Abstract
In this paper we introduce a model of a Quantum Branching Program (QBP) and study 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(2n), contrary to the analogous situation for quantum finite automata. Further we display certain symmetric Boolean function which is computable by a read-once QBP with O(logn) width, which requires a width Ω(n) on any deterministic read-once BP and (classical) randomized read-once BP with permanent transitions in each levels.
We present a general lower bound for the width of read-once QBPs, showing that the upper bound for the considered symmetric function is almost tight.
Supported by Russia Fund for Basic Research 99-01-00163 and Fund “Russia Universities” 04.01.52. Research partially done while visiting Dept. of Computer Science, University of Bonn.
Supported by Russia Fund for Basic Research 99-01-00163 and Fund “Russia Universities” 04.01.52.
Supported in part by DFG grants, DIMACS, and IST grant 14036 (RAND-APX).
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References
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Ablayev, F., Gainutdinova, A., Karpinski, M. (2001). On Computational Power of Quantum Branching Programs. In: Freivalds, R. (eds) Fundamentals of Computation Theory. FCT 2001. Lecture Notes in Computer Science, vol 2138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44669-9_8
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DOI: https://doi.org/10.1007/3-540-44669-9_8
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