Superconducting Circuits and Qubits

Mentor:Mikhail Fistul

Course Summary

The course of lectures introduces into the physical principles of quantum information and macroscopic quantum phenomena in superconducting (Josephson) systems. The course of lectures will provide students with a basic understanding of various phenomena in the field of quantum information. In the first part of the course (3 lectures, 6 hours) the basic phenomena in the field of quantum information is considered. The lectures material will address the principles of “quantum computer”, “adiabatic quantum computer”, quantum logic and algorithms, “quantum games” quantum teleportation and quantum cryptography. The second part of the course (3 lectures, 6 hours) will be devoted to the theoretical foundations and experimental observations of the various superconducting systems in the macroscopic quantum regime. The important issues related to the choice of the parameters of these systems, the effect of temperature and dissipation, the interaction with the microwave radiation and the measurement of macroscopic quantum effects are addressed.

Course Format

Hours of lectureHours of discussionHours of independent studyHours total
34174596

Please note that students are expected to study outside of class for three hours for every hour in class.

Course Content

The plan is to work through the following topics:

  1. Physical principles of quantum information
    1. Quantum calculations:
      1. qubits, addressing of qubits, quantum logics
      2. simple quantum algorithms, quantum games
    2. Quantum teleportation and entanglement
      1. Quantum entanglement and teleportation
      2. Quantum cryptography, sophisticated quantum algorithms
    3. Adiabatic quantum computer
      1. adiabatic processes in quantum mechanics
      2. adiabatic quantum computing
  2. Superconducting systems for quantum information processing.
    1. Superconducting systems: potential, effective mass, macroscopic energy levels, frequency of small oscillations
      1. Single Josephson junctions: phase and charge qubits
      2. Single Josephson junction or a few Josephson junctions inserted in a superconducting ring: the role of ring geometry
      3. Josephson junction embedded in the resonator and the transmission line.
    2. Macroscopic quantum effects: temperature, dissipations, interaction with microwave radiation
      1. Macroscopic quantum tunneling
      2. Resonant enhancement of MQT in the presence of microwave radiation.
      3. Rabi oscillations
      4. Ramsey fringes and "spin-echo"phenomenon
      5. Interaction of Josephson junctions with the photons of resonator.
    3. Measurements of macroscopic quantum effects
      1. Transition from the superconducting state to a resistive one.
      2. Inductive measurements
      3. The transmission and reflection of electromagnetic waves interacting with the quantum objects.

Textbooks

Primary textbooks:

  1. C. Kittel. Quantum theory of solids. — Wiley&Sons, New York, 1987.

Additional textbooks:

  1. Neil W. Ashcroft, D. Mermin. Solid state physics. — Brooks Cole, 1976.

Homework Assignments

Weekly, 12 problem sets in total, due at the beginning of the lecture. You may also submit via e-mail before the due date/time. It is of outmost importance that you invest your own effort into solving problems. Should you consult any sources, please provide references. Homework assignments should be typed. Legible handwritten assignments are acceptable.

Grading

Class participation10%
Homework assignments20%
Midterm exam20%
Final exam50%