Abstract

Abstract. In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs (QBPs), which provide a graphic description of sequential quantum algorithms. In the first part of the paper, simulations between QBPs and nonuniform quantum Turing machines are presented, which allow to transfer lower and upper bound results between the two models. Using additional insights about the connection between running time and the precision of amplitudes, it is shown that nonuniform quantum Turing machines with algebraic amplitudes and QBPs with a suitable analogous set of amplitudes are equivalent in computational power if both models work with bounded or unbounded error. Quantum ordered binary decision diagrams (QOBDDs) are a restricted variant of QBPs, which can be considered as nonuniform analog of one-way quantum finite automata. In the second part of the paper, lower and upper bound results for QOBDDs are presented in order to compare variants of QOBDDs with their deterministic and randomized counterparts. In the third part QBPs are considered where the performed unitary operation may depend on the result of a previous measurement. For this model a simulation of randomized OBDDs and exponential lower bounds are presented.

Citations