Multiplicative group of quantum representations of signals

This paper defines an operation of multiplication of qubits and describes a subspace of multi-qubit superpositions on which this operation can be applied. In this subspace of superpositions, we describe the operation of quantum convolution using the Fourier transform. The multiplicative group of qubits is described with inverse operations and division of qubits. Since the quantum superpositions require the normalization of amplitudes of the basis states, all these operations are operations composed of Givens rotations. Examples of the ideal low-pass and high-pass filters over the quantum signals described by such superpositions are given. Also, we describe qubit quadratic equations and solutions with an example.