A PROGRAMMING LANGUAGE APPROACH TO QUANTUM SPEED UP

Quantum technologies promise an immense advancement in communication and computation, but there still are numerous engineering and theoretical hurdles to the realization of scalable and practical quantum computing. The principal question of this project is exactly which property of quantum physics provides computational resources for quantum computation and in exactly what ways. Not only is this a theoretically interesting question, but an adequate answer to it should also teach us how to exploit the advantage of quantum computing in a more principled fashion. Professor Kishida aims to derive a novel answer from a perspective of quantum programming languages.

In this project, Professor Kishida plans to first extend his previous investigations in the foundations of quantum physics by connecting the structural characterizations of contextuality and other properties of quantum physics to categorical quantum mechanics. He will also extend his second area of research in quantum programming languages by incorporating the recently developing method of cost-aware programming languages. A synthesis of these two lines of research will help express the quantum computational resource in a cost-aware language of quantum programming. The goal is to achieve theorems that elucidate, in programming-language terms, the connection between properties of quantum physics and quantum advantage in computing.