Type II quantum algorithms

We review and analyze the hybrid quantum-classical NMR computing methodology referred to as Type II quantum computing. We show that all such algorithms considered so far within this paradigm are equivalent to some classical lattice Boltzmann scheme. We derive a sufficient and necessary constraint on the unitary operator representing the quantum mechanical part of the computation which ensures that the model reproduces the Boltzmann approximation of a lattice-gas model satisfying semi-detailed balance. Models which do not satisfy this constraint represent new lattice Boltzmann schemes which cannot be formulated as the average over some underlying lattice-gas. We conclude the paper with some discussion of the strengths, weaknesses and possible future direction of Type II quantum computing.