Research output

Quantum PCA offers theoretical speedups over classical algorithms for dimensionality reduction in high-dimensional settings. This survey synthesizes recent developments in quantum PCA variants, including the HHL-based approach, quantum singular value decomposition methods, and dequantization results that challenge the original speedup claims. We analyze circuit complexity, sample complexity, and p…

We investigate generalization properties of variational quantum circuits (VQCs) used as machine learning models. Drawing on statistical learning theory, we derive uniform convergence bounds for VQC function classes and connect expressivity to generalization through covering number arguments. Our analysis demonstrates that overparameterization in VQCs exhibits qualitatively different behavior compa…

Scientific ML tasks often involve structured data with physical symmetries that quantum systems can naturally encode. We present a framework for hybrid quantum-classical pipelines that leverage quantum subroutines for feature encoding and kernel estimation while using classical deep learning for higher-level pattern recognition. We benchmark our approach on molecular property prediction and fluid…

Parameterized quantum circuits (PQCs) underpin most near-term quantum machine learning proposals, yet their optimization properties remain poorly understood. We characterize the loss landscape of common PQC architectures, including hardware-efficient ansätze and chemically motivated circuits, identifying conditions for barren plateaus, spurious local minima, and trainability. Our analysis extends…

Barren plateaus pose a fundamental challenge to training deep quantum neural networks: gradients vanish exponentially with system size under generic initialization and global cost functions. We systematically compare mitigation strategies including layer-by-layer training, identity-block initialization, problem-inspired ansätze design, local cost function formulations, and quantum natural gradient…

Quantum kernel methods provide a principled approach to quantum-enhanced learning by defining feature maps through quantum circuits whose inner products are intractable to estimate classically. We analyze the conditions under which quantum kernels outperform classical alternatives, examining the role of circuit depth, entanglement structure, and data encoding strategies. Using both simulated and r…

Quantum machine learning sits at the intersection of quantum computing, linear algebra, probability theory, and statistical learning. Newcomers face a steep and fragmented learning path. This work presents a structured curriculum developed through three iterations of MIC's internal reading group, covering mathematical prerequisites, quantum circuit model fundamentals, variational algorithms, quant…