Syllabus Application
Mathematical Introduction to Quantum Algorithms and Post-Quantum Cryptography
MATH 584
Faculty:
Faculty of Engineering and Natural Sciences
Semester:
Fall 2025-2026
Course:
Mathematical Introduction to Quantum Algorithms and Post-Quantum Cryptography - MATH 584
Classroom:
FENS-G029,FENS-L035
Level of course:
Masters
Course Credits:
SU Credit:3.000, ECTS:10
Prerequisites:
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Corequisites:
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Course Type:
Lecture
Instructor(s) Information
Ferruh Özbudak
Course Information
Catalog Course Description
This course provides a rigorous mathematical introduction to quantum algorithms and post-quantum cryptography, focusing on theoretical foundations rather than physical realizations. It covers Hilbert spaces, unitary transformations, quantum gates, and computational complexity theory. The course emphasizes algorithmic aspects, including Deutsch’s algorithm, Simon’s algorithm, Grover’s search, and Shor’s factorization algorithm, with a strong algebraic and complexity-theoretic approach. The final four weeks introduce post-quantum cryptography from a mathematical perspective, covering code-based and lattice-based cryptographic techniques that ensure security in a quantum computing era. Graduate students will engage with additional research-based assignments and theoretical proofs.
Course Learning Outcomes:
| 1. | Understand the mathematical foundations of quantum computing, including Hilbert spaces, unitary quantum circuits. |
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| 2. | Analyze and apply quantum algorithms, such as Deutsch?s algorithm, Grover?s search, Simon?s algorithm, and Shor?s factorization method, from an algebraic and complexity theoretic perspective |
| 3. | Develop mathematical reasoning for quantum cryptography, including the security implications of quantum computing on classical cryptographic protocols |
| 4. | Explore post-quantum cryptographic schemes, particularly code-based and lattice based cryptography, and evaluate their mathematical structures assumptions. |
| 5. | Compare and contrast quantum computing with classical complexity computing, focusing on classes, computational advantages, and cryptographic impact. |
| 6. | Apply theoretical knowledge to solve research-oriented problems in quantum computing and post-quantum cryptography, particularly through project-based learning. |
Course Objective
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Course Materials
Resources:
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Technology Requirements:
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