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Programmable unitary converters are powerful tools for realizing unitarytransformations, advancing fields of computing and communication. The accuracyof these unitary transformations is crucial for maintaining high fidelity insuch applications. However, various physical artifacts can impair the accuracyof the synthesized transformations. A commonly employed approach uses thesystem's gradient to restore accuracy. Matrix norm is used to define errorbetween matrices, and minimization of this norm using the gradient restores theaccuracy. Although this gradient can indeed be physically measured usingexternal equipment, it leads to a rather complex optical system. In this study,we propose a standalone method for measuring matrix norm gradients, where`standalone' means that no additional optical equipment is needed. This methodis based on the mathematical fact that the central difference, which isgenerally used for the approximation of differentiation, can yield exactdifferentiation for any unitary converters. Furthermore, we introduce a newmatrix distance that is suitable for optimizing unitary converters which useintensity detectors at the output. This distance also yields the exactdifferentiation with the central difference. Numerical analysis demonstratesthat our method exhibits orders of magnitude higher tolerance to measurementnoise than prior similar approaches.

Standalone gradient measurement of matrix norm for programmable unitary converters