Quantum Computation 2024/25

Learning Outcomes

On successful completion of the course students should be able

Computability and complexity
- Mathematical backgound: sets, orders, groups.
- Turing machines and computability.
- Computational complexity. Algorithms and complexity classes.
Quantum computation and algorithms
- The quantum computational model (gates, measurements, and circuits).
- Introduction to quantum algorithms.
- Algorithms based on phase amplification.
- Algorithms based on the quantum Fourier transform.
- Case studies in quantum algorithmics.
Quantum programming
- Quantum programming in Qiskit and other tools

Sep 11 (09:00 - 11:00)	Introduction to Quantum Computation and the course dynamics (slides) Mathematical background for the study of computability and computational complexity (notes).
Sep 16 (11:00 - 13:00)	Introduction to quantum algorithms. The Deutsch problem (slides).
Sep 25 (09:00 - 11:00)	Quantum algorithms: the pahse kick-back pattern (slides). Bernstein-Varizani algorithm. Deutsch-Joza algorithm. (Informal) introduction to Grover's algorithm.
Oct 9 (09:00 - 11:00)	No class due to adverse weather conditions (to be replaced).
Oct 16 (09:00 - 11:00)	Unstructured search problems and Grover's algorithm (slides).
Oct 21 (16:00 - 18:00)	Grover's algorithm for multiple solutions. Amplitude amplification as a basic programming technique (slides). Background for the next lecture: groups (notes).
Oct 30 (09:00 - 11:00)	Simon's algorithm (slides). (Informal) introduction to its generalization.
Nov 13 (09:00 - 11:00)	Quantum phase estimation (slides). Introduction to the quantum Fourier transform.
Nov 18 (16:00 - 18:00)	Revisiting the quantum Fourier transform as a main algorithmic component (slides). Application to eigenvalue estimation (slides).
Nov 20 (09:00 - 11:00)	Shor's algoritm (slides).

Sep 30 (16:00 - 18:00)	Quantum computing introduction with pennylane (Notebook)
Oct 7 (11:00 - 13:00)	Multiqubit operations and entanglement (Notebook)
Oct 7 (16:00 - 18:00)	Pauli rotations and expectation value of observables (Continuing Notebook 2)
Oct 14 (16:00 - 18:00)	Deutsch-Jozsa algoritm (Notebook)
Nov 4 (16:00 - 18:00)	Deutsch-Jozsa algoritm (Cont)
Nov 6 (09:00 - 11:00)	Grover's algoritm (Notebook)
Nov 11 (16:00 - 18:00)	Grover's algoritm review and multiple number of solutions
Nov 25 (16:00 - 18:00)	Generalized amplitude amplification and unknown number of solutions (Notebook)
Dec 2 (16:00 - 18:00)	QFT (Notebook)

H. R. Lewis and C. H. Papadimitriou. Elements of the Theory of Computation. Prentice Hall (2nd Ed), 1997.
S. Arora and B. Barak. Computational Complexity: A Modern Approach. Cambridge University Press, 2009.
C. Moore and S. Mertens The nature of computation. Oxford University Press, 2011.

M. A. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information (10th Anniversary Edition). Cambridge University Press, 2010
E. Rieffel and W. Polak. Quantum Computing: A Gentle Introduction. MIT Press, 2011.
F. Kaye, R. Laflamme and M. Mosca. An Introduction to Quantum Computing. Oxford University Press, 2007.
N. S. Yanofsky and M. A. Mannucci. Quantum Computing for Computer Scientists. Cambridge University Press, 2008.
W. Scherer. Mathematics of Quantum Computing. Springer, 2019.

N. S. Yanofsky. The Outer Limits of Reason. MIT Press, 2013.
S. Aaronson. Quantum Computing since Democritus. Cambridge University Press, 2013.
J. Preskill Quantum Computing in the NISQ era and beyond. Quantum 2, 79, 2018.

Individual assignment on programming quantum algorithms, with written report and oral defense (60%) - Assignment
Individual written test (40%)

Appointments - Luis: Wed, 18:00-20:00 and Fri, 18:00-20:00 (please send an email the day before)
Appointments - Andre: Thu, 16:00-18:00 and Fri, 14:00-16:00 (please send an email the day before)
Email: lsb at di dot uminho dot pt (Luis) and andresequeira401 at gmail dot com (André)
Last update: 2024.11.20