Kvantumszámítógép-architektúrák

Quantum Computing Architectures

Course Information, 2018

• Lecturers: András Pályi, Péter Makk
• Responsible lecturer: András Pályi
• Language: English
• Location: building H, room H601
• Time: Wednesdays, 12:15-13:45
• Schedule: first lecture: Sep 5; no lecture on Sep 12, Sep 26, Oct 10, and nov 14; last lecture: Dec 5.
• Neptun Code: BMETE15MF60
• Credits: 3
• Exam: Short written test + oral exam. Dates: Dec 17, Jan 7, Jan 14, Jan 21. Exams start at 8:00am.

Slides

Lecture 1: File:Lecture01.pdf
Lecture 2: File:Lecture02.pdf
Lecture 3: File:Lecture03.pdf
Lecture 4: File:Lecture04.pdf
Lecture 5: File:Lecture05.pdf
Lecture 6: File:Lecture6.pdf
Lecture 7: File:Lecture07.pdf
Lecture 8: File:Lecture08.pdf
Lecture 9: File:Lecture09.pdf
Lecture 10: File:Lecture10.pdf

Control questions, exercises (Oct 25, 2018): File:ControlQuestionsExercises-v6.pdf

Syllabus

The building blocks of nowadays electronic devices have already reached a few tens on nanometers sizes, and further miniaturization requires the introduction of novel technologies. At such small length-scales the coherent behavior and the interaction of electrons, together with the atomic granularity of matter induce several striking phenomena, that are not observed at the macroscopic scale. The course gives an introduction to a broad set of nanoscale phenomena following the topics bellow:

• 1. Quantum bits

Qubits, dynamics, measurement, polarization vector, composite systems, logical gates, circuits, algorithms.

• 2. Control of quantum systems.

Hamiltonians, propagators, and quantum gates. Larmor precession, Rabi oscillations, dispersive resonator shift in the Jaynes-Cummings model, exchange interaction, virtual photon exchange.

• 3. Qubits based on the electron spin.

Quantum dots, energy scales. Interactions: Zeeman, spin-orbit, hyperfine, electron-phonon, electron-electron.

• 4. Coherent control of electron spins.

Single-qubit gates: magnetic resonance, electrically driven spin resonance. Two-qubit gates: sqrt-of-swap via exchange interaction, CPhase. Error mechanisms during qubit control.

• 5. Information loss mechanisms for electron spins.

Qubit relaxation due to spin-orbit interaction and phonons. Qubit dephasing due to nuclear spins. Decoherence due to charge noise. Hahn echo and Car-Purcell-Meibloom-Gill (CPMG) schemes for prolonging the decoherence time.

• 6. Introduction to superconductivity.

Basics of superconductivity. Josephson junctions. Current-phase and voltage-phase Josephson relations. Andreev reflection. Andreev Bound State picture of the current-phase Josephson relation.

• 7. Josephson devices.

Resistively and capacitively shunted junction (RCSJ) model, junction dynamics, switching voltages, macroscopic quantum tunnelling, Superconducting Quantum Interference Device (SQUID), Fraunhofer pattern, spatial distribution of the Josephson current, radiofrequency (RF) SQUID.

• 8. Control and readout of single qubits.

Quantization of RF circuits, phase and charge as conjugate variables. Different qubit architectures: flux, charge, phase. Single-qubit gates and readout.

• 9. Information loss in superconducting qubits.

Experiments on single qubits. Deceoherence in qubits, sweet spots. Transmon as a noise-resistant qubit architecture.

• 10. Circuit quantum electrodynamics.

Superconducting resonators and their interaction with a transmon qubit. Strong coupling in circuit quantum electrodynamics. Single-qubit gates and dispersive readout via the resonator.

• 11. Entanglement in superconducting qubits.

Two-qubit coupling mechanisms: capacitive, resonator-based. Two-qubit gates. State tomography, Bell inequalities.

• 12. Multi-qubit devices.

Realization of basic quantum algorithms. Error correction: repetition code, surface code.

• 13. Overview of current research directions.

Quantum simulation. Intermediate-scale quantum computers (Google, IBM, Intel, D-Wave).

Literature

• T. Ihn: Semiconducting nanosctructures, Oxford University Press, 2010.
• Y.V. Nazarov, Y.M. Blanter: Quantum Transport: Introduction to Nanoscience, Cambridge University Press, 2009.
• Zwanenburg et al., Rev. Mod. Phys. 85, 961 (2013)
• Nanofizika tudásbázis