Quantum Computing has emerged as a technology capable of changing paradigms on multiple fields. In the other hand, current development of such applications is tampered by noisy quantum hardware.
Hybrid Quantum Classical Computation leverages the strengths of both Quantum and Classical Computers (such as High Performance Computers (HPC)) to create a bridge that seamlessly integrates and exploits the advantages of each. This field is still overlooked, being under the shadow of the great advancement in the field of quantum hardware. Currently, there is a noticeable void where efforts to develop algorithms that use the power of both technologies.
In this work we will explore hybrid computing as a whole, understand all of its fundamental parts and its limitations. We began with an introduction of the necessary theoretical background and a study of the state of the art related to hybrid algorithm developments. Then we will present the framework for the quantum walk algorithm, exploring some of its capabilities. Next we will propose an hybrid architecture and application on an unexplored domain, the simulation of Dirac free particle. Then we will do a test of our hybrid algorithm for simple problems, using real quantum hardware, exposing the limitations of it. As a final approach we will use a simulator of quantum hardware ran on a classical High Performance Computer provided by the Laboratory for Advanced Computing of the University of Coimbra, to execute the quantum walk algorithm of the Dirac free-particle trapped in a square potential.