FET: Small: Optimizing quantum circuit design

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The quantum approximate optimization algorithm (QAOA) is a leading candidate for leveraging quantum computing techniques to solve complex combinatorial optimization (CO) problems. The algorithm is performed in iterations; while it has been proven always to find an optimal solution to a CO problem, it may not always find the solution in a finite number of iterations. Thus, better techniques are required to find optimal solutions to CO problems more quickly. This project investigates a new modification to the algorithm called ma-QAOA, which expands the number of parameters that QAOA uses and allows for additional degrees of freedom. These changes increase the likelihood of finding optimal solutions to CO problems more quickly. If successful, this project will develop new techniques for solving currently intractable problems from a diverse range of applications, including operations research and computer science. This project will also become the basis for a graduate-level quantum algorithms class that expands competency in quantum-based optimization and operations research.The main restriction for quantum computing applications is the reliability of gates. Errors increase exponentially with the number of gates used in a circuit, and the larger the error, the more samples are required to obtain high-fidelity solutions. The time required to collect these samples can outweigh any time savings associated with a given solution. By relying on classical optimization and graph theory techniques, this project seeks to reduce the total number of gates needed to solve complex combinatorial optimization problems. The first objective of this project is to determine how many iterations of QAOA are required to achieve results comparable to those of ma-QAOA for specific problem instances. The second objective is to use machine learning methods to determine how to select parameters for ma-QAOA optimally. The third objective will use graph theory techniques to design circuits that can efficiently implement ma-QAOA, and the fourth objective is to determine the physical significance of incorporating additional parameters into the algorithm.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.