In the simulation of quantum circuits the matrices and vectors used to represent unitary operations and qubit states grow exponentially as the number of qubits increase. For instance, the evolution of an n-qubit quantum system in an initial superposition state is described by a 2n x 2n unitary matrix. However, the evolution of an n-qubit quantum system can be described as well as a composition of single-qubit and controlled-not unitary operations which are equivalent to the 2n x 2n unitary matrix. A strategy is suggested for the mapping of onequibit and two-qubit gates onto a three PE systolic array, and then we show how the interconnection of those systolic arrays can be used to implement or describe quantum circuits. As a case study we present the description of the teleportation algorithm.