Learning Unitaries by Gradient Descent

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 s...

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Veröffentlicht in:	arXiv.org 2020-02
Hauptverfasser:	Bobak Toussi Kiani, Lloyd, Seth, Maity, Reevu
Format:	Artikel
Sprache:	eng
Schlagworte:	Algorithms Controllability Convergence Critical point Learning Optimization Parameters Phase transitions Polynomials Sequences Stability
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creator	Bobak Toussi Kiani Lloyd, Seth Maity, Reevu
description	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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subjects	Algorithms Controllability Convergence Critical point Learning Optimization Parameters Phase transitions Polynomials Sequences Stability
title	Learning Unitaries by Gradient Descent
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