Methods of Quantum Circuit Simulation: A Comprehensive Comparative Analysis

The advent of quantum computing has ushered in a new era of computational capabilities, promising to solve problems that were previously intractable for classical computers. Quantum circuit simulation is an essential aspect of harnessing the potential of quantum algorithms, and understanding quantum systems. This thesis presents an exploration and comparative analysis of various methods used in the simulation of quantum circuits, aimed at providing a comprehensive understanding of their strengths, weaknesses, and practical applications. This starts with a dive into the foundational concepts of quantum circuits, quantum gates, and the fundamental principles underlying quantum computation. Quantum circuit simulation emphasizes the growing significance of quantum technologies, as they become more accessible, and play a pivotal role in quantum algorithm development. To this end, a rigorous analysis of simulation methods, including state vector, matrix product state, density matrix is conducted. Gaps in each method are identified, with potential solutions offered. With the limitations of the full suite of simulators gleaned from these experiments, a more robust understanding of the proper usage of each can be inferred and used in future experiments and analysis.