  We present a class of hybrid classical systems using quantum co-processors
and point out that unlike purely quantum computers, such hybrids can be both
universal and Turing complete; we introduce such quantum-classical hybrids as
"quassical." We discuss the benefits of quassical architectures from a
theoretical point of view: for some classes of problems they achieve
computational supremacy. From a practical point of view, quassical
architectures can also reduce the overhead burden imposed by most error
correction schemes and minimize the challenges of interconnecting qubits in a
usefully large connection graph. All quantum computing systems are
cyber-physical machines and thus quassical to at least a trivial degree but
only the more profoundly quassical hybrids can exhibit an optimum
problem-solving capability for the amount of quantum resources deployed. Most
significantly, quassical architectures advance our thinking past that of seeing
quantum machines as simply quantum embodiments of classical ones and can
enliven whole new fields of analytical thinking that takes us beyond quantum
information science per se into a deeper understanding of the duality between
quantum information and fundamental thermodynamics, possibly suggesting
unexpectedly useful new technologies.
