  We propose a novel qubit architecture based on a planar $c$-axis Josephson
junction between a thin flake $d$-wave superconductor ($d$SC), such as a
high-$T_c$ cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$, and a conventional $s$-wave
superconductor. When operated in the transmon regime the device -- that we call
"$d$-mon" -- becomes insensitive to offset charge fluctuations and,
importantly, exhibits at the same time energy level spectrum with strong
anharmonicity that is widely tunable through the device geometry and applied
magnetic flux. Crucially, unlike previous qubit designs based on $d$-wave
superconductors the proposed device operates in a regime where quasiparticles
are fully gapped and can be therefore expected to achieve long coherence times.
