Schrieffer-Wolff Methods for Interacting Superconducting Qubits*

There are many possible methods for implementing a low-energy Pauli decomposition of a quantum circuit Hamiltonian as a continuous function of qubit and coupler control fields. Effective low energy models are helpful designs tools to optimize performance in device applications where quantum effects are important. In this talk, we report a method based on the Bravyi et al Schrieffer-Wolff transformation [1] that provides a Pauli decomposition with the following desirable properties: (i) the effective Hamiltonian remains block diagonal so that the computational subspace is completely decoupled from the non-computational states, (ii) the adiabatic connection terms generated by the time dependence of the computational subspace are block off-diagonal and thus do not generate any terms within the computational subspace, and (iii) the computational subspace has a non-trivial holonomy over the control parameter manifold. We report application of these methods to tunable flux qubits comparing results to more explicit models and experimental measurements.
[1] Bravyi et al, Annals of Physics 326, 2793 (2011)