#### Document Type

Event

#### Start Date

1-12-2022 5:00 PM

#### Description

Quantum computing has completely changed the computing paradigm. These special computers leverage the unique properties of quantum mechanics to solve problems that a classical computer cannot solve in polynomial time. Quantum mechanics such as superposition and entanglement are used to boost computational power exponentially in many problems . Many traditionally NP-complete problems, such as breaking the encryption of public-private key systems, are solvable with quantum computing in polynomial time. In this project, we will review quantum computing basics using real quantum computers and build on those basics to solve a subset of a graph optimization problems using both existing and new methodologies. Our research focuses on a subset of graphs named “Cascading Graphs” and finding the “best” path based on a predetermined metric. To solve this problem, we plan to use a mixed approach for finding a mathematical algorithm and creating an implementation of the algorithm in a quantum computer. This mixed approach will be based on a cycle consisting of trying a find a mathematically rigorous proof and testing different cases to help build an understanding of the problem, which will then be verified using a quantitative approach.

#### Included in

UR-302 Using Quantum Computing to Determine the Optimal Path on Cascading Graphs

Quantum computing has completely changed the computing paradigm. These special computers leverage the unique properties of quantum mechanics to solve problems that a classical computer cannot solve in polynomial time. Quantum mechanics such as superposition and entanglement are used to boost computational power exponentially in many problems . Many traditionally NP-complete problems, such as breaking the encryption of public-private key systems, are solvable with quantum computing in polynomial time. In this project, we will review quantum computing basics using real quantum computers and build on those basics to solve a subset of a graph optimization problems using both existing and new methodologies. Our research focuses on a subset of graphs named “Cascading Graphs” and finding the “best” path based on a predetermined metric. To solve this problem, we plan to use a mixed approach for finding a mathematical algorithm and creating an implementation of the algorithm in a quantum computer. This mixed approach will be based on a cycle consisting of trying a find a mathematically rigorous proof and testing different cases to help build an understanding of the problem, which will then be verified using a quantitative approach.