Non-perturbative analytical diagonalization of Hamiltonians with application to ZZ-coupling suppression and enhancement in circuit-QED

Deriving effective Hamiltonian models plays an essential role in many quantum control and engineering problems. In this talk, we present two symbolic methods for effectively eliminating auxiliary space: the Non-perturbative Analytical Diagonalization (NPAD) and the Recursive Schrieffer-Wolff Transformation (RSWT). While NPAD makes use of the Jacobi iteration and works without the assumption of perturbation, RSWT takes advantage of the recursive structure and avoids the exponentially increasing number of terms in high-order perturbation. Both methods consist of elementary expressions and can be easily automated to obtain closed-form expressions. This opens the possibility for fast operations using adiabatic techniques such as DRAG and STA beyond the perturbative regime.

To demonstrate their application, we studied the ZZ interaction of superconducting qubits. In a near-resonant regime, the algorithm produces an analytical expression for the effective ZZ interaction strength, with an improvement of at least one order of magnitude compared to neglecting the further detuned state. In a weak-dispersive regime, we calculated perturbative correction up to the 8th order and accurately identified a regime with suppressed ZZ interaction in a simple transmon-resonator-transmon model.