  Variational quantum eigensolvers (VQEs) are successful algorithms for
studying physical systems on quantum computers. Recently, they were extended to
the measurement-based model of quantum computing, bringing resource graph
states and their advantages into the realm of quantum simulation. In this work,
we incorporate such ideas into traditional VQE circuits. This enables novel
problem-informed designs and versatile implementations of many-body
Hamiltonians. We showcase our approach on real superconducting quantum
computers by performing VQE simulations of testbed systems including the
perturbed planar code, Z2 lattice gauge theory, 1D quantum chromodynamics, and
the LiH molecule.
