Binary superposed quantum decision diagrams

Kamil Ravilevich Khadiev, Aliya Khadieva

Michael D. Miller, Mitchell Aaron Thornton

Aida Gainutdinova

We consider a model of computation for discrete functions—Ordered Binary Decision Diagrams (OBDD).We investigate comparative complexity of quantum, deterministic, probabilistic and nondeterministic (quantum and classical) OBDDs for total and partial functions. The measure of complexity is a width of OBDD. It is known that for total functions bounded error quantum OBDDs can be exponentially more effective than deterministic and bounded error probabilistic OBDDs. We show that such quantum OBDDs also can be exponentially more effective than nondeterministic OBDDs (both quantum and classical). For partial functions the gap can be more significant. For partial function depending on a parameter k exact quantum OBDD has the width two. Deterministic and bounded error probabilistic OBDD for this function must have a width exponentially depending on k .

Robert Wille, Stefan Hillmich, Lukas Burgholzer

Matthias Homeister, Stephan Waack

Quantum branching programs (quantum binary decision diagrams, respectively) are a convenient tool for examining quantum computations using only a logarithmic amount of space. Recently several types of restricted quantum branching programs have been considered, e. g. read--once quantum branching programs. This paper considers quantum ordered binary decision diagrams (QOBDDs) and answers the question: How does the computational power of QOBDDs increase, if we allow repeated tests. Additionally it is described how to synthesize QOBDDs according to Boolean operations.

Farid Mansurovich Ablayev, Aida Gainutdinova, Kamil Ravilevich Khadiev +1 more

In the paper we investigate Ordered Binary Decision Diagrams (OBDDs)–a model for computing Boolean functions. We present a series of results on the comparative complexity for several variants of OBDDmodels. • We present results on the comparative complexity of classical and quantum OBDDs. We consider a partial function depending on a parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2, but any classical OBDD (deterministic or stable bounded-error probabilistic) needs width 2 k+1. • We consider quantum and classical nondeterminism. We show that quantum nondeterminismcan bemore efficient than classical nondeterminism. In particular, an explicit function is presented that is computed by a quantum nondeterministic OBDD of constant width but any classical nondeterministic OBDD for this function needs non-constant width. • We also present new hierarchies on widths of deterministic and nondeterministic OBDDs.