Exploring new frontiers with superconducting qubit circuits: expanding the Hilbert space beyond qubits and pushing qubit-cavity coupling to the deep strong regime

Superconducting qubits are based on nonlinear electric circuits that support multiple quantum states. Although only two states are used to realize a qubit, it is possible to utilize more states and realize qudits (d-level quantum systems). We have proposed and experimentally demonstrated optimized implementations of qutrit gates. We have also investigated the time-optimal implementation of two-qubit gates in weakly anharmonic superconducting circuits. We found that the presence of additional energy levels can either speed up or slow down two-qubit gates, depending on the different system parameters, especially the anharmonicity. In a different line of research, we investigate the deep strong coupling between a superconducting qubit and a single-mode or multimode resonator. In the deep-strong coupling regime, the qubit and resonator are strongly correlated even in the ground state, leading to spectra and dynamics that are qualitatively different from those encountered in the standard Jaynes-Cummings model. These studies led to investigations of fundamental questions, such as the renormalization of the system parameters and the nature of the symmetry in quantum Rabi Hamiltonian. I will talk about our recent work on these topics.