Quantum many-body phenomena have been a focal point of the physics community for the last several decades. From material science and chemistry to model systems and quantum computing, diverse problems share mathematical description and challenges. A key roadblock in many subfields is the exponential increase in problem size with increasing number of quantum constituents. Therefore, development of efficient compression and approximation methods is the only way to move forward. Parameterized models coming from the field of machine learning have successfully been applied to very large classical problems where data is abundant, leveraging recent advances in high-performance computing.
In this thesis, state-of-the-art methods relying on such models are applied to the quantum many-body problem in two distinct ways: from first principles and data-driven, as described in chapter 1. In chapters 2 and 3, the framework of quantum Monte Carlo is used to efficiently manipulate variational approximations of many-body states, obtaining non-equilibrium states occurring in quantum circuits and real-time dynamics of large systems. In chapters 4 and 5, simulated synthetic data is used to train surrogate models that enhance original methods, allowing for computations that would otherwise be out of reach for conventional solvers.
In all cases, a computational advantage is established when using machine learning methods to compress different versions of the quantum many-body problem. Each chapter is concluded by proposing extensions and novel applications of new compressed representation of the problem.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/p4g4-4b54 |
| Date | January 2024 |
| Creators | Medvidovic, Matija |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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