New Operations of Qubits
Artyom M. Grigoryan, Sos S. Agaian · 2025
This chapter shows that single qubits with real amplitudes can be multiplied and divided similarly to complex numbers. The inverse qubit is the complex conjugate qubit. The chapter describes new operations of qubits and quantum representations, which include multiplication of single qubits and properties; multiplication, division, and inverse between quantum superpositions; new representation of the quantum Fourier transform; ideal low- and high-pass filtration; and qubit quadratic equations. These operations can be used to process quantum computation images and signals. There are models of signal and image quantum representation, which use single qubits containing information of the signal or intensities or colors of the image at each point. The chapter considers a quadratic qubit equation and its solution with an example. There is a need to find new efficient operations on qubits, two-qubits, multi-qubits, and quantum superpositions to expand the capabilities in processing signals and images.