Theory of Computing ------------------- Title : Efficient Rounding for the Noncommutative Grothendieck Inequality Authors : Assaf Naor, Oded Regev, and Thomas Vidick Volume : 10 Number : 11 Pages : 257-295 URL : https://theoryofcomputing.org/articles/v010a011 Abstract -------- The classical Grothendieck inequality has applications to the design of approximation algorithms for NP-hard optimization problems. We show that an algorithmic interpretation may also be given for a _noncommutative_ generalization of the Grothendieck inequality due to Pisier and Haagerup. Our main result, an efficient rounding procedure for this inequality, leads to a polynomial-time constant-factor approximation algorithm for an optimization problem which generalizes the Cut Norm problem of Frieze and Kannan, and is shown here to have additional applications to robust principal component analysis and the orthogonal Procrustes problem.