Realization of the Hadamard gate based on superposition of the composite solitons

In this article, we propose the implementation of quantum Hadamard gate through the superposition of composite solitons. Single qubit of the quantum state is defined by the components of the composite soliton which are the exact solution of the Manakov system. Through a rotation operation with an appropriate rotation angle, the Hadamard operation is realized on the single qubit, leading to the superposition state in which the measurement probability of individual qubits is half. Subsequently, repeating the similar Hadamard operation on the superposition state leads to the restoration of the original states of the qubit, as expected. Additionally, the measure of quantum fidelity of the qubit is expressed through the density operator matrix using Uhlmann-Jozsa fidelity. The versatility in the application of composite solitons to accomplish the quantum Hadamard operation through diverse physical systems is also demonstrated through suitable examples.