MAT4XXX

Introduction to Quantum Information Science and Engineering - MAT4XXX/5XXX

Course description

This course will be an introduction accessible and welcoming to all STEM students. No prior quantum mechanics courses are expected since all the principles and techniques of quantum information will be taught during the course. The focus will be on qubits, entanglement, and decoherence, three key building blocks of quantum computing. Topics: Foundations of quantum mechanics such as unitary time evolution, entanglement, and the EPR paradox approached from the information perspective, and quantum entropy. Information and its encoding into physical systems such as photons, atoms, and superconducting circuits. Quantum control using quantum logic gates, providing a foundation for quantum programming. Applications: quantum teleportation, quantum cryptography, quantum computing. Pre-requisites: QST 6203 and QST

Catalog entry

Prerequisite: Linear Algebra MAT2214, Applied Linear Algebra MAT2214, or Engineering Mathematics, MAT3613 with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.

Content: 1. Computational Science, Engineering, and Mathematics (a) Linear Algebra and Computational Science & Engineering (b) Applied Math and Computational Science & Engineering (c) Fourier Series and Integrals (d) Laplace Transform and Spectral Methods (e) Initial Value Problems (f) Conjugate Gradients and Krylov Subspaces (g) Minimum Principles 2. Data Science and Machine Learning: a Mathematical Perspective (a) Principal Components and the Best Low Rank Matrix (b) Randomized Linear Algebra (c) Low Rank and Compressed Sensing (d) Markov Chains (e) Stochastic Gradient Descent and ADAM (f) Introduction to Machine Learning: Neural Networks

Textbooks:

• Strang, G. Computational Science & Engineering. USA, Wellesley-Cambridge, 2007.
• Strang, G. Linear Algebra and Learning from Data. Wellesley-Cambridge Press, 2019.

Topics List

Date	Sections	Topics	Prerequisite Skills	Student Learning Outcomes
Week 1		Strang's 4 special matrices
Week 2		Differences, Derivatives, BC. Gradient, Divergence. Laplace equation.
Week 3		Inverses. Positive Definite Matrices
Week 4		Stiffness Matrices. Oscillations & Newton's Laws.
Week 5		Graph Models. Networks. Clustering and k-means.
Week 6		Fourier Series. Chebyshev, Legendre, and Bessel
Week 7		Fast Fourier Transform (FFT). Convolution and Signal Processing.
Week 8		Fourier Integrals. Deconvolution, Integral Equations. Wavelets, Signal Processing.
Week 9		Computational implementation of Laplace and z- Transforms. Spectral Methods.
Week 10		Finite Difference for ODEs. Accuracy & Stability. Conservation Laws, diffusion, fluids
Week 11		Elimination with reordering, multigrid methods, conjugate gradients, Krylov subspaces
Week 12		Regular. least sq. Linear programming. Adjoint. Stoch. Gradient Descent. ADAM.
Week 13		Matrix-matrix Multiplication. 4 Fundamental Subspaces. Orthogonal Matrices. Best low rank matrix. Rayleigh quotients. Factoring matrices and tensors.
Week 14		Randomized Linear Algebra. Low rank signals. Singular values. Compressed sensing. Covariance Matrices. Multivariate Gaussian. Weighted least squares. Markov chains. Neural Networks. Backpropagation. Machine Learning.