Quantum Science Related

Courses at UCLA

  • systems of linear equations, linear independence, subspaces, bases and dimension, orthogonality determinants, eigenvalues and eigenvectors, matrix diagonalization, and symmetric matrices.

    (Absolutely needed for undergraduate quantum mechanics class. Take it as soon as possible)

  • linear independence, bases, orthogonality, linear transformations, eigenvalues and eigenvectors, inner product spaces, adjoint transformations, and the spectral decomposition theorem for self-adjoint operators.

    (Essential for any advanced study of quantum information. Read a few chapters of Nielsen and Chuang you’ll see. This class is proof based, for undergraduate experimental research, it is not necessary)

  • Classical background. Basic ideas of quantum nature of light, wave-particle duality, Heisenberg uncertainty principle, Schrödinger equation. One-dimensional square well and harmonic oscillator problems. One-dimensional scattering, Formal theory, Hilbert spaces, and Dirac notation. P/NP or letter grading.

    (If you want research in quantum science, take this as soon as possible!! You don’t need physics lower level classes, after taking math 33A just take physics 115A as freshman.)

  • Three-dimensional problems. Central potentials. Hydrogen atom. Angular momentum and spin, identical particles, and Pauli exclusion principle. Electrons in electromagnetic field.

    (Central potential is essential for studying AMO qubits, angular momentum essential for studying spin qubit. Anyways, learn everything in this class multiple times and make sure you entirely grasp it)

  • Time-independent perturbation theory, application to atomic spectra. Time-dependent perturbation theory. Fermi's golden rule. Scattering. Wentzel-Kramers-Brillouin (WKB) approximation

    (Essential for understanding quantum dynamics. Idealized qubit is a two-level system and you’ll learn it in this class)

  • This class covers topics of physics 115A and 115B with more depth and formal treatments. If you are mathematically prepared, and read books in advance, it is possible that you take this along with 115A.

    Quote from a UCLA professor “this is the most important graduate physics course!”

  • Symmetries and conservation laws, perturbation theory (time dependent and time independent), scattering theory. Special topics such as Berry's phase and related geometric and topological aspects

    (Perturbation theory is essential for analytical and numerical treatment of quantum dynamics)

Quantum Mechanics

Quantum Information Theory

  • Quantum circuits, quantum Fourier transform, quantum algorithms, physical implementations and Jaynes-Cummings model

    (You will learn to theoretically model a quantum system (e.g. how to write the Hamiltonian of two boson coupled through a harmonic oscillator, it allows you to model two qubit gates). Very amazing class!)

  • Introduction to the basic principles of quantum information processing technology. Covers fundamental concepts, including qubits, states and observables, measurement uncertainty, quantum dynamics, nonlocality, and entanglement. Several applications will be explored, such as quantum teleportation, communication, cryptography, computing, and error correction.

AMO Physics / Quantum Optics

  • Theory of atomic structure. Interaction of radiation with matter

    (You will learn selection rules and spherical tensor treatment of light-atom interaction, a more powerful way than that learned in undergrad quantum mechanics class)

  • Use of techniques of quantum optics to demonstrate concepts of quantum mechanics, including superposition, quantum measurement, hidden variable theories, and Bell's inequality. Examination and use of modern optics, including lasers, optics, fibers, polarization manipulation, and photon counting.

    (The class is more optics than quantum, you spent most of the time aligning and couple beams. Sometimes you have to spend entire day working in the lab. Very tedious)

  • Quantum optics, quantum entanglement, quantum information processing, quantum sensing, quantum communication

  • Development of solid foundation on essential principles of photonics from ground up with minimum prior knowledge on this subject. Topics include optical properties of materials, optical wave propagation and modes, optical interferometers and resonators, optical coupling and modulation, optical absorption and emission, principles of lasers and light-emitting diodes, and optical detection.

  • Coverage of laser physics, related photonic devices, and applications of lasers. Topics include resonators, thermal radiation, Einstein coefficients, optical amplification, semiconductor lasers, optical modulation and detection

  • Introduction to various phases of matter that exhibit quantum mechanics on a macroscopic scale. Topics may include superconductivity, superfluidity, magnetism, density waves, and the integer quantum Hall effect. Landau's phenomenological theory of symmetry-breaking phase transitions, including the application of Ginzburg-Landau theory to superconductivity.

    (The course will cover the theory of superconductivity and Josephson Junctions, it is essential for understanding superconducting qubit)

  • Fundamentals of solid-state, introduction to quantum mechanics and quantum statistics applied to solid-state. Crystal structure, energy levels in solids, and band theory and semiconductor properties

  • Discussion of solid-state properties, lattice vibrations, thermal properties, dielectric, magnetic, and superconducting properties

  • Energy band theory, electronic band structure of various elementary, compound, and alloy semiconductors, defects in semiconductors.

  • Techniques to solve Boltzmann transport equation, various scattering mechanisms in semiconductors, high field transport properties in semiconductors, Monte Carlo method in transport.

  • Theoretical methods for circulating electronics and optical properties of semiconductor structures. Quantum size effects and low-dimensional systems. Application to semiconductor nanometer scale devices, including negative resistance diodes, transistors, and detectors

Solid State Physics

Device Design and Fabrication

  • Introduction to fundamentals of nanoscience for electronics nanosystems. Principles of fundamental quantities: electron charge, effective mass, Bohr magneton, and spin, as well as theoretical approaches. From these nanoscale components, discussion of basic behaviors of nanosystems such as analysis of dynamics, variability, and noise, contrasted with those of scaled CMOS. Incorporation of design project in which students are challenged to design electronics nanosystems

  • Capstone design course, with emphasis on transmission line-based circuits and components to address need in industry and research community for students with microwave and wireless circuit design experiences. Standard design procedure for waveguide and transmission line-based microwave circuits and systems to gain experience in using Microwave CAD software such as Agilent ADS or HFSS. How to fabricate and test these designs

  • Design of radio frequency circuits and systems, with emphasis on both theoretical foundations and hands-on experience. Design of radio frequency transceivers and their building blocks according to given specifications or in form of open-ended problems. Introduction to advanced topics related to projects through lecture and laboratories. Creation by students of end-to-end systems in application context, managing trade-offs across subsystems while meeting constraints and optimizing metrics related to cost, performance, ease of use, manufacturability, testing, and other real-world issues.

  • Design fabrication and characterization of p-n junction and transistors. Students perform various processing tasks such as wafer preparation, oxidation, diffusion, metallization, and photolithography. Introduction to CAD tools used in integrated circuit processing and device design. Device structure optimization tool based on MEDICI; process integration tool based on SUPREM. Course familiarizes students with those tools. Using CAD tools, CMOS process integration to be designed

  • Techniques to solve Boltzmann transport equation, various scattering mechanisms in semiconductors, high field transport properties in semiconductors, Monte Carlo method in transport.

  • Sinusoidal excitation and phasors, AC steady state analysis, AC steady state power, network functions, poles and zeros, frequency response, mutual inductance, ideal transformer, application of Laplace transforms to circuit analysis.