Superconducting Qubits (WS13/14)

 

Superconducting Qubits (WS 2013/14)

by Terhal, DiVincenzo & Catelani.

Lecture & Presentations held in IQI seminar room MBP2 116 on Mondays 10.15-11.45.

Topics (roughly): Circuit Quantization and Its Applications to Various Qubits [DiV], Spectra & decoherence of modern qubits [Cat], Circuit QED as quantum optics: tools and applications [Ter].

The emphasis in the seminar is on discussion & understanding of current literature.

Overview:

  • [DiV] Oct. 21 I will begin with a discussion of equations of motion and Hamiltonians for circuits. There are three basic papers, Devoret , "BKD", and Burkard; I will follow Burkard almost completely. I will concentrate on the theme of "singular perturbations", i.e., the fact that adding a very small additional element (e.g., capacitor, inductor) can completely change our description of the system. I will illustrate this with the problem of the DC SQUID with an additional inductance, and the transmon with additional "parasitic" elements. An exercise will be given (see Oct. 28). Here are lecture notes.
  • [DiV] Oct. 28 Students will present an analysis, based on the ideas of Mooij, of the flux qubit with and without a loop inductance. Here are lecture notes.
  • [DiV] Nov. 4 By a combination of a lecture presentation and student work, we will tackle the problem of the superinductance qubit of Kitaev. Here are lecture notes and the mathematica notebook with coordinate transformation we discussed. Here is a more extensive lecture writeup of D. Weigand.
  • [Cat] Nov. 11 Microscopics: BCS theory, Bogoliubov transformation, tunneling Hamiltonian, ... Here are lecture notes .
  • [DiV] Nov. 18 We will save further study of the Brooks, Preskill, Kitaev qubit to later in the semester. Today we will see how circuit models can be derived from physical models of electrical structures. The "black box" approach of Nigg et al. is explained, put in the context of the general theory of electric response; we will learn about "positive real" responses (from the book by Newcomb 'Linear Multiport Synthesis', Chapters 3 and 4), the limitations of "lossy Foster synthesis" (see Montgomery et al., p. 216), and derive the general Brune representation of electric response (see selection from E. Guillemin, Synthesis of Passive Networks ). Another good source for network theory is Carlin . Here are the lecture notes.
  • [Cat] Nov. 25 Energy levels in Cooper pair box and transmon (both single junction and with a SQUID), parity; phase and flux qubits; fluxonium & superinductance. See III and Sec. II in PRA 76, 042319 (2007) [arXiv:cond-mat/0703002]. Lecture notes .
  • [Cat] Dec. 2 Introduction to decoherence; some examples of models for relaxation (using Fermi's Golden Rule) and dephasing [by charge fluctuations - see e.g. PRB 75, 054515 (2007) up to Eq.(21)]. Noise and decoherence [see e.g. Sec. III & III.A in PRB 72, 134519 (2005) and Ch. 5 in Girvin 's Les Houches lecture notes]. References here , lecture notes here .
  • [Cat] Dec. 9 Dephasing by two-level fluctuator (continued). Quasiparticle effects [see PRB 84, 064517 (2011), Sec. II & III]. Lecture notes here and here .
  • [Ter] Dec. 16. Interaction of cavity+qubits with external fields. Prepare by reading Appendix C1, D1 and E2 of the Clerk et al. Review. Lecture notes here See also: pictures of various experimental setups.
  • [Ter] Jan. 10. Description of measurement and drives on transmon qubits inside cavity. Lecture notes here
  • [Ter] Jan. 16 at 14.30. Modeling measurement & gates. Exercise matching phase shifts: Mathematica Notebook .
  • Jan. 20 Terhal/Presentations I (Firat/Giovanni)
  • Jan. 27 Presentations II (Shabir/Ben+Michael/Thilo).
  • Febr. 17 Presentations III.

Papers for Presentations

Previous Lecture Notes and Other Material

Superconducting Qubits I , II , III , IV (hand-written notes from course Quantum Information). Other: