This course aims at an introduction to quantum computation, the cutting-edge field that tries to harness the amazing laws of quantum mechanics to process the information significantly more efficiently. The course is intended for undergraduate students, including computer science majors who do not have any prior exposure to quantum mechanics, interested in gaining basic knowledge about foundations of modern quantum mechanics and its practical applications for quantum computation. The course does not assume any prior background in quantum mechanics and can be viewed as a very simple and conceptual introduction to that field.
Topics covered in this course
1. Wave-particle duality, Heisenberg’s uncertainty principle.
2. Postulates of quantum mechanics and Schrodinger representation of QM: wavefunction, wavefunction space, linear Hermitian operators, eigenvalue problem, eigenfunctions, eigenvalues, the measurement problem, quantum contextuality (Kochen–Specker theorem), time evolution of wave functions, average values, expectation values, Ehrenfest’s theorem, Schrodinger equation,
3. Problems with analytical solutions: particle in a box, harmonic oscillator, hydrogen atom.
4. Multi-electron systems, the Pauli principle, electron spin, electronic configuration
5. Superposition of states and a concept of qubits (quantum bits), quantum entanglement, non-local correlations, the no-cloning theorem and quantum teleportation.
6. Classical Public Key and Quantum computational cryptography
7. The fundamentals of quantum algorithms.
8. The experimental realization of quantum computers.
Topics covered during these classes:
1. The qubit, Bloch sphere, decoherence.
2. Single-qubit gates, universal quantum gates.
3. Selected quantum algorithms: Deutsch–Jozsa, Shor’s, Grover’s, quantum phase estimation, quantum simulation, quantum optimization.
4. Quantum error correction.
4. Public key cryptography, elliptic-curve cryptography, RSA method, Public Key Infrastructure, digital signatures.
5. Quantum cryptography, quantum key distribution
6. Quantum teleportation.