Quantum Speedup and Limitations on Matroid Property Problems

This paper initiates the study of quantum algorithms for matroid property problems. It is shown that quadratic speedup possible calculation problem finding girth or number circuits (bases, flats, hyperplanes) a matroid, and decision deciding whether uniform Eulerian, by giving lower bound $\Omega(\sqrt{\binom{n}{\lfloor n/2\rfloor}})$ on query complexity all these On other hand, problem, an asymptotically optimal algorithm proposed which achieves bound, almost given with $O(\log n\sqrt{\binom{n}{\lfloor n/2\rfloor}})$. In addition, paving n/2\rfloor}/n})$ obtained, $O(\sqrt{\binom{n}{\lfloor presented.