S18 - Quantum Machine Learning II

Quantum circuits are inherently parametric and optimization of the parameters is required. While this might be explicit as with a Variational-Quantum-Algorithm (VQA), or implicit as with the Quantum-Singular-Value-Transform, the optimal choice of parameters depends not only on the desired algorithm, but also hardware characteristics such as the set of basis gates. As quantum circuits are typically only part of a larger problem setting, and it is desirable to optimize circuits in terms of runtimes, fidelities, or other desired quantities, it can be helpful to also consider the context of the larger problem as in the end we are often interested in the overall time-to-solution, and not just the time-to-readout of the quantum subroutine. 
This opportunity arises, for instance, in machine learning tasks as the outer level of the problem scope. For example, a quantum neural network (QNN) requires the optimization of weights, often represented by parameters such as rotation angles of quantum gates, or the training of Gaussian process (GP) emulators. Traditionally, GPs have mostly been used for classification and regression tasks. Their generalization into GP emulators aims at substituting computationally expensive models, e.g., simulation models, via a cheap-to-evaluate, uncertainty-informed alternative. In particular, their ability to quantify uncertainty makes them a powerful tool for high-throughput tasks [1,2,3], as it enables the separation of surrogate-induced uncertainty from other sources of input uncertainty. Training a GP emulator requires inverting a potentially dense matrix, which has O(N^3) computational complexity and therefore limits its applicability to a moderate number of dimensions in the design parameter space. 
While quantum algorithms have been proposed to tackle this computational bottleneck, any real-world speedups would be lost in an attempt to read the inverted matrix from the quantum computer due to the readout-problem. However, the main task in GP emulator training is formulated as a hyper-parameter tuning, where the hyper-parameters determine how to populate the covariance matrix to invert. It is therefore possible to not only optimize the quantum circuit in a black-box manner, but also with respect to this hyper-parameter tuning.

Identifying exoplanets from light curves has become a primary method for exoplanet detection, with many deep learning classification models having been applied to exoplanetary transit data. 


Due to the difficulty of detecting exoplanets, mission data is heavily biased towards non-exoplanet light curves. As most machine learning based classification tasks assume an equal distribution of classes, the lack of data could decrease the performance of vetting processes (Leevy et al. 2018; Pratyush & Gangrade 2021) . The ability to generate synthetic exoplanetary data could therefore be highly beneficial for models using exoplanetary data, such as exoplanet classification, and could help mitigate issues such as overfitting and poor representation of the data features. 


We consider the ability of a 1D hybrid quantum-classical autoencoder (QAE) and an equivalent classical autoencoder trained on synthetic exoplanet candidate light curves (Fuentes & Solar 2024) to generate exoplanetary transit light curves samples to reduce the data imbalance. We also investigate how the model can be applied to the task of exoplanet classification through reconstruction error. 

Quantum kernel methods promise classification advantages in high-dimensional feature spaces by computing kernel functions in exponentially large Hilbert spaces, yet a critical practical bottleneck remains unresolved: how to prepare classical input features for quantum circuits with limited qubit counts. Near-term quantum devices and simulators typically support fewer than 12 qubits, while real-world feature vectors from imaging, materials characterisation, and biomedical diagnostics routinely contain tens to hundreds of dimensions. Dimensionality reduction is therefore unavoidable, but the choice of reduction method determines what geometric and statistical information reaches the quantum circuit and whether the resulting quantum kernel can match or exceed classical alternatives.
This problem is particularly acute in biomedical imaging applications such as trabecular bone classification from micro-computed tomography (micro-CT). Trabecular bone microarchitecture is a critical determinant of bone quality and fracture risk, characterised by morphometric parameters including bone volume fraction (BV/TV), trabecular thickness, number, and spacing. Automated classification of bone quality from image texture features could enable faster clinical screening, but the high-dimensional texture descriptors extracted from micro-CT slices must be drastically compressed before quantum encoding. If the wrong reduction method is chosen, the quantum kernel may lose competitiveness entirely, negating any potential benefit of the quantum approach.
Despite growing interest in quantum machine learning pipelines, no prior study has systematically compared multiple families of dimensionality reduction - linear, random, supervised, and nonlinear manifold methods - against each other as preprocessing for quantum kernel support vector machines. Existing work has examined individual methods such as PCA or autoencoders in isolation, but the interaction between reduction strategy and quantum kernel performance remains poorly understood. This gap leaves practitioners without clear guidance on how to engineer features for near-term quantum classifiers, risking wasted computational resources on quantum pipelines that underperform simple classical baselines due to suboptimal preprocessing choices.