Information
We will offer this course again in 2020 Fall semester.
Course information  2018 Fall Semester

Lecturers: András Pályi, Péter Makk

Responsible lecturer: András Pályi

Language: English

Location: building H, room H601

Time: Wednesdays, 12:1513:45

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

Quantum bits

Control of quantum systems

Qubits based on the electron spin

Coherent control of electron spins

Information loss mechanisms for electron spins

Superconducting qubits: basic architectures

Flux and charge qubits, cQED

Qubitqubit coupling

State tomography

Grover algorithm, quantum teleportation
Contents

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

Control of quantum systems.
Hamiltonians, propagators, and quantum gates. Larmor precession, Rabi oscillations, dispersive resonator shift in the JaynesCummings model, exchange interaction, virtual photon exchange.

Qubits based on the electron spin.
Quantum dots, energy scales. Interactions: Zeeman, spinorbit, hyperfine, electronphonon, electronelectron.

Coherent control of electron spins.
Singlequbit gates: magnetic resonance, electrically driven spin resonance. Twoqubit gates: sqrtofswap via exchange interaction, CPhase. Error mechanisms during qubit control.

Information loss mechanisms for electron spins.
Qubit relaxation due to spinorbit interaction and phonons. Qubit dephasing due to nuclear spins. Decoherence due to charge noise. Hahn echo and CarPurcellMeibloomGill (CPMG) schemes for prolonging the decoherence time.

Introduction to superconductivity.
Basics of superconductivity. Josephson junctions. Currentphase and voltagephase Josephson relations. Andreev reflection. Andreev Bound State picture of the currentphase Josephson relation.

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.

Control and readout of single qubits.
Quantization of RF circuits, phase and charge as conjugate variables. Different qubit architectures: flux, charge, phase. Singlequbit gates and readout.

Information loss in superconducting qubits.
Experiments on single qubits. Deceoherence in qubits, sweet spots. Transmon as a noiseresistant qubit architecture.

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

Entanglement in superconducting qubits.
Twoqubit coupling mechanisms: capacitive, resonatorbased. Twoqubit gates. State tomography, Bell inequalities.

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

Overview of current research directions.
Quantum simulation. Intermediatescale quantum computers (Google, IBM, Intel, DWave).
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