On successful completion of the course students should be able
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Background: Discrete mathematical structures -- sets and cardinality (lecture notes).
Background: Discrete mathematical structures -- groups (lecture notes).
Introduction to computability. Turing machines and universal Turing machines. Recursive functions (lecture notes).
Introduction to computational complexity. Basic notions and tools. Complexity classes (lecture notes).
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Amplitude amplification as an algorithimic technique. Search problems and Grover's algorithm. (slides).
Further quantum algorithms: Bernstein-Vazirani and Simon. Variants. (slides).
Case study: Quantum Bayesian decision making (slides) (paper). The quantum phase estimation problem (slides).
Quantum Fourier transform. The eigenvalue estimation problem (slides; first section)
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Case study: Quantum reinforcement learning (slides). Resolution of the QFT exercise (note).
The algorithm of Shor. Reduction to order-finding. (slides)
The hidden subgroup problem and its instances: finding the period of a periodic function; the discrete logarithm problem. (slides)
Case study: Quantum walks. (notebook)
Introduction to the practical component of the course.
Problem Set 1 - Haskell -- (exercises) and (support material).
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Solutions and other notes
Problem Set 2 - Algebra of quantum operations -- (exercises) and (support material).
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Problem Set 3 - Simulation of quantum circuits -- (exercises) and (support material).
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Conclusion of Problem Sets 3 and 2.
Problem Set 4 - Quantum projects -- (exercises).
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Conclusion of Problem Set 4.
Qiskit 1: Quantum Operations and Simulations -- (exercises).
Link: here
Qiskit 2 -- (exercises)
Working with the IBM Q backends.
Quantum Teleportation Protocol.
Link: here
Qiskit 3 -- (exercises)
Deutsch-Josza Algorithm.
Grover's algorithm.
Solving a 3-SAT problem with Grover's algorithm (Part 1).
Link: here
Qiskit 4 -- (exercises)
Solving a 3-SAT problem with Grover's algorithm.
[Ed.7-1.09]
Qiskit 5 -- (exercises)
C^{n}NOT decomposition;
Quantum State Tomography;
Maesurement Errors Mitigation;
Bernstein-Vazirani Algorithm
Qiskit 6 -- (exercises)
Simon's Algorithm
Quantum Fourier Transform
Qiskit 7 -- (exercises)
Quantum Period Finding
Quantum Phase Estimation
Qiskit 8 -- (exercises)
Shor's Algorthm
Quantum Counting
Qiskit 9 -- (exercises)
Variational Quantum Eigensolver with Qiskit Aqua
Discussing ongoing experimental assignments. Link: here