Learning Unitaries by Gradient Descent

Bobak Toussi Kiani; Seth Lloyd; Reevu Maity

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arXiv · 2001.11897

Learning Unitaries by Gradient Descent

Bobak Toussi Kiani·Seth Lloyd·Reevu Maity

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Abstract

We study the hardness of learning unitary transformations in $U(d)$ via gradient descent on time parameters of alternating operator sequences. We provide numerical evidence that, despite the non-convex nature of the loss landscape, gradient descent always converges to the target unitary when the sequence contains $d^2$ or more parameters. Rates of convergence indicate a "computational phase transition." With less than $d^2$ parameters, gradient descent converges to a sub-optimal solution, whereas with more than $d^2$ parameters, gradient descent converges exponentially to an optimal solution.

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Bobak Toussi Kiani, Seth Lloyd, Reevu Maity. 2020-01-31. Learning Unitaries by Gradient Descent. https://arxiv.org/abs/2001.11897

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