Informacje ogólne:
Nazwa:
Quantum Mechanics & Quantum Computing
Kod:
int.courses-299
Profil kształcenia:
Ogólnoakademicki (A)
Język wykładowy:
Angielski
Semestr:
letni
Osoba odpowiedzialna:
prof. dr hab. inż. Koleżyński Andrzej (kolezyn@agh.edu.pl)
Osoby prowadzące:
prof. dr hab. inż. Koleżyński Andrzej (kolezyn@agh.edu.pl)
Krótka charakterystyka modułu

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

Opis efektów kształcenia dla modułu zajęć
Kod EKM Student, który zaliczył moduł zajęć wie/umie/potrafi Powiązania z EKK Sposób weryfikacji efektów kształcenia (forma zaliczeń)
Wiedza
M_W001 Student has basic knowledge of fundamentals of quantum mechanics and its most important approximations. Egzamin
M_W002 Student has basic knowledge of fundamentals of quantum algorithms and the basic ideas behind the experimental realization of quantum computers. Egzamin
Umiejętności
M_U001 Student can analyze practical problem he/she is facing in quantum computing and select the appropriate algorithm to solve it. Egzamin
Kompetencje społeczne
M_K001 Student is prepared to effectively select appropriate algorithms of quantum computation to solve typical numerical problems.
Matryca efektów kształcenia w odniesieniu do form zajęć
Kod EKM Student, który zaliczył moduł zajęć wie/umie/potrafi Forma zajęć
Wykład
Ćwicz. aud
Ćwicz. lab
Ćw. proj.
Konw.
Zaj. sem.
Zaj. prakt
Zaj. terenowe
Zaj. warsztatowe
Inne
E-learning
Wiedza
M_W001 Student has basic knowledge of fundamentals of quantum mechanics and its most important approximations. + - - - - - - - - - -
M_W002 Student has basic knowledge of fundamentals of quantum algorithms and the basic ideas behind the experimental realization of quantum computers. + - - - - - - - - - -
Umiejętności
M_U001 Student can analyze practical problem he/she is facing in quantum computing and select the appropriate algorithm to solve it. - + - - - - - - - - -
Kompetencje społeczne
M_K001 Student is prepared to effectively select appropriate algorithms of quantum computation to solve typical numerical problems. - + - - - - - - - - -
Treść modułu zajęć (program wykładów i pozostałych zajęć)
Wykład:

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, Hermitian operators, eigenvalue problem, eigenfunctions, eigenvalues, the measurement problem, average values, time evolution of wave functions, Schrodinger equation, Ehrenfest’s theorem.
4) Problems with analytical solutions: particle in a box, harmonic oscillator, hydrogen atom.
5) Multi-electron atoms, the Pauli principle, electron spin, electronic configuration
6) Superposition of states and a concept of qubits (quantum bits), quantum entanglement, non-local correlations, the no-cloning theorem and quantum teleportation.
7) Quantum computational cryptography
8) The fundamentals of quantum algorithms.
9. The experimental realization of quantum computers.

Ćwiczenia audytoryjne:

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.

Nakład pracy studenta (bilans punktów ECTS)
Forma aktywności studenta Obciążenie studenta
Sumaryczne obciążenie pracą studenta 102 godz
Punkty ECTS za moduł 4 ECTS
Udział w wykładach 15 godz
Udział w zajęciach praktycznych 15 godz
Egzamin lub kolokwium zaliczeniowe 2 godz
Samodzielne studiowanie tematyki zajęć 40 godz
Dodatkowe godziny kontaktowe z nauczycielem 15 godz
Przygotowanie do zajęć 15 godz
Pozostałe informacje
Sposób obliczania oceny końcowej:

The final grade is calculated as a weighted average of partial grades: activity during classes (30%), attendance (10%) and exam results (60%).

Wymagania wstępne i dodatkowe:

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.

Zalecana literatura i pomoce naukowe:

1. G. Benenti, G. Casati, G. Strini, Principles of Quantum Computation and Information. Volume I: Basic Concepts, World Scientific Publishing Co. Pte. Ltd. (2004).
2. M. A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press New York (2010)
3. J.A. Jones, D. Jaksch, Quantum Information, Computation and Communication, Cambridge University Press New York (2012)
4. E. Rieffel, W. Polak, Quantum Computing. A Gentle Introduction, The MIT Press (2011)
5. M. Le Bellac, A Short Introduction to Quantum Information and Quantum Computation, Cambridge University Press (2006)
6. D. Mermin, Quantum Computer Science: An Introduction, Cambridge University Press, (2007)

Publikacje naukowe osób prowadzących zajęcia związane z tematyką modułu:

1. A. Koleżyński, “FP-LAPW study of anhydrous cadmium and silver oxalates: electronic structure and electron density topology”, Phys. B, 405 3650–3657 (2010); DOI: 10.1016/j.physb.2010.05.059.
2. J. Leszczyński, A. Koleżyński, K.T. Wojciechowski, “Electronic and transport properties of polycrystalline Ba8Ga15Ge31 type I clathrate prepared by SPS method”, J. Sol. State Chem., 193 114-121 (2012); DOI: 10.1016/j.jssc.2012.03.067.
3. W. Szczypka, P. Jeleń, A. Koleżyński, “Theoretical studies of bonding properties and vibrational spectra of chosen ladder-like silsesquioxane clusters”, J. Mol. Struct., 1075 599–604 (2014), DOI: 10.1016/j.molstruc.2014.05.037.
4. A. Koleżyński, P. Nieroda, K. T. Wojciechowski, “Li doped Mg2Si p-type thermoelectric material: theoretical and experimental study”, Comp. Mat. Sci., 100 84–88 (2015), DOI: 10.1016/j.commatsci.2014.11.015.
5. A. Mikuła, M. Król, A. Koleżyński, “The influence of the long-range order on the vibrational spectra of structures based on sodalite cage”, Spectrochim. Acta. A, 144 273–280 (2015), DOI: 10.1016/j.saa.2015.02.073.
6. P. Nieroda, A. Kolezynski, M. Oszajca, J. Milczarek, K. T. Wojciechowski, “Structural and Thermoelectric Properties of Polycrystalline p-Type Mg2-xLixSi”, J. Electronic Mat., 45 3418-3426 (2016), DOI: 10.1007/s11664-016-4486-5.
7. A. Koleżyński, W. Szczypka, “First-Principles Study of the Electronic Structure and Bonding Properties of X8C46 and X8B6C40 (X: Li, Na, Mg, Ca) Carbon Clathrates”, J. Electronic Mat., 45 1336–1345 (2016), DOI: 10.1007/s11664-015-4028-6.
8. A. Koleżyński, W. Szczypka, “Towards band gap engineering in skutterudites: The role of X4 rings geometry in CoSb3-RhSb3 system”, J. Alloys Compd., 691 299-307 (2017), DOI: 10.1016/j.jallcom.2016.08.235
9. E. Drożdż, A. Koleżyński, “The structure, electrical properties and chemical stability of porous Nb-doped SrTiO3 – experimental and theoretical studies”, RSC Advances, 7 28898-28908 (2017), DOI: 10.1039/C7RA04205A.
10. J. Leszczyński, W. Szczypka, Ch. Candolfi, A. Dauscher, B. Lenoir, A. Koleżyński, “HPHT synthesis of highly doped InxCo4Sb12 – experimental and theoretical study”, J. Alloys Compd., 727 1178-1188 (2017), DOI: 10.1016/j.jallcom.2017.08.194.
11. W. Szczypka, A. Koleżyński, “Theoretical studies of cation sublattice ordering in AgSbTe2 and AgSbSe2 – Electron density topology and bonding properties”, J. Alloys Compd., 732 293-299 (2018), DOI: 10.1016/j.jallcom.2017.10.199.
12. A. Mikuła, E. Drożdż, A. Koleżyński, “Electronic structure and structural properties of Cr-doped SrTiO3– Theoretical investigation”, J. Alloys Compd., 749 931-938 (2018), DOI: 10.1016/j.jallcom.2018.03.317.

Informacje dodatkowe:

The course starts with a simple introduction to the fundamental principles and concepts of quantum mechanics, emphasizing the paradoxical nature of the subject, including a superposition of states (and a concept of qubits – quantum bits), entanglement, non-local correlations, the no-cloning theorem and quantum teleportation. The course covers the fundamentals of quantum algorithms and discusses the basic ideas behind the experimental realization of quantum computers.