Geodesic
On the relative complexity of quantum and classical branching programs
Diskretnaya Matematika, Tome 14 (2002) no. 3, pp. 109-121

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We give a definition of a quantum branching program. A well-known Boolean function $\operatorname{MOD}_p$ is considered. We prove that any deterministic branching program and any probabilistic ordered stable branching program which $(1/2+\varepsilon)$-compute the function $\operatorname{MOD}_p$ are of width no less than $p$. We construct a stable quantum branching program of width $O(\log p)$ which computes the function $\operatorname{MOD}_p$ with one-sided error $\varepsilon>0$. 
@article{DM_2002_14_3_a10,
     author = {A. F. Gainutdinova},
     title = {On the relative complexity of quantum and classical branching programs},
     journal = {Diskretnaya Matematika},
     pages = {109--121},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2002_14_3_a10/}
}
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A. F. Gainutdinova. On the relative complexity of quantum and classical branching programs. Diskretnaya Matematika, Tome 14 (2002) no. 3, pp. 109-121. http://geodesic.mathdoc.fr/item/DM_2002_14_3_a10/