Analysis and Synthesis of Superconducting Qubits with the BKD & Burkard methods
Adrián Parra (University of the Basque Country)
Place: Sala de Reuniones 7
Title: Analysis and Synthesis of Superconducting Qubits with the BKD & Burkard methods
Most of the previous works on Superconducting Qubits treated decoherence using the spin-boson model (neglecting leakage effects). Firstly, I will introduce the BKD and Burkard models [1,2] for treating the multilevel quantum description of a lumped element superconducting circuit. By means of electrical graph theory it derives a Hamiltonian for two classes of circuits. The dissipative elements are treated with the Caldeira & Leggett model. A Master equation in the Born-Markov approximation is cast into the Redfield-Bloch form to describe multilevel dissipative quantum dynamics. As a special case, truncation of the Hilbert space and derivation of relaxation (T 1 ) and dephasing (T 2 ) times. Secondly, I will introduce my Master Thesis project where I continued the GUI program started by C. B. Lirakis at IBM to automate all the calculations of the original papers. A simple energy spectrum solver (for 1D and 2D slow degrees of freedom)  was programmed to output numerical approximations for decoherence rates in user-designed circuit. Finally, I will present a part of F. Solgun’s PhD Thesis [4,5,6] that shows how to quantize a single-port and multi-port impedance (microwave environment) by means of Burkard/BKD theories and Brune’s circuit synthesis.
1. G. Burkard, R. H. Koch, and D. P. DiVincenzo, “Multi-level quantum description of decoherence in superconducting qubits”, Phys. Rev. B, 69, 064503 (2004).
2. G. Burkard, “Circuit theory for decoherence in superconducting charge qubits”, Phys. Rev. B, 71,144511 (2005).
3. D. P. DiVincenzo, F. Brito, and R. H. Koch, “Decoherence rates in complex Josephson qubit circuits”, Phys. Rev. B, 74, 014514 (2006).
4. F. Solgun, D. W. Abraham, D. P. DiVincenzo, “Blackbox Quantization of Superconducting Circuits using Impedance Synthesis”, arXiv:1403.7341v1, 2014.
5. F. Solgun, D. P. DiVincenzo, “Multiport Impedance Quantization”, arXiv:1505.04116.
6. F. Solgun, PhD Thesis: “Analysis and Synthesis of Multi-Qubit, Multi-Mode Quantum Devices” (2015).