Exploring Quantum Circuit Implementations for the X Z Spin Model in Higher Dimensions

In recent years, computational condensed matter research has increasingly explored quantum computers as tools to advance the study of quantum many-body systems. Traditional simulations in this field, while robust, are often limited by classical hardware, making quantum computing a natural next step due to its potential to handle complex interactions and states. With the rapid evolution of quantum hardware, the field now faces the challenge of determining how effectively these systems can model more complex, multi dimensional systems, particularly less established ones like the X Z model. In 2019, an IBM team demonstrated this potential by simulating one dimensional spin models on quantum computers, showing that with proper mapping, quantum simulations of many body systems are feasible. Building on this foundation, this project aims to extend those methods to multi dimensional spin systems, focusing on spin directionality and lattice dimensionality. In this presentation, I demonstrate the implementation of a quantum circuit designed for simulating the X Z model, evaluate its accuracy, and present preliminary calculations of key observables. These results offer insight into the viability of current quantum hardware for studying complex multi dimensional spin systems and provide a basis for comparison with classical simulations.