  The Variational Quantum Eigensolver (VQE) is widely considered to be a
promising candidate for a quantum-classical algorithm which could achieve
near-term quantum advantage. However, current levels of hardware noise can
require extensive application of error-mitigation techniques to achieve
reliable computations. In this work, we use several IBM devices to explore a
finite-size spin model with multiple `phase-like' regions characterized by
distinct ground-state configurations. Using pre-optimized VQE solutions, we
demonstrate that in contrast to calculating the energy, where zero-noise
extrapolation is required in order to obtain qualitatively accurate yet still
unreliable results, calculations of the energy derivative, two-site spin
correlation functions, and the fidelity susceptibility yield accurate behavior
across multiple regions, even with minimal or no application of
error-mitigation approaches. Taken together, these sets of observables could be
used to identify level crossings in VQE solutions in a simple and noise-robust
manner, with potential near-term application to identifying quantum phase
transitions, avoided crossings and non-adiabatic conical intersections in
electronic structure calculations.
