Harnessing Quantum Computational Methods, Tensor Networks, and Machine Learning for Advanced Simulations in Quantum Field Theories

The objective of this PhD project is to create a robust framework for simulating quantum field theories (QFTs) by integrating quantum computational methods, tensor network theories (TNT), and machine learning (ML) techniques. This interdisciplinary endeavour aims to mitigate computational challenges inherent in classical simulations of QFTs, paving the way for deeper insights into fundamental physics and high-energy phenomena. Quantum algorithms tailored for QFT simulations on quantum hardware will be developed alongside quantum-classical hybrid algorithms to harness both computational paradigms. The project will implement tensor network decomposition methods to efficiently represent and manipulate states and operators in QFTs, exploring the entanglement structures and devising efficient algorithms for simulating low-dimensional QFTs. Machine learning techniques will be employed to optimize tensor network structures and quantum circuits, as well as for error mitigation to enhance the robustness and accuracy of quantum simulations. Benchmarking against classical methods and existing quantum simulation approaches will validate the developed frameworks. Performance optimization for different quantum hardware architectures will be carried out to investigate the scalability and real and near-term quantum computer performance. The expected outcomes include an optimized framework for QFT simulations leveraging quantum computing, tensor networks, and ML, benchmark results showcasing the performance and accuracy against classical methods, and new insights into the entanglement structure of QFTs. This project has the potential to significantly influence the way QFT simulations are conducted, fostering further innovations at the nexus of quantum computing, machine learning, and high-energy physics. Moreover, the project could be extended to explore applications in other physics areas like condensed matter physics or quantum gravity and employ advanced ML techniques like deep learning or reinforcement learning for further optimization of the simulation framework. The candidate will engage in a cutting-edge interdisciplinary field with extensive potential for theoretical and practical advancements in quantum computing and high-energy physics through this project.