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We demonstrate superconducting qubits using epitaxially grown Josephson junctions. A fully epitaxial NbN/AlN/NbN trilayer on MgO (100) substrate is processed by photolithography and dry-etching into transmon qubits with a large Josephson energy. The tunnel barrier made of cubic-phase AlN, rather than the ordinary hexagonal phase, is the key to avoid piezoelectric coupling to the phonon bath. The energy-relaxation time and the spin-echo decay time of ∼500 ns are observed in the qubits that are coupled to a monolithically made coplanar waveguide resonator. [ABSTRACT FROM AUTHOR]