The quantum analogue of ptychography, a powerful coherent diffractive imaging technique, is a simple method for reconstructing $d$-dimensional pure states. It relies on measuring partially overlapping parts of the input state in a single orthonormal basis and feeding the outcomes to an iterative phase retrieval algorithm for postprocessing. We provide a proof of concept demonstration of this method by determining pure states given by superpositions of $d$ transverse spatial modes of an optical field. A set of $n$ rank-$r$ projectors, diagonal in the spatial mode basis, is used to generate $n$ partially overlapping parts of the input, and each part is projectively measured in the Fourier transformed basis. For $d$ up to 32, we successfully reconstructed hundreds of random states using $n = 5$ and $n = d$ rank-$\lceil d/2 \rceil$ projectors. The extension of quantum ptychography for other types of photonic spatial modes is outlined.
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29 October 2020: A correction was made to the funding section.
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