  Hybrid algorithms that combine quantum and classical resources have become
commonplace in quantum computing. The variational quantum eigensolver (VQE) is
routinely used to solve prototype problems. Currently, hybrid algorithms use no
more than one kind of quantum computer connected to a classical computer. In
this work, a novel triple-hybrid algorithm combines the effective use of a
classical computer, a gate-based quantum computer, and a quantum annealer. The
solution of a graph coloring problem found using a quantum annealer reduces the
resources needed from a gate-based quantum computer to accelerate VQE by
allowing simultaneous measurements within commuting groups of Pauli operators.
We experimentally validate our algorithm by evaluating the ground state energy
of H$_2$ using different IBM Q devices and the DWave Advantage system requiring
only half the resources of standard VQE. Other larger problems we consider
exhibit even more significant VQE acceleration. Several examples of algorithms
are provided to further motivate a new field of multi-hybrid algorithms that
leverage different kinds of quantum computers to gain performance improvements.
