The SDP value for random two-eigenvalue CSPs
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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 2XOR and NAE-3SAT, and includes new cases such as random Sort_4 (equivalently, CHSH) and Forrelation CSPs. Our techniques include new generalizations of the nonbacktracking operator, the Ihara–Bass Formula, and the Friedman/Bordenave proof of Alon's Conjecture.
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