Information compression via hidden subgroup quantum autoencoders

TL;DR

This paper introduces a quantum autoencoder that leverages hidden subgroup algorithms to efficiently compress data with unknown symmetries, outperforming classical methods and revealing thermodynamic implications.

Contribution

It presents a novel quantum algorithm for data compression exploiting hidden subgroup structures, with a variational approach for identifying symmetries and outperforming classical autoencoders.

Findings

Quantum algorithm achieves exponential speedup over classical methods.

The quantum autoencoder outperforms classical autoencoders on test data.

Thermodynamical analysis shows higher free energy for quantum agents.

Abstract

We design a quantum method for classical information compression that exploits the hidden subgroup quantum algorithm. We consider sequence data in a database with a priori unknown symmetries of the hidden subgroup type. We prove that data with a given group structure can be compressed with the same query complexity as the hidden subgroup problem, which is exponentially faster than the best known classical algorithms. We moreover design a quantum algorithm that variationally finds the group structure and uses it to compress the data. There is an encoder and a decoder, along the paradigm of quantum autoencoders. After the training, the encoder outputs a compressed data string and a description of the hidden subgroup symmetry, from which the input data can be recovered by the decoder. In illustrative examples, our algorithm outperforms the classical autoencoder on the mean squared value of test data. This classical-quantum separation in information compression capability has thermodynamical significance: the free energy assigned by a quantum agent to a system can be much higher than that of a classical agent. Taken together, our results show that a possible application of quantum computers is to efficiently compress certain types of data that cannot be efficiently compressed by current methods using classical computers.