Abstract: The nuclear shell model is one of the prime many-body methods to study the structure of atomic nuclei, but it is hampered by an exponential scaling on the basis size as the number of particles increases. We present a shell-model quantum circuit design strategy to find nuclear ground states that circumvents this limitation by exploiting an adaptive variational quantum eigensolver algorithm. Our circuit implementation is in excellent agreement with classical shell-model calculations for a dozen of light and medium-mass nuclei, including neon and calcium isotopes. We quantify the circuit depth, width and number of gates to encode realistic shell-model wavefunctions. Our simulated circuits approach the benchmark results exponentially with a polynomial scaling in quantum resources for each nucleus and configuration space. This work paves the way for quantum computing shell-model studies across the nuclear chart.