The purpose of this paper is to show how a class of classical linear stochastic systems can be physically implemented using quantum optical components. Quantum optical systems typically have much higher bandwidth than electronic devices, meaning faster response and processing times, and hence have the potential for providing better performance than classical systems. A procedure is provided for constructing the quantum optical realization. The paper also describes the use of the quantum optical realization in a measurement feedback loop. Some examples are given to illustrate the application of the main results. (C) 2013 Elsevier Ltd. All rights reserved.