The SDP value for random two-eigenvalue CSPs

Sidhanth Mohanty; Ryan O'Donnell; Pedro Paredes

The SDP value for random two-eigenvalue CSPs

Data Structures and Algorithms 2019-06-18 v1 Computational Complexity Discrete Mathematics Combinatorics Probability

Authors: Sidhanth Mohanty , Ryan O'Donnell , Pedro Paredes

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.

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@article{arxiv.1906.06732,
  title  = {The SDP value for random two-eigenvalue CSPs},
  author = {Sidhanth Mohanty and Ryan O'Donnell and Pedro Paredes},
  journal= {arXiv preprint arXiv:1906.06732},
  year   = {2019}
}

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50 pages excluding title page and table of contents

The SDP value for random two-eigenvalue CSPs

Abstract

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