Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.
LEARNING OUTCOMES
After completing this course, the student is able to
- Apply the theoretical framework of quantum mechanics in electric
circuits and devices, that is, circuit quantum electrodynamics - Design and model superconducting quantum circuits: from resonators to qubits
- Identity electrical circuits of practical interest that behave quantum mechanically
- Distinguish between linear and non‐linear electronic systems and utilize them for the desired functionalities, for example
- Hypothesize on the behavior of quantum systems
Credits: 5
Schedule: 01.03.2021 - 12.04.2021
Teacher in charge (valid 01.08.2020-31.07.2022): Jan Goetz, Gheorghe-Sorin Paraoanu
Teacher in charge (applies in this implementation): Jan Goetz, Gheorghe-Sorin Paraoanu
Contact information for the course (valid 10.02.2021-21.12.2112):
Sorin Paraoanu, sorin.paraoanu@aalto.fi
Jan Goetz, jan.goetz@meetiqm.com
Mikko Möttönen, mikko.mottonen@aalto.fi
CEFR level (applies in this implementation):
Language of instruction and studies (valid 01.08.2020-31.07.2022):
Teaching language: English
Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
Valid 01.08.2020-31.07.2022:
The physical foundations and implementation of solid-state quantum electronics has attracted broad interest in the context of the realization of quantum information processing systems. In this course, we address the physics of superconducting quantum circuits and show how such circuits can be implemented based on superconducting thin films and nanostructures. We discuss the application of superconducting quantum circuits in quantum information processing systems and in quantum simulation. The following specific topics will be addressed:
- quantization of Josephson junction devices
- systematic quantization of a network of electric lumped-element components
- quantum mechanics of 1D transmission lines and resonators
- cavity–qubit systems
- operation of superconducting qubits: reset, quantum logic, and readout.
Applies in this implementation:
1. Lecture 1: Key concepts from
quantum mechanics and solid-state physics. Hilbert space, qubits and
harmonic oscillators. Quantum mechanics in second quantization formulation.
Density of states.2. Lecture 2: Components. Resistors, capacitors, inductors, filters.
Transmission lines and resonators.3. Lecture 3: Noise in classical and
quantum electrical circuits. Nyquist theorem and the crossover from quantum
to classical.4. Lecture 4: Superconductivity and
the Josephson effect. The superconducting order parameter and phase. Tunnel
barriers and the Josephson effect. Interference and SQUIDs.5. Lecture 5: Introduction to
simulation and Multiphysics problems using COMSOL. Mathematical preliminaries: a crash course on
partial differential order equations and boundary value problem; the finite
element method. Introduction to
Multiphysics. COMSOL: A tool for modeling Multiphysics: Walk around COMSOL
desktop; COMSOL geometry; COMSOL physics;
results and post-processing of data. A real-time
example: Transmission line and electrostatics.6. Lecture 6: Advanced circuit
simulations in COMSOL.Hands-on approach: thermal management, electromagnetism,
microwave engineering - one model circuit will be discussed in detail.7. Lecture 7: Quantization of
electrical networks. DiVicenzo criteria and how they are related to this
course. Basic concepts: Lagrangian, Legendre transform to Hamiltonian. Example
1: harmonic oscillator. Example 2: an-harmonic oscillator. Example 3: harmonic
oscillator coupled to qubit.8. Lecture 8: Superconducting
quantum bits. Introducing the transmon
qubit, the charge qubit, and the flux qubit. Elements of circuit QED: the Rabi
model and the Jaynes-Cummings model.9. Lecture 9: Single-qubit
operations. The transmon: initialization, control and readout. T1 and T2
measurements. Randomized benchmarking.10. Lecture 10: Architectures for
2-qubit gates. Realization of: iSWAP,
cPhase, and CNOT. Deep dive: Google’s quantum supremacy experiment.11. Lecture 11: Quantum algorithms.
Introduction to VQE and Grover search.12. Lecture 12: Challenges in quantum
computing. Scaling, the SW-HW gap, and error-correction.
Assessment Methods and Criteria
Valid 01.08.2020-31.07.2022:
Teaching methods: lectures and exercises
Assessment methods: exercises and exam
Applies in this implementation:
Exercises will count as 50%. Feedback from the exercises will be given by the TAs. Exam will count as 50%.
Workload
Valid 01.08.2020-31.07.2022:
Lectures: 24 h, exercises: 12 h, exam: 3 h + independent work
Applies in this implementation:
Contact hours: 24h lectures + 12 h exercises. Independent work: maximum 72 h.
DETAILS
Study Material
Applies in this implementation:
The course does not follow a single book or reference. Course materials will be indicated for every lecture.
Prerequisites
Valid 01.08.2020-31.07.2022:
Basic knowledge in quantum mechanics including second quantization and harmonic oscillator. Basic knowledge on condensed-matter physics.