Transmon qubit, based on a superconducting Josephson junction shunted by a large capacitance, is the workhorse component powering the majority of intermediate scale quantum computers currently in operation. I this talk I will describe a theoretical proposal for a novel transmon architecture dubbed "d-mon" that uses unconventional oxide superconductors and is designed to overcome one of the key shortcomings of the conventional transmon. The proposed d-mon architecture is based on a c-axis Josephson junction between a d-wave high-Tc cuprate and a conventional s-wave superconductor. Its chief advantage lies in the large and tunable anharmonicity of its energy spectrum that we predict should enable faster and more reliable gate operation. In contrast to some earlier cuprate-based qubit designs d-mon operates in the regime where quasiparticles are fully gapped and can be therefore expected to achieve long coherence times.