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The SDP value for random two-eigenvalue CSPs (1906.06732v1)
Published 16 Jun 2019 in cs.DS, cs.CC, cs.DM, math.CO, and math.PR
Abstract: We precisely determine the SDP value (equivalently, quantum value) of large random instances of certain kinds of constraint satisfaction problems, ``two-eigenvalue 2CSPs''. We show this SDP value coincides with the spectral relaxation value, possibly indicating a computational threshold. Our analysis extends the previously resolved cases of random regular $\mathsf{2XOR}$ and $\textsf{NAE-3SAT}$, and includes new cases such as random $\mathsf{Sort}_4$ (equivalently, $\mathsf{CHSH}$) and $\mathsf{Forrelation}$ CSPs. Our techniques include new generalizations of the nonbacktracking operator, the Ihara--Bass Formula, and the Friedman/Bordenave proof of Alon's Conjecture.