We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine ideas from quantum Gibbs sampling and matrix exponent updates. A de-quantization of the algorithm also leads to a faster classical solver. For generic instances, our quantum solver gives a nearly quadratic speedup over state-of-the-art algorithms. Such instances include approximating the ground state of spin glasses and MaxCut on Erd\"{o}s-R\'enyi graphs. We also provide an efficient randomized rounding procedure that converts approximately optimal SDP solutions into approximations of the original quadratic optimization problem.

翻译：我们用量子加速来解答二次二次二次优化的罐体半确定性编程松动。 这种组合优化的松动类型至今尚未成功。 我们的方法将量子 Gibbs 取样和矩阵引言更新中的想法结合起来。 算法的去量化还会导致一个更快的古典解答器。 对于一般情况, 我们的量子解析器给最先进的算法提供了近乎四倍的加速。 此类例子包括旋转眼镜和Erd\' {o}s- R\'enyi 图形上的 MaxCut 接近地面状态。 我们还提供了一个高效随机化的圆环程序, 将大约最佳 SDP 解决方案转换为原始二次优化问题的近似值 。