Photonic implementation of quantum hidden subgroup database compression

TL;DR

This paper demonstrates a photonic quantum autoencoder that learns hidden symmetries in classical data, enabling efficient compression of databases with symmetries that are hard for classical algorithms to detect.

Contribution

It introduces an experimental photonic quantum autoencoder capable of autonomously learning symmetry structures for data compression, showcasing quantum advantage in symmetry detection.

Findings

Successful training of the autoencoder with gradient descent

Effective compression by identifying hidden symmetries

Proof-of-principle demonstration with photonic quantum processor

Abstract

We experimentally demonstrate quantum data compression exploiting hidden subgroup symmetries using a photonic quantum processor. Classical databases containing generalized periodicities-symmetries that are in the worst cases inefficient for known classical algorithms to be detect-can efficiently compressed by quantum hidden subgroup algorithms. We implement a variational quantum autoencoder that autonomously learns both the symmetry type (e.g., $\mathbb{Z}_2 \times \mathbb{Z}_2$ vs. $\mathbb{Z}_4$) and the generalized period from structured data. The system uses single photons encoded in path, polarization, and time-bin degrees of freedom, with electronically controlled waveplates enabling tunable quantum gates. Training via gradient descent successfully identifies the hidden symmetry structure, achieving compression by eliminating redundant database entries. We demonstrate two circuit ansatzes: a parametrized generalized Fourier transform and a less-restricted architecture for Simon's symmetry. Both converge successfully, with the cost function approaching zero as training proceeds. These results provide experimental proof-of-principle that photonic quantum computers can compress classical databases by learning symmetries inaccessible to known efficient classical methods, opening pathways for quantum-enhanced information processing.