dalidovich

Topics may include: Free fermions (bands and band topology), Linear response theory for many-body systems, Coherent state path integrals for bosons, Superfluidity and superfluid-to-Mott insulator transition, Coherent state path integrals for fermions, Density and spin response of free fermions, Interacting fermions: Collective modes

*MAT1723* **Mathematical Foundations of Quantum Mechanics and Quantum Information Theory**

Key concepts and mathematical structure of Quantum Mechanics, with applications to topics of current interest such as quantum information theory. The core part of the course covers the following topics: Schroedinger equation, quantum observables, spectrum and evolution, motion in electro-magnetic field, angular momentum and O(3) and SU(2) groups, spin and statistics, semi-classical asymptotics, perturbation theory. More advanced topics may include: adiabatic theory and geometrical phases, Hartree-Fock theory, Bose-Einstein condensation, the second quantization, density matrix and quantum statistics, open systems and Lindblad evolution, quantum entropy, quantum channels, quantum Shannon theorems.

*ECE1531* **Quantum Information Theory**

This is a first course on quantum information and communications theory. Topics covered include: (1) basics of quantum mechanics and quantum information, (2) resource model of quantum information processing, (3) entanglement and entanglement distillation protocols, (4) quantum cryptography and security proofs.

CHM 1478H **Quantum Mechanics for Physical Chemists**

A course in Quantum Mechanics in Hilbert Space with a focus on operator formalism. Covering Schrodinger, Heisenberg and Interaction Pictures, Coordinate, Momentum and Phase Space Representations, Symmetry and Conservation Laws, Angular Momentum Coupling, Density Matrices, Introduction to Entanglement, Non-locality, Bell's Theorem, etc.

*PHY2203H F SPECIALIZED* **Quantum Optics I**

PHY2203H explores atom-photon interactions with a semi-classical treatment: how does a quantum system respond to a classical drive field? We begin by discussing how an atom driven by an optical field reduces to a dipole interaction Hamiltonian. The atom-photon problem can then be mapped onto a spin one-half electron in a magnetic field, since both are driven two-level quantum systems. We develop the Bloch equations, Rabi oscillations, and magnetic resonance. Returning to the optical regime a treatment using density matrices is necessary to include the effects of damping. Dynamics of the density operator are described by the optical Bloch equations, with which one can understand a wide range of current experiments in atomic, molecular, and optical physics and solid-state physics. These quantum dynamics are contrasted to classical (Lorentz-model) dynamics, such as quantum saturation. In the context of a diagonalized atom-photon Hamiltonian, we discuss inversion, dressed states and light shifts. Applications of this foundational material include electromagnetically induced transparency, slow light, dark states, and laser cooling.

*PHY2109 0.25 FCE* **Special Topics in Physics - Nuclei**

This half-term course is an introduction to the physics of atomic nuclei. The purpose of the course is to explore ways in which the techniques of quantum optics and atomic physics can be applied to the strongly-interacting fermion soup within a nucleus. The selection of topics covered in this seminar course will be idiosyncratic. Background preparation from PHY 2203/04 will be useful, but is not essential.

*PHY2108 0.25FCE SECTION* **Special Topics in Physics: Ultracold Atoms I**

The first of the two special-topics courses offered this year on ultracold atoms will have an emphasis on bosons. We begin with a discussion of Bose-Einstein condensation of non-interacting bosons, held in a harmonic trap. We discuss basic experimental techniques, including trapping, evaporative cooling, imaging, and Bragg scattering. With weak interactions, a mean-field treatment leads to the Gross-Pitaevskii equation and Bogoliubov excitations. Time permitting, we will discuss bosons in optical lattices, and under quasi-two-dimensional confinement. Overall, this special topic will allow for an elegant synthesis of optics, atomic physics, statistical mechanics, and field theory.

The course will assume fluency in electromagnetism, quantum mechanics, statistical mechanics, and rudimentary field theory (such as raising and lowering operators). The course will not be based on a textbook, but a good reference is Bose-Einstein condensation in Dilute Gases by Pethick and Smith.

## Winter 2025 - Click to expand

(Organized alphabetically by course title)

PHY1491H S **Current interpretations of quantum mechanics**

Realist, phenomenalist, and pragmatist perspectives on scientific theories. Review of conventional textbook quantum mechanics. Local causality and signal locality. Elements of formal measurement theory and wave function collapse; decoherence and the classical/quantum boundary. Copenhagen interpretation of quantum mechanics. Operationalist quantum mechanics. Hidden variable theories: possibilities and problems. Contextuality and nonlocality; Bell’s theorem. Bohm deBroglie theory and generalizations. Modal interpretations and consistent histories quantum mechanics of Gell-Mann, Hartle, Omnes. Relative state interpretations (Everett’s “many worlds,” more recent work by Wallace and Carroll). Quantum Darwinism. QBism. Relational Quantum Mechanics. A sketch of collapse theories.

*ECE1365S* **High Frequency Integrated Circuits Design**

A design intensive overview of high-speed, RF, mm-wave monolithic, and silicon photonics integrated circuits for wireless, automotive radar sensors, optical fiber systems and quantum processors, with an emphasis on specific high-frequency circuit analysis and design methodologies, device-circuit topology interaction and optimization. Small-signal, noise, large-signal, high-frequency common-mode and differential-mode matching and stability, digital control of tuned circuits, methodologies for maximizing circuit bandwidth, high speed CML gate design, as well as layout and isolation techniques will be discussed. Students will participate in assignments on mm-wave circuits, optical fiber circuits and classical control circuits for qubits using 22nm FDSOI technology and Cadence Analog Artist.

*PHY1485H S (FAS PHY485H)* **Laser Physics**

This course covers a broad range of advanced topics in classical optics, with the laser as a unifying theme. Topics include atom-photon interactions (absorption, radiation, and stimulated emission), how a laser works (gain, pumping, rate equation models, threshold, and gain clamping), optical resonators (their spectrum, finesse, stability, and transverse modes), propagation of Gaussian beams and paraxial rays, and the statistics of optical fields (spatial and temporal coherence). Time permitting, pulse propagation and pulsed lasers will be discussed.

*CHM1449HS* **Machine Learning and Physics Based View on Chemical Compound Space**

This is an advanced, continuously updated research-oriented course for students with interests in computational and theoretical chemistry/physics/materials. Prerequisites include undergraduate knowledge in terms of: statistical mechanics, computer programming, quantum mechanics, applied math (linear algebra, differential equations), and atomistic simulation.

This course offers an introduction to the concepts underlying nonlinear optical phenomena. Topics include: Basic formalism and classification of nonlinear optical processes through the framework of nonlinear susceptibilities: Non-phase-matched processes (e.g. rectification, Kerr effect, soliton generation, Pockels effect, two-photon absorption, degenerate four-wave mixing); phase-matched processes (parametric conversion, harmonic and difference frequency generation); Raman and Brillouin scattering. Microscopic (quantum) origin of nonlinear susceptibilities, and subtleties associated with their calculation for solids associated with band structure topology. The use of nonlinear optics to generate nonclassical states of light for quantum information processing, particularly in integrated photonics, and connections between the classical and quantum regimes.

Students taking this course should be thoroughly familiar with the material covered in PHY1510 (Electromagnetism) and PHY1520 (Quantum mechanics). It is also recommended that they have taken PHY1485 (Laser Physics) or its equivalent.

*PHY2204* **Quantum Optics II**

This course will examine the physics of the quantum electromagnetic field, and its interaction with other quantum mechanical objects. The broad purpose of the course is to equip students with the tools and background needed to connect with current research in quantum optics. Outline of topics: Quantization of the electromagnetic field; Quantum Coherence Theory; Representation of Quantum States; Squeezed Light; Master Equations; Light Matter Interactions.

*PHY2303H S SPECIALIZED* **Quantum Theory of Solids - II**

We will discuss various concepts relevant to a modern understanding of quantum materials, including the physics of Mott insulators, magnetism, superconductivity, and Kondo effect.

*MSE1022* **Special Topics in Materials Science I: Quantum Transport**

The course is concerned with quantum transport and focuses on semiconductor nanostructures. Applications of this concepts are relevant to next generation electronics and quantum computing. The course will provide an introduction to important relevant concepts in solid state physics as well as to the fabrication of such nanostructures. The course will cover structures for electron transmission, tunnelling, and interference. Students will be responsible for preparing a critical review on the current relevant literature, presented as a term paper and a class presentation.

*PHY2109H S 0.25FCE* **Special Topics in Physics: Ultracold Atoms II**

The second of the two special-topics courses offered this year on ultracold atoms will have an emphasis on strongly interacting fermions. We start with the scattering problem, to relate interaction strength to the scattering length. The scattering phase can be tuned using Feshbach resonance. We discuss how to generalize thermodynamics to isolated systems, and identify the contact parameter as the conjugate of the scattering length. We then discuss the Cooper problem and fermionic superfluidity. Time permitting, we discuss the Hubbard model and fermions in one dimension.

I teach the theory of statistical mechanics hand in hand with its applications to molecular and materials simulations, covering both algorithms and hands-on computer implementation exercises. Importantly - and that should be the main appeal to quantum students, tools that we cover in the course have direct quantum extensions with applications to open quantum systems, including Monte Carlo and molecular dynamics simulations, Langevin and Fokker Planck equations and the Master equation formalism.

**About Quantum Graduate Courses:** One objective of CQIQC is to foster interactions between students in QIS at UofT, and expose them to the breadth of topics in QIS beyond their research field. This is achieved through the Centre’s programs and via involvement in graduate curriculum, which is aimed at advocating the adoption of courses and coordinating courses in various departments to ensure a good coverage of topics.