A quantum algorithm for uniform sampling of models of propositional logic based on quantum probability

Abstract

We describe a class of quantum algorithms to generate models of propositional logic with equal probability. We consider quantum stochastic flows that are the quantum analogues of classical Markov chains and establish a relation between fixed points on the two flows. We construct chains inspired by von Neumann algorithms using uniform measures as fixed points to construct the corresponding irreversible quantum stochastic flows. We formulate sampling models of propositions in the framework of adiabatic quantum computing and solve the underlying satisfiability instances. Satisfiability formulation is an important and successful technique in modeling the decision theoretic problems in a classical context. We discuss some features of the proposed algorithms tested on an existing quantum annealer D-Wave II extending the simulation of decision theoretic problems to a quantum context.

Formal verification of communication protocols using quantized Horn clauses

“…We will work within the open quantum formalism by realizing the effect of the coin through the operators driving the discrete quantum noises (the three martingales). We recommend the works on discrete processes [15,55] for the readers to gain understanding in rigorous establishment of their existence and their applications respectively. Some essential features are provided in the Appendix for a quick reference.…”