Regensburg 2022 – scientific programme
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QI: Fachverband Quanteninformation
QI 5: Implementations: Solid state systems
QI 5.6: Talk
Tuesday, September 6, 2022, 11:15–11:30, H8
Modelling and engineering cQED devices via effective Hamiltonians — •Boxi Li1,2, Tommaso Calarco1,2, and Felix Motzoi1 — 1Forschungszentrum Jülich, D-52425 Jülich, Germany — 2Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
Deriving effective Hamiltonian models plays an essential role in quantum theory, with particular emphasis in recent years on control and engineering problems. To develop fast, high-fidelity operations on cQED devices, there are also increasing demands on modelling tools that go beyond the strong perturbative regime and accurately capture the dynamics.
To this goal, we present two symbolic methods for computing effective Hamiltonian models. The first method makes use of the Jacobi iteration and works without the assumptions of perturbation theory while retaining convergence. In the perturbation regime, it reduces to a variant of the Schrieffer-Wolff method, which takes advantage of a recursive structure and exponentially decreases the number of terms in the high-order expansion. Both methods consist of algebraic expressions and can be easily automated for symbolic computation.
Based on these methods, we perform (semi-)analytical calculations that compute the effective Hamiltonian. We investigate both the ZZ and the cross-resonance interaction in the quasi-dispersive regimes. By choosing a proper frame transformation, we show that one can develop control pulses to suppress noises such as leakage and dynamical ZZ crosstalk, improving upon the conventional perturbative calculation.