Gate-tunable spectrum and charge dispersion mitigation in a graphene superconducting qubit

Controlling the energy spectrum of quantum-coherent superconducting circuits, i.e. the energies of excited states, the circuit anharmonicity and the states' charge dispersion, is essential for designing performant qubits. This control is usually achieved by adjusting the circuit's geometry. In-situ control is traditionally obtained via an external magnetic field, in the case of tunnel Josephson junctions. More recently, semiconductor-weak-links-based Josephson junctions have emerged as an alternative building block with the advantage of tunability via the electric-field effect. Gate-tunable Josephson junctions have been succesfully integrated in superconducting circuits using for instance semiconducting nanowires or two-dimensional electron gases. In this work we demonstrate, in a graphene superconducting circuit, a large gate-tunability of qubit properties: frequency, anharmonicity and charge dispersion. We rationalize these features using a model considering the transmission of Cooper pairs through Andreev bound states. Noticeably, we show that the high transmission of Cooper pairs in such weak link strongly suppresses the charge dispersion. Our work illustrates the potential for graphene-based qubits as versatile building-blocks in advanced quantum circuits.