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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.
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