# Mukund Raman

Coppell High SchoolClass of 2023Coppell, TX

#### About

Hello, my name is Mukund, and I'm currently a senior at Coppell High School. My Polygence project is on the topic of spin glasses, a statistical mechanics phenomenon in which the magnetic spins of particles are aligned randomly. I want to study the properties of these spin glasses and how to compute their ground energy states by converting them into the Max Cut problem, a graph-based NP optimization problem that can be solved efficiently by the using the Quantum Approximate Optimization Algorithm (QAOA). I chose to work on this project because I wanted to learn more about quantum computing algorithms and explore the unique problem of spin glasses. After completing my project, I'd like to look at how the quantum statistical techniques I used in my research could be applied to NP problems in general, and what insights could be generated from taking such a approach to these problems.#### Projects

- "Solving the Max Cut Problem using the Quantum Approximate Optimization Algorithm to find the Ground State of Ising Spin Glasses in an External Magnetic Field" with mentor Yash (Working project)

#### Project Portfolio

# Solving the Max Cut Problem using the Quantum Approximate Optimization Algorithm to find the Ground State of Ising Spin Glasses in an External Magnetic Field

Started June 17, 2022

## Abstract or project description

The study of spin glasses was inspired by the physics of structural glasses, in which there are amorphous arrangements of atoms, unlike typical solids, which have a well-defined crystalline structure. Just like how structural glass has its atoms trapped in the local minima of its energy state space, spin glasses have various random spins with frustrated bonds that can cause its energy to be trapped as well. In order to compute the ground energy state of spin glasses, the spin glass needs to be represented through the statistical Edwards-Anderson Ising model. This value can be computed by classical algorithms efficiently in two dimensions, but it becomes NP-Hard when a magnetic field is added or if 3 dimensions are considered, and so quantum computation can provide significant assistance. In this paper, I will solve specific instances of 2D spin glass systems in an external magnetic field by first transforming its structure into the Max Cut problem, an NP-hard problem of finding the optimal cut between a graph’s nodes. This is done by transforming the energy Hamiltonian of the spin glass system into a graph with the edges weighted according to the Hamiltonian. I will then use the Quantum Approximate Optimization algorithm to determine the graph’s optimal cut, producing a quantum state that can be traced back to the original problem to find the ground energy state. As a next step, the quantum-statistical techniques used in this study could be applied to other NP problems to generate significant insights about their properties.