Classical autoencoders are neural networks that can learn efficient codings of large datasets. The task of an autoencoder is, given an input $x$, to simply reproduce $x$ at the output with the smallest possible error. For one class of autoencoders, the structure of the underlying network forces the autoencoder to represent the data on a smaller number of bits than the input length, effectively compressing the input. Inspired by this idea, we introduce the model of a quantum autoencoder to perform similar tasks on quantum data. The quantum autoencoder is trained to compress a particular dataset, where an otherwise efficient compression algorithm cannot be employed. The training of the quantum autoencoder is done using classical optimization algorithms. We show that efficient quantum autoencoders can be obtained using simple circuit heuristics. We apply our model to compress molecular wavefunctions with applications in quantum simulation of chemistry.
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