Unitary fractional-order derivative operators for quantum computation

Abstract

Along with recent progresses in quantum computation technologies, researchers have addressed practical computational supremacies of quantum computers. The research works in the quantum computation domain mainly focus on progressive quantum algorithms and circuits in order to cope with computationally expensive engineering problems. This study aims to introduce possible implications of fractional calculus in quantum computation practice. In this perspective, a unitary fractional-order derivative operator family, which can be implemented by using phase operators, is defined and their possible utilizations for modeling and controlling quantum circuits are discussed. Moreover, the study demonstrates that the fractional derivative order can be used for controlling Shannon entropy of measurement probability distribution of qubits. Operation modes of single-sided and double-sided quantum interference circuits are analyzed, and optimal design of quantum interference circuits to obtain target probability distributions is investigated by using a genetic algorithm. This groundwork is helpful to extend topics of fractional calculus to quantum fractional calculus. © 2022 Elsevier Inc. All rights reserved.