On Computational Power of Quantum Branching Programs [chapter]

Farid Ablayev, Aida Gainutdinova, Marek Karpinski
2001 Lecture Notes in Computer Science  
In this paper we study a model of Quantum Branching Program (QBP) and investigate its computational power. We define several natural restrictions of a general QBP model, such as a read-once and a read-k-times QBP, noting that obliviousness is inherent in a quantum nature of such programs. In particular we show that any Boolean function can be computed deterministically (exactly) by a read-once QBP in width O(2 n ), contrary to the analogous situation for quantum finite automata. Further we
more » ... ay certain symmetric Boolean function which is computable by a read-once QBP with O(log n) width, which requires a width Ω(n) on any deterministic read-once BP and (classical) randomized read-once BP with permanent transitions at each level. We present a general lower bound for the width of read-once QBPs, showing that the upper bound for a considered symmetric function is almost tight.
doi:10.1007/3-540-44669-9_8 fatcat:ps2dy7oagrcitahfy3tynjocu4