Learning Reduced Representations for Quantum Classifiers

TL;DR

The paper tackles the obstacle of high‑dimensional data for quantum ML by systematically benchmarking conventional dimensionality reduction and autoencoder methods on a 67‑feature HEP dataset, then evaluating their impact on a quantum support vector machine. It demonstrates that autoencoder‑based reductions, particularly the Sinkclass architecture that couples an encoder to a classifier with Sinkhorn regularization, produce more discriminative latent spaces than traditional methods, achieving a QSVM AUC around 0.73–0.74 on the ttH(bb) task. The study provides a practical recipe for applying dimensionality reduction in QML, showing how to balance reconstruction with downstream classification performance and offering public data and code for reproducibility. Overall, the work broadens the applicability of quantum classifiers to high‑dimensional scientific data and guides future QML pipelines in choosing effective reduction strategies.

Abstract

Data sets that are specified by a large number of features are currently outside the area of applicability for quantum machine learning algorithms. An immediate solution to this impasse is the application of dimensionality reduction methods before passing the data to the quantum algorithm. We investigate six conventional feature extraction algorithms and five autoencoder-based dimensionality reduction models to a particle physics data set with 67 features. The reduced representations generated by these models are then used to train a quantum support vector machine for solving a binary classification problem: whether a Higgs boson is produced in proton collisions at the LHC. We show that the autoencoder methods learn a better lower-dimensional representation of the data, with the method we design, the Sinkclass autoencoder, performing 40% better than the baseline. The methods developed here open up the applicability of quantum machine learning to a larger array of data sets. Moreover, we provide a recipe for effective dimensionality reduction in this context.

Figures (4)

• Figure 1: Schematic of the end-to-end Sinkhorn autoencoder with a classifier attached to its latent space; called the sinkclass autoencoder here. The standard encoder-decoder structure is present. Furthermore, the truth labels, whether a sample contains a higgs boson or not, are fed to a one layer neural network. Simultaneously, a sample from a standard Gaussian distribution is given to a two layer neural network. The output of both networks are concatenated and given to a three layer network $\mathscr{N}_\gamma$ that connects to the latent space $z$ of the encoder. Similar to the variational autoencoder depicted in Fig. \ref{['fig:variationalAE']}, the AE component is trying to match the output of $\mathscr{N}_\gamma$ when computing $z$. The obtained $z$ is given to a conventional neural network classifier; its output is compared with the truth label and this information is used to compute an easier to classify $z$ for the next sample. Furthermore, the decoder $\mathscr{D}_\rho$ reconstructs the original data from $z$. The goal of this network is to minimise the difference between $x$ and $\hat{x}$, to produce a $z$ that is close to the output of $\mathscr{N}_\gamma$, and that $z$ is easy to classify by $\mathscr{C}_\upsilon$
• Figure 2: a) The quantum kernel circuit, given a data encoding circuit $U$, from which the quantum kernel values are extracted via the measurement of the expected value defined in Eq. \ref{['eq:quantum_kernel']}. b) The architecture of the data encoding circuit from Belis:2023atb. c) The components of the data encoding circuit, where $G(\theta,\phi,\lambda)$ is the universal one-qubit gate, $\mathbf{x}^{(j)}_k$ is the $k$-th element of the input data vector $\mathbf{x}^{(j)}$
• Figure 3: Schematic of a conventional autoencoder architecture. The input data $x$ is given to an encoder neural network $\mathscr{E}_\omega$, here depicted with three fully connected layers. The neural network processes the data and generates a lower dimensional representation $z$, called the latent space. The decoder neural network $\mathscr{D}_\rho$ depicted still with three fully connected layers processes $z$ to generate a reconstruction of the original data $\hat{x}$. The task of this network is to minimise the difference between $x$ and $\hat{x}$
• Figure 4: Schematic of the variational autoencoder. This model functions under the same principles as the vanilla AE depcited in Fig. \ref{['fig:vanillaAE']}. However, the vanilla encoder $\mathscr{E}_\omega$ is connected at the end with two additional layers $g$ and $h$, that generate the mean $\mu$ and standard deviation $\sigma$ of a reference standard Gaussian distribution, respectively. The latent space of the variational autoencoder is generated by using these values as shown in the figure. Once $z$ is obtained, the decoder $\mathscr{D}_\rho$ proceeds to reconstruct the original data from it. Again, the learning goal of this model is to minimise the difference between $x$ and $\hat{x}$, but also to produce a $z$ that mimics samples from a standard Gaussian distribution $\xi$