Difference between revisions of "MAT4XXX"

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(Created page with "=Mathematical Physics - MAT4XXX/5XXX= ==Course description== The course intends to be a basic introduction to the mathematical and computational techniques in applied mathema...")
 
 
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=Mathematical Physics - MAT4XXX/5XXX=
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=Introduction to Quantum Information Science and Engineering - MAT4XXX/5XXX=
  
 
==Course description==
 
==Course description==
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The course intends to be a basic introduction to the mathematical
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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.  
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and computational techniques in applied mathematics, computational science & engineer�ing, and data science & machine learning. This course will stress then how the methods of
 
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mathematical modeling in the STEM disciplines have transitioned from the analytical (as in
 
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Theoretical Physics) to the numerical (as in traditional methods in Computational Science
 
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and Engineering) and more recently to Data-based methods (as in current developments in
 
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Data Science and Machine Learning). The student will acquire the basic skills needed broadly
 
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in Computational Science and Engineering, of which Computational Physics, Data Science,
 
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Machine Learning, and Numerical Modeling in the Mathematical Sciences are a subset.
 
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==Catalog entry==
 
==Catalog entry==
  
 
''Prerequisite'':  
 
''Prerequisite'':  
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Calculus III [[MAT2214]] and Differential Equations I [[MAT3613]] with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.
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Linear Algebra [[MAT2233]] or Applied Linear Algebra [[MAT2253]], or equivalent (can be waived with approval of instructor), with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.  
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''Content'':  
 
''Content'':  
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1. Computational Science, Engineering, and Mathematics
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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.
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(a) Linear Algebra and Computational Science & Engineering
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Quantum control using quantum logic gates, providing a foundation for quantum programming.
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(b) Applied Math and Computational Science & Engineering
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Applications: quantum teleportation, quantum cryptography, quantum computing.
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(c) Fourier Series and Integrals
 
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(d) Laplace Transform and Spectral Methods
 
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(e) Initial Value Problems
 
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(f) Conjugate Gradients and Krylov Subspaces
 
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(g) Minimum Principles
 
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2. Data Science and Machine Learning: a Mathematical Perspective
 
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(a) Principal Components and the Best Low Rank Matrix
 
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(b) Randomized Linear Algebra
 
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(c) Low Rank and Compressed Sensing
 
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(d) Markov Chains
 
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(e) Stochastic Gradient Descent and ADAM
 
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(f) Introduction to Machine Learning: Neural Networks
 
  
  
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'''Textbooks:'''
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'''Textbook:'''
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* Strang, G. Computational Science & Engineering. USA, Wellesley-Cambridge, 2007.
 
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* Strang, G. Linear Algebra and Learning from Data. Wellesley-Cambridge Press, 2019.
 
  
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* Nielsen, M. and Chuang, I. Quantum Computation and Quantum Information. UK, Cambridge University Press, 2012.
  
  
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*  
 
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Strang's 4 special matrices (Part 1)
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An overview of quantum computing and information.
 
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* Strang's 4 special matrices (continued)
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*  
 
|-
 
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|Week 2
 
|Week 2
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*  
 
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Differences, Derivatives, BC.  
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Classical Information Theory. Connection between information and thermodynamics
 
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*Gradient, Divergence. Laplace equation.
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*
 
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|Week 3
 
|Week 3
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*  
 
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Inverses.  
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Communications Theory. Physical qubits: spinning particles and photons
 
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* Positive De�nite Matrices
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*  
 
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|Week 4
 
|Week 4
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*  
 
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Stiffness Matrices.  
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Operators in Quantum Mechanics. Classical cryptography
 
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* Oscillations & Newton's Laws.
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*  
 
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|Week 5
 
|Week 5
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*  
 
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Graph Models. Networks.  
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Quantum cryptography. Entanglement.
 
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* Clustering and k-means.
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*  
 
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|Week 6
 
|Week 6
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*  
 
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Fourier Series.  
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Mixed states and the density operator. Local measurements & open quantum systems.
 
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* Chebyshev, Legendre, and Bessel
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*  
 
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|Week 7
 
|Week 7
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*  
 
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Fast Fourier Transform (FFT).
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Quantum non-locality and the Einstein-Podolsky-Rosen paradox
 
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* Convolution and Signal Processing.
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*  
 
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|Week 8
 
|Week 8
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*  
 
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Fourier Integrals. Deconvolution, Integral Equations.  
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Bell’s inequality. Quantum dense coding. Quantum teleportation
 
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* Wavelets, Signal Processing.
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*  
 
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|Week 9
 
|Week 9
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*  
 
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Computational implementation of Laplace and z- Transforms.
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Quantum non-locality and the Einstein-Podolsky-Rosen paradox
 
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* Spectral Methods.
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*  
 
|-
 
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|Week 10
 
|Week 10
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Finite Difference for ODEs.  
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Quantum computation.
 
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* Accuracy & Stability. Conservation Laws, diffusion, fluids
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*  
 
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|Week 11
 
|Week 11
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*  
 
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Elimination with reordering, multigrid methods, conjugate gradients
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Von Neumann measurements
 
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* Krylov subspaces
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Regular. least sq. Linear programming.  
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Many-worlds interpretation of quantum mechanics.
 
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*   
 
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* Adjoint. Stoch. Gradient Descent. ADAM.
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*  
 
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|Week 13
 
|Week 13
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*  
 
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Matrix-matrix Multiplication. 4 Fundamental Subspaces. Orthogonal Matrices.
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Selected topic 1.
 
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*  Best low rank matrix. Rayleigh quotients. Factoring matrices and tensors.
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*   
 
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|Week 14
 
|Week 14
 
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* Randomized Linear Algebra. Low rank signals. Singular values. Compressed sensing.
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*  
 
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Covariance Matrices. Multivariate Gaussian. Weighted least squares. Markov chains.
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Presentations by students
 
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*  Neural Networks (Convolutional, Deep).
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*   
 
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*  Backpropagation. Machine Learning.
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*   
 
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Latest revision as of 15:50, 24 January 2025

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.

Catalog entry

Prerequisite: Linear Algebra MAT2233 or Applied Linear Algebra MAT2253, or equivalent (can be waived with approval of instructor), with a letter grade of C- or better, or successful completion of at least three credits of equivalent courses.


Content: 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.


Textbook:

  • Nielsen, M. and Chuang, I. Quantum Computation and Quantum Information. UK, Cambridge University Press, 2012.


Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1

An overview of quantum computing and information.

Week 2

Classical Information Theory. Connection between information and thermodynamics

Week 3

Communications Theory. Physical qubits: spinning particles and photons

Week 4

Operators in Quantum Mechanics. Classical cryptography

Week 5

Quantum cryptography. Entanglement.

Week 6

Mixed states and the density operator. Local measurements & open quantum systems.

Week 7

Quantum non-locality and the Einstein-Podolsky-Rosen paradox

Week 8

Bell’s inequality. Quantum dense coding. Quantum teleportation

Week 9

Quantum non-locality and the Einstein-Podolsky-Rosen paradox

Week 10

Quantum computation.

Week 11

Von Neumann measurements

Week 12

Many-worlds interpretation of quantum mechanics.

Week 13

Selected topic 1.

Week 14

Presentations by students

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