Controlled nth root of X gate on a real quantum computer

Abstract

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The qubit state is represented by a coherent superposition of its orthonormal basis states (|0〉 and |1〉). The probability distribution of a qubit is a discrete probability distribution of the qubits probability amplitudes. Setting a custom probability amplitudes allows a qubit to evolve to any desired state. In this paper a controlled n-root of X gate is simulated on a real quantum processor using IBMs Quantum Experience platform. A custom quantum gate could be constructed where the only inputs are the control and target qubits and the desired probability distribution for the target qubit.