Advanced Schrieffer-Wolff transformation techniques for circuit QED

The Schrieffer-Wolff transformation is a renowned method to obtain renormalized effective Hamiltonians. Originally popularized for relating the Anderson impurity Hamiltonian to the Kondo Hamiltonian, the Schrieffer-Wolff transformation is increasingly being used in circuit QED. Despite the many successful examples such as effective models for gate dynamics, the method is notorious for its convoluted commutator expressions which are inefficient to handle. To unravel the commutators, we developed in [1] a diagram expansion technique, and we applied it to describe the ZZ coupling between transmon qubits. In this talk, we expand our previous technique to different approximation schemes, operator solutions, and block diagonalization. We expect that our contributions to the Schrieffer-Wolff transformation will make the method more accessible and facilitate its use for analyzing quantum processors beyond a few qubits.

[1] Pettersson Fors et al., arXiv:2408.15402