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Quantum vs. classical readonce branching programs
, 504
"... Abstract. The paper presents the first nontrivial upper and lower bounds for (nonoblivious) quantum readonce branching programs. It is shown that the computational power of quantum and classical readonce branching programs is incomparable in the following sense: (i) A simple, explicit boolean func ..."
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Abstract. The paper presents the first nontrivial upper and lower bounds for (nonoblivious) quantum readonce branching programs. It is shown that the computational power of quantum and classical readonce branching programs is incomparable in the following sense: (i) A simple, explicit boolean function on 2n input bits is presented that is computable by errorfree quantum readonce branching programs of size O � n 3 � , while each classical randomized readonce branching program and each quantum OBDD for this function with bounded twosided error requires size 2 Ω(n). (ii) Quantum branching programs reading each input variable exactly once are shown to require size 2 Ω(n) for computing the setdisjointness function DISJn from communication complexity theory with twosided error bounded by a constant smaller than 1/2−2 √ 3/7. This function is trivially computable even by deterministic OBDDs of linear size. The technically most involved part is the proof of the lower bound in (ii). For this, a new model of quantum multipartition communication protocols is introduced and a suitable extension of the information cost technique of Jain, Radhakrishnan, and Sen (2003) to this model is presented. 1.
Abstract
, 2005
"... 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 progr ..."
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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.