  We design a quantum method for non-linear classical information compression.
For compressing data obeying symmetries of the so-called hidden subgroup type,
we prove an exponential speedup of quantum algorithm in terms of query
complexity. We then generalize the method to a variational quantum algorithm
that automatically compresses time-series data stored in a database with a
priori unknown symmetries of the hidden subgroup type. The automatic
compression exploits an encoder that computes the hidden subgroup and a decoder
that reconstructs the data using the group structure. The algorithm can thus be
viewed as a synthesis of hidden subgroup quantum computing and quantum
autoencoders. The output of our algorithm compares favourably with that of a
deep classical autoencoder for a tractable illustrative example. Our results
show how quantum computers can efficiently compress certain types of data that
cannot be efficiently compressible by classical computers. As an additional
application, the computational advantage of the quantum compressor over its
classical counterpart can be transformed into a quantum advantage for
intelligent energy harvesting.

Quantum Physics