Quantum Finite State Machines as Sequential Quantum Circuits

In this paper we present the synthesis process of quantum finite state machines for sequence detection based on the synthesis of quantum sequential circuits. Such machines have many applications for instance in robotics. We show the relation between the quantum circuit and the natural ability of quantum systems to retain the quantum state. We consider cases where a single qubit in a circuit represents a quantum state and another is used as the input qubit. We analyze some of the well known circuits as sequence detectors and describe their behaviors. We show that the standard quantum logic synthesis can be used for both the synthesis of quantum circuits as well as for quantum finite state machines used as sequence detectors.