  With a view toward addressing the explosive growth in the computational
demands of nuclear structure and reactions modeling, we develop a novel quantum
algorithm for neutron-nucleus simulations with general potentials, which
provides acceptable bound-state energies even in the presence of noise, through
the noise-resilient training method. In particular, the algorithm can now solve
for any band-diagonal to full Hamiltonian matrices, as needed to accommodate a
general central potential. This includes exponential Gaussian-like potentials
and ab initio inter-cluster potentials (optical potentials). The approach can
also accommodate the complete form of the chiral effective-field-theory
nucleon-nucleon potentials used in ab initio nuclear calculations. We make this
potential available for three different qubit encodings, including the one-hot
(OHE), binary (BE), and Gray encodings (GE), and we provide a comprehensive
analysis of the number of Pauli terms and commuting sets involved. We find that
the GE allows for an efficient scaling of the model-space size $N$ (or number
of basis states used) and is more resource efficient not only for tridiagonal
Hamiltonians, but also for band-diagonal Hamiltonians having bandwidth up to
$N$. We introduce a new commutativity scheme called distance-grouped
commutativity (DGC) and compare its performance with the well-known
qubit-commutativity (QC) scheme. We lay out the explicit grouping of Pauli
strings and the diagonalizing unitary under the DGC scheme, and we find that it
outperforms the QC scheme, at the cost of a more complex diagonalizing unitary.
Lastly, we provide first solutions of the neutron-alpha dynamics from quantum
simulations suitable for NISQ processors, using an optical potential rooted in
first principles, and a study of the bound-state physics in neutron-Carbon
systems, along with a comparison of the efficacy of the OHE and GE.
