  Current quantum simulators suffer from multiple limitations such as short
coherence time, noisy operations, faulty readout and restricted qubit
connectivity in some platforms. Variational quantum algorithms are the most
promising approach in near-term quantum simulation to achieve practical quantum
advantage over classical computers. Here, we explore variational quantum
algorithms, with different levels of qubit connectivity, for digital simulation
of the ground state of long-range interacting systems as well as generation of
spin squeezed states. We find that as the interaction becomes more long-ranged,
the variational algorithms become less efficient, achieving lower fidelity and
demanding more optimization iterations. In particular, when the system is near
its criticality the efficiency is even lower. Increasing the connectivity
between distant qubits improves the results, even with less quantum and
classical resources. Our results show that by mixing circuit layers with
different levels of connectivity one can sensibly improve the performance.
Interestingly, the order of layers becomes very important and grouping the
layers with long-distance connectivity at the beginning of the circuit
outperforms other permutations. The same design of circuits can also be used to
variationally produce spin squeezed states, as a resource for quantum
metrology.
