  Efficient preparation of arbitrary entangled quantum states is crucial for
quantum computation. This is particularly important for noisy intermediate
scale quantum simulators relying on variational hybrid quantum-classical
algorithms. To that end, we propose symmetry-conserving modified quantum
approximate optimization algorithm~(SCom-QAOA) circuits. The depths of these
circuits depend not only on the desired fidelity to the target state, but also
on the amount of entanglement the state contains. The parameters of the
SCom-QAOA circuits are optimized using the quantum natural gradient method
based on the Fubini-Study metric. The SCom-QAOA circuit transforms an
unentangled state into a ground state of a gapped one-dimensional Hamiltonian
with a circuit-depth that depends not on the system-size, but rather on the
finite correlation length. In contrast, the circuit depth grows proportionally
to the system size for preparing low-lying states of critical one-dimensional
systems. Even in the latter case, SCom-QAOA circuits with depth less than the
system-size were sufficient to generate states with fidelity in excess of 99\%,
which is relevant for near-term applications. The proposed scheme enlarges the
set of the initial states accessible for variational quantum algorithms and
widens the scope of investigation of non-equilibrium phenomena in quantum
simulators.
