  We explore the preparation of specific nuclear states on gate-based quantum
hardware using variational algorithms. Large scale classical diagonalization of
the nuclear shell model have reached sizes of $10^9 - 10^{10}$ basis states,
but are still severely limited by computational resources. Quantum computing
can, in principle, solve such systems exactly with exponentially fewer
resources than classical computing. Exact solutions for large systems require
many qubits and large gate depth, but variational approaches can effectively
limit the required gate depth.
  We use the unitary coupled cluster approach to construct approximations of
the ground-state vectors, later to be used in dynamics calculations. The
testing ground is the phenomenological shell model space, which allows us to
mimic the complexity of the inter-nucleon interactions. We find that often one
needs to minimize over a large number of parameters, using a large number of
entanglements that makes challenging the application on existing hardware.
Prospects for rapid improvements with more capable hardware are, however, very
encouraging.
