Rate-equation approach for qudits

Qubits (two-level quantum systems) play a key role in building and development of quantum computers. However, there are systems, which can enhance the efficiency of quantum algorithms and simplify the experimental setup, such systems are qudits (d-level quantum systems). In our research we theoretically investigate the influence of strong driving on one of such systems. The results can give appropriate information about ways of controlling and characterizing qudit states. One of possible tools for theoretical analysis of multi-level quantum systems properties is the rate-equation formalism. The great advantage of considered approach is its simplicity. Firstly we applied the formalism for description of a two-level system and then expanded it on a case of a multi-level system. Obtained theoretical results have good agreement with experiments [1, 2]. Also we compared rate-equation formalism with Lindblad equation approach and got good agreement between them. The presented approach can be considered as one additional way for exploring properties of quantum systems and underlying physical processes such as, for example, interference and Landau-Zener-Stuckelberg-Majorana transition.

[1] D. M. Berns, et al., “Coherent quasiclassical dynamics of a persistent current qubit, ” Phys. Rev. Lett. 97, 150502 (2006).

[2] D. Berns, et al., “Amplitude spectroscopy of a solid-state artificial atom, ”Nature 455, 51–57 (2008).