On the computational power of probabilistic and quantum branching program

Farid Ablayev, Aida Gainutdinova, Marek Karpinski, Cristopher Moore, Christopher Pollett
2005 Information and Computation  
In this paper, we show that one-qubit polynomial time computations are as powerful as NC 1 circuits. More generally, we define syntactic models for quantum and stochastic branching programs of bounded width and prove upper and lower bounds on their power. We show that any NC 1 language can be accepted exactly by a width-2 quantum branching program of polynomial length, in contrast to the classical case where width 5 is necessary unless NC 1 = ACC. This separates width-2 quantum programs from
more » ... th-2 doubly stochastic programs as we show the latter cannot compute the middle bit of multiplication. Finally, we show that bounded-width quantum and stochastic programs can be simulated by classical programs of larger but bounded width, and thus are in NC 1 . For read-oncequantum branching programs (QBPs), we give a symmetric Boolean
doi:10.1016/j.ic.2005.04.003 fatcat:mncsgr5c5rhn3h7yh7izipf6du