CSE 494/598 : Quantum Computation
Overview
Quantum computing is not merely a novel computational paradigm—it represents an opportunity to exploit the counterintuitive principles of quantum mechanics for real-time problem solving. This course focuses on the cutting-edge field of Quantum Machine Learning (QML) with an emphasis on the mathematical and coding aspects.
Syllabus:
Prerequisites
- Linear Algebra: A strong foundation in linear algebra, including vectors, matrices, determinants, eigenvalues, and eigenvectors, is essential.
- Probability and Statistics: Familiarity with probability theory, statistical distributions, and basic statistical inference is necessary.
- Programming: Proficiency in a programming language like Python is recommended, as it is widely used in quantum computing and machine learning.
- Classical Machine Learning: A foundational understanding of classical machine learning algorithms and techniques (e.g., linear regression, logistic regression, neural networks) would be beneficial.
- Basic Complex Analysis: Familiarity with complex numbers and their properties will be valuable.
Main Topics
Quantum Computation
- Single Qubit Systems
- Multi-Qubit Systems
- Entanglement
- Measurement
- Quantum Algorithms
Machine Learning
- Intro to Vector Spaces
- Kernel Machine Learning
- Feature Maps
- Gradients and Optimization
Quantum Machine Learning
- Parameterized Quantum Circuits
- Data Re-Uploading Models
- Quantum Kernel Machine Learning
Learning Outcomes
Upon completion of this course, students will be able to –
- Explain the main physics experiments that helped develop quantum physics and understand the postulates of quantum computing.
- Demonstrate the evolution of quantum states in single-bit and multi-bit quantum circuits.
- Demonstrate understanding and operation of the main quantum computing algorithms.
- Explain the main sources of noise in quantum computation and why NISQ devices exist.
- Explain the main methods of classical data encoding into quantum circuits.
- Demonstrate understanding of main quantum machine learning algorithms, including variational quantum circuits, data re-uploading, quantum kernels, and quantum generative models.