Course by the same professor at St. Petersburg University who taught this course (extremely math heavy, not a great experience for me). This course claims to focus “on how the mathematical model of quantum computing grows out from physics and experiment, while omitting most of the formulas (when possible) and rigorous proofs.”
Begins with math of quantum computing, then math of quantum physics, then a bit of physics
MIT: Quantum Information Science II EDX (archived, free / $49) – Chuang, Harrow
Assumes strong background in quantum mechanics.
Part one: Quantum states, noise and error correction – density matrices and noisy quantum operations, and advanced quantum error correction codes.
Part two: Fault tolerance & complexity – fault-tolerant computation, quantum supremacy, quantum algorithms at scale.
Part three: Advanced algorithms & information theory – Hamiltonian simulation, the hidden subgroup problem, linear systems, and noisy quantum channels.
Quantum-enhanced machine learning, focusing on algorithms challenging to classical computers. Implement protocols using open-source tools in Python.
Describe and implement classical-quantum hybrid learning algorithms. Encode classical information in quantum systems. Perform discrete optimization in ensembles and unsupervised machine learning with different quantum computing paradigms. Sample quantum states for probabilistic models. Experiment with unusual kernel functions on quantum computers
Demonstrate coherent quantum machine learning protocols and estimate their resources requirements. Summarize quantum Fourier transformation, quantum phase estimation and quantum matrix, and implement these algorithms. General linear algebra subroutines by quantum algorithms. Gaussian processes on a quantum computer.
Wavefunctions and their probabilistic interpretation, how to solve the Schrödinger equation for a particle moving in one-dimensional potentials, scattering, central potentials, and the hydrogen atom
Probably a good place to start, then do Mastering QM
First in 3 courses, but this one seems most relevant
de Broglie waves, the wavefunction, and its probability interpretation. We then introduce the Schrodinger equation, inner products, and Hermitian operators. We also study the time-evolution of wave-packets, Ehrenfest’s theorem, and uncertainty relations.
MIT: Mastering Quantum Mechanics EDX
“Completing the 3-part Quantum Mechanics series will give you the necessary foundation to pursue advanced study or research at the graduate level in areas related to quantum mechanics.” Follows MIT’s 8.05.
Part 1: Wave Mechanics (4 weeks, self-paced, free / $50)
Some knowledge of wave mechanics at undergrad introductory level required
Must have seen Schrödinger’s equation, solutions for square well potential, harmonic oscillator, hydrogen atom. Maybe one can get away without this because the course doesn’t build on it.