Photonic implementation of quantum hidden subgroup database compression

TL;DR

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.

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.

Figures (3)

• Figure 1: Schematic representation of database compression through photonic quantum hidden subgroup compression. The initial database $\mathcal{Q}$ has duplication of entries in accordance with a hidden subgroup symmetry. $\mathcal{Q}$ undergoes interaction with a quantum photonic system via a quantum hidden subgroup algorithm to find generalized periods, associated with repeated entries in $\mathcal{Q}$. Training is used to find the symmetry the database has and this results in a compressed database $\mathcal{Q}_{\text{comp}}$.
• Figure 2: Photonic set-up for quantum part of information compression via tuneable quantum hidden subgroup algorithm. (a) Quantum circuit for information compression. The parameter $\theta$ governs the controlled gate (when $\theta=1$, the gate is active, and when $\theta=0$, it is inactive). The top two qubits are the IN-register associated with $x$, and the bottom qubit is the OUT-register associated with $f(x)$. (b) Experimental setup for database compression. Pairs of photons are generated via spontaneous parametric down-conversion (SPDC) by pumping a periodically poled KTiOPO$_4$ (PPKTP) crystal. One photon is immediately detected by an avalanche photodiode (APD), $\mathrm{D}_\mathrm{T}$, to serve as a trigger, while its twin is directed into the subsequent setup. From bottom to top, the four spatial paths encode the IN-register qubit states $\ket{10}_{IN}$, $\ket{00}_{IN}$, $\ket{11}_{IN}$, and $\ket{01}_{IN}$, respectively. A beam displacer (BD) implements the oracle unitary operation $U_f$, and an electrically controlled quarter-wave plate (E-QWP) serves as the switch for the controlled gate. In this configuration, setting the E-QWP at $90^\circ$ leaves the IN qubits unchanged, while setting it at $0^\circ$ applies a phase shift of $e^{i\pi/2}$ specifically to photons in the $\ket{11}$ state. A polarizing beam splitter (PBS) and half-wave plates (HWPs) are also used to modulate states of photons. (c) Tuneable circuit capable of finding Simon's symmetry. $\theta_1$ and $\theta_2$ are tuneable parameters. (d) Experimental setup for finding Simon's symmetry in the case $n=2$. Tunable gates shown in (c) are realized by four electronically controlled half-wave plates (E-HWPs). The oracle unitary operation is applied by a fixed HWP. From bottom to top, the four path modes, correspond to $\ket{00}_{IN}$, $\ket{01}_{IN}$, $\ket{10}_{IN}$, and $\ket{11}_{IN}$ for $s=01$, and to $\ket{00}_{IN}$, $\ket{10}_{IN}$, $\ket{01}_{IN}$, and $\ket{11}_{IN}$ for $s=10$, respectively.
• Figure 3: Training succeeds in finding the symmetry.$\gamma$ is a tuneable parameter such that $p(\theta=1)=\mathrm{max}(0,\mathrm{min}(\gamma,1))$, where $\theta$ is shown in Fig. \ref{['fig:exp_up_all']} (a). Solid lines represent the mean values, while shaded areas denote values within one standard deviation of the mean.