  Variational quantum algorithms involve training parameterized quantum
circuits using a classical co-processor. An important variational algorithm,
designed for combinatorial optimization, is the quantum approximate
optimization algorithm. Realization of this algorithm on any modern quantum
processor requires either embedding a problem instance into a Hamiltonian or
emulating the corresponding propagator by a gate sequence. For a vast range of
problem instances this is impossible due to current circuit depth and hardware
limitations. Hence we adapt the variational approach -- using ion native
Hamiltonians -- to create ansatze families that can prepare the ground states
of more general problem Hamiltonians. We analytically determine symmetry
protected classes that make certain problem instances inaccessible unless this
symmetry is broken. We exhaustively search over six qubits and consider upto
twenty circuit layers, demonstrating that symmetry can be broken to solve all
problem instances of the Sherrington-Kirkpatrick Hamiltonian. Going further, we
numerically demonstrate training convergence and level-wise improvement for up
to twenty qubits. Specifically these findings widen the class problem instances
which might be solved by ion based quantum processors. Generally these results
serve as a test-bed for quantum approximate optimization approaches based on
system native Hamiltonians and symmetry protection.
