Bounded Quantum Regular Language Generator

We develop a quantum algorithm to verify the correctness of systems modeled by nondeterministic finite-state automata-a problem that is computationally intractable on conventional computers. Specifically, our algorithm solves the language containment problem in three steps. First, we translate a nondeterministic finite-state automaton into a quantum finite state automaton (QFA) circuit. Second, the QFA is embedded into a larger circuit which generates a superposed set of all bounded strings that are marked to indicate whether they are accepted or not. Finally, we amplify the amplitudes of accepted strings so that they are measured more frequently. The last step may be done either by using Grover's algorithm, or by using FnR, a custom algorithm that we have developed for the cases where Grover's algorithm is not effective. Our work represents the first proposal to apply quantum computing to the problem of verifying conventional systems; our approach would facilitate software verification, program analysis, protocol design, and verification of circuits, among other applications.