The quantum hypercube as a k-mer graph

Abstract

The application of quantum principles in computing has garnered interest since the 1980s. Today, this concept is not only theoretical, but we have the means to design and execute techniques that leverage the quantum principles to perform calculations. The emergence of the quantum walk search technique exemplifies the practical application of quantum concepts and their potential to revolutionize information technologies. It promises to be versatile and may be applied to various problems. For example, the coined quantum walk search allows for identifying a marked item in a combinatorial search space, such as the quantum hypercube. The quantum hypercube organizes the qubits such that the qubit states represent the vertices and the edges represent the transitions to the states differing by one qubit state. It offers a novel framework to represent k-mer graphs in the quantum realm. Thus, the quantum hypercube facilitates the exploitation of parallelism, which is made possible through superposition and entanglement to search for a marked k-mer. However, as found in the analysis of the results, the search is only sometimes successful in hitting the target. Thus, through a meticulous examination of the quantum walk search circuit outcomes, evaluating what input-target combinations are useful, and a visionary exploration of DNA k-mer search, this paper opens the door to innovative possibilities, laying down the groundwork for further research to bridge the gap between theoretical conjecture in quantum computing and a tangible impact in bioinformatics.