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Thesis/Dissertation Seminars

Dissertation Defense: Solving Constraint Satisfaction Problems with Matrix Product States

PSB 160
August 17, 2017 @ 10:00 AM - 12:00 PM

Announcing the Final Examination of Sabine Pelton for the Degree of Doctor of Philosophy in Physics

In the past decade, Matrix Product State (MPS) algorithms have emerged as an e_cient method of modeling some many-body quantum spin systems. Since spin system Hamiltonians can be considered constraint satisfaction problems (CSPs), it follows that MPS should provide a versatile framework for studying a variety of general CSPs. In this thesis, we apply MPS to two types of CSP. First, we use MPS to simulate adiabatic quantum computation (AQC), where the target Hamiltonians are instances of a fully connected, random Ising spin glass. Results of the simulations help shed light on why AQC fails for some optimization problems. We then present the novel application of a modi_ed MPS algorithm to classical Boolean satis_ability problems, speci_cally k-SAT and max k-SAT. By construction, the algorithm also counts solutions to a given Boolean formula (#-SAT). For easy satis_able instances, the method is more expensive than other existing algorithms; however, for hard and unsatis_able instances, the method succeeds with subexponential scaling where other algorithms fail to converge.

Committee in Charge: Eduardo Mucciolo (Chair), Aniket Bhattacharya, Richard Klemm, Pawel Wocjan


 

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