Fig. 1: Realization of CCI with a hybrid digital–analog approach.
From: Experimental realization of phase-controlled dynamics with hybrid digital–analog approach
a A three-level system (a qutrit) driven by two detuned external fields (described by a Hamiltonian of H0), when combined with specially designed digital modules (the T block) constructed from discrete quantum gates, can be used to realize the Hamiltonian H hosting an inherent CCI: \(T{e}^{-i{H}_{0}t}{T}^{\dagger }\equiv {e}^{-iHt}\), with a gauge-invariant phase ϕ. For consistency with the literature, we relabel the states of the qutrit as \(\left|g\right\rangle ,\left|e\right\rangle ,\left|f\right\rangle =1,2,3\). b In a similar way, combining the natural evolution of two resonant qutrits driven by two external fields (with identical amplitudes and phases, indicated by different colors) with certain digital modules can result in a CCI in a subspace of the system. Here 1, 2, and 3 correspond to \(\left|gg\right\rangle\), \(\left|ge\right\rangle\), and \(\left|eg\right\rangle\), respectively. The gray sphere beside the state of three represents a dark state that is decoupled from the evolution of the system (see Methods section).
