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Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to…

The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for current and near-term quantum devices. Despite its initial success, there is a lack of understanding involving several of its key aspects. There…

Electronic spins in Silicon (Si) are rising contenders for qubits -- the logical unit of quantum computation-- owing to its outstanding spin coherence properties and compatibility to standard electronics. A remarkable limitation for spin…

We present a novel method for determining gradients of parameterised quantum circuits (PQCs) in hybrid quantum-classical machine learning models by applying the multivariate version of the simultaneous perturbation stochastic approximation…

Quantum computing holds promise across various fields, particularly with the advent of Noisy Intermediate-Scale Quantum (NISQ) devices, which can outperform classical supercomputers in specific tasks. However, challenges such as noise and…

This thesis investigates sampling-based quantum algorithms for electronic ground state energy estimation, focusing on Quantum-Selected Configuration Interaction (QSCI) and Sample-Based Quantum Diagonalization (SQD) as near-term alternatives…

Variational algorithms require architectures that naturally constrain the optimization space to run efficiently. Geometric quantum machine learning achieves this goal by encoding group structure into parameterized quantum circuits to…

Adaptive variational quantum eigensolvers (ADAPT-VQEs) are promising candidates for simulations of strongly correlated systems on near-term quantum hardware. To further improve the noise resilience of these algorithms, recent efforts have…

Variational quantum eigensolver (VQE) is a promising algorithm suitable for near-term quantum machines. VQE aims to approximate the lowest eigenvalue of an exponentially sized matrix in polynomial time. It minimizes quantum resource…

Learning discrete representations with vector quantization (VQ) has emerged as a powerful approach in various generative models. However, most VQ-based models rely on a single, fixed-rate codebook, requiring extensive retraining for new…

We consider realistic, multi-parameter error models and investigate the performance of the surface code for three possible fault-tolerant superconducting quantum computer architectures. We map amplitude and phase damping to a diagonal Pauli…

Recent research has shown that wavefunction evolution in real- and imaginary-time can generate quantum subspaces with significant utility for obtaining accurate ground state energies. Inspired by these methods, we propose combining quantum…

The study of variational quantum algorithms (VQCs) has received significant attention from the quantum computing community in recent years. These hybrid algorithms, utilizing both classical and quantum components, are well-suited for noisy…

The Variational Quantum Eigensolver (VQE) algorithm is gaining interest for its potential use in near-term quantum devices. In the VQE algorithm, parameterized quantum circuits (PQCs) are employed to prepare quantum states, which are then…

This work presents an optimization-based scalable quantum neural network framework for approximating $n$-qubit unitaries through generic parametric representation of unitaries, which are obtained as product of exponential of basis elements…

Variational quantum circuits with angle encoding implement truncated Fourier series, and architectures arranging $N$ qubits with $L$ encoding layers each -- sharing encoding budget $E = NL$ -- generate identical frequency spectra, identical…

Quantum variational algorithms (QVAs) are increasingly potent tools for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. This work examines the application of the Variational Quantum Eigensolver (VQE)…

Variational Quantum Circuits (VQCs) have emerged as a powerful quantum computing paradigm, demonstrating a scaling advantage for problems intractable for classical computation. As VQCs require substantial resources and specialized expertise…

Variational quantum-classical hybrid algorithms are seen as a promising strategy for solving practical problems on quantum computers in the near term. While this approach reduces the number of qubits and operations required from the quantum…

Vector Quantized Variational Autoencoder (VQ-VAE) has become a fundamental framework for learning discrete representations in image modeling. However, VQ-VAE models must tokenize entire images using a finite set of codebook vectors, and…