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Optimization methods for spin glass problems via accelerated macroscopic quantum tunneling
Sagal, Jacob M.
Sagal, Jacob M.
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2024
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Quantum Computing could offer significant improvements to certain problems over their classical counterparts. A commonly studied problem is the Constraint Satisfaction Problem (CSP) which often finds itself in the NP-Hard complexity class. Current algorithms often struggle to get out of local minima leading to sub-optimal results, requiring new approaches to approximating these problems. This thesis explores the prototypically hard MAX-3-XORSAT problem and various methods for approximating its ground state. We first review current methods for quantum optimization as well as the failure mechanisms that prevent them from being practically useful on near-term and future-term hardware. We apply a quasi-greedy classical search algorithm to random hypergraph instances and conclude its inefficiency as a good approximator. We use these results to better understand the complex energy landscape of MAX-3-XORSAT. Furthermore, we introduce IST-SAT, an iterative quantum algorithm that relies on accelerated macroscopic quantum tunneling to speed up the Time-To-Solution (TTS) of MAX-3-XORSAT. We show that by recycling returned bitstrings in an iterative process, we can approximate the ground state with a polynomial number of iterations. This method does not guarantee a quantum advantage for all NP-Hard CSPs, however it does show promise that quantum computers can provide use for optimization problems.
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