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TT: Fachverband Tiefe Temperaturen
TT 17: Superconductivity: Qubits II
TT 17.1: Talk
Monday, March 12, 2018, 15:00–15:15, H 2053
Effective Evolution of a Driven Qubit Beyond the Rotating Wave Approximation — •Daniel Zeuch1, Fabian Hassler2, and David P. DiVincenzo1,2 — 1Peter Gruenberg Institut, Forschungszentrum Juelich, Juelich, Germany — 2JARA-Institute for Quantum Information, RWTH Aachen University, Aachen, Germany
Decreasing the duration of quantum gates requires high-amplitude pulses. In the high-amplitude regime one needs to take into account effects beyond those captured by the rotating wave approximation. Such effects include rapid oscillations on the time scale of 1/ω, where ω is the qubit frequency, making it difficult to accurately describe the state evolution. For constant-amplitude pulses there is an effective Hamiltonian which describes shifts of the resonance frequency, known as the Bloch-Siegert shift [1], and of the Rabi frequency. For the case of time-dependent amplitudes of the order of the qubit frequency, we employ the Magnus expansion [2] to analytically determine an effective Hamiltonian which depends on time only through the amplitude. The time evolution due to our effective Hamiltonian is a family of rotating-frame trajectories, each of which agrees at periodic points in time with the actual state trajectory. We expect that using such effective Hamiltonians will reduce computational resources when designing pulse shapes.
[1] F. Bloch and A. Siegert, Physical Review 57, 522 (1940).
[2] R. R. Ernst, G. Bodenhausen, A. Wokaun, Clarendon Press, Oxford (1987)