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This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest x^∈R^n from m quadratic equations/samples y_i=(a_i^x^)^2, 1≤ i≤ m. This problem, also dubbed as phase retrieval, spans multiple domains including physical sciences and machine learning. We investigate the efficiency of gradient descent (or Wirtinger flow) designed for the nonconvex least squares problem. We prove that under Gaussian designs, gradient descent --- when randomlyarXiv:1803.07726v2 fatcat:jemo7c7olzg2natul5n5adrc3y