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In hybrid classical-quantum computing, variational quantum algorithms (VQAs) have emerged as a promising approach in the Noisy Intermediate-Scale Quantum (NISQ) era; however, their performance is often hindered by barren plateaus, where…
Variational quantum algorithms (VQAs) that estimate values of widely used physical quantities such as the rank, quantum entropies, the Bures fidelity and the quantum Fisher information of mixed quantum states are developed. In addition,…
Variational quantum algorithms (VQAs) incorporate hybrid quantum-classical computation aimed at harnessing the power of noisy intermediate-scale quantum (NISQ) computers to solve challenging computational problems. In this thesis, three…
In variational quantum algorithms the parameters of a parameterized quantum circuit are optimized in order to minimize a cost function that encodes the solution of the problem. The barren plateau phenomenon manifests as an exponentially…
Hybrid variational quantum algorithms (VQAs) are promising for solving practical problems such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers.…
Parameterized quantum circuits (PQCs) have been widely used as a machine learning model to explore the potential of achieving quantum advantages for various tasks. However, training PQCs is notoriously challenging owing to the phenomenon of…
The Quantum Approximate Optimization Algorithm (QAOA), which is a variational quantum algorithm, aims to give sub-optimal solutions of combinatorial optimization problems. It is widely believed that QAOA has the potential to demonstrate…
In recent times, Variational Quantum Circuits (VQC) have been widely adopted to different tasks in machine learning such as Combinatorial Optimization and Supervised Learning. With the growing interest, it is pertinent to study the…
Quantum generative models exploit quantum superposition and entanglement to enhance learning efficiency for both classical and quantum data. Recently, inspired by classical diffusion frameworks, the quantum denoising diffusion probabilistic…
Vanishing gradients can pose substantial obstacles for high-dimensional optimization problems. Here we consider energy minimization problems for quantum many-body systems with extensive Hamiltonians and finite-range interactions, which can…
Quantum computers currently rely on a hybrid quantum-classical approach known as Variational Quantum Algorithms (VQAs) to solve problems. Still, there are several challenges with VQAs on the classical computing side: it corresponds to a…
Variational Quantum Eigensolvers (VQEs) are a leading class of noisy intermediate-scale quantum (NISQ) algorithms with broad applications in quantum physics and quantum chemistry. However, as system size increases, VQE optimization is…
The Quantum Approximate Optimization Algorithm (QAOA) is a powerful tool in solving various combinatorial problems such as Maximum Satisfiability and Maximum Cut. Hard computational problems, however, require deep circuits that place high…
Barren plateaus are fundamentally a statement about quantum loss landscapes on average but there can, and generally will, exist patches of barren plateau landscapes with substantial gradients. Previous work has studied certain classes of…
Variational quantum circuits (VQCs) are a central component of many quantum machine learning algorithms, offering a hybrid quantum-classical framework that, under certain aspects, can be considered similar to classical deep neural networks.…
Variational quantum algorithms are promising candidates for near-term quantum computing but can be hindered by barren plateaus, where gradients vanish exponentially and optimization becomes intractable. Noise-Induced Barren Plateaus (NIBP)…
Barren plateau landscapes correspond to gradients that vanish exponentially in the number of qubits. Such landscapes have been demonstrated for variational quantum algorithms and quantum neural networks with either deep circuits or global…
In this article we introduce an algorithm for mitigating the adverse effects of noise on gradient descent in variational quantum algorithms. This is accomplished by computing a {\emph{regularized}} local classical approximation to the…
Barren plateaus in variational quantum algorithms are typically described by gradient concentration at random initialization. In contrast, rigorous results for the Hessian, even at the level of entry-wise variance, remain limited. In this…
Variational quantum algorithms (VQAs) are expected to be a path to quantum advantages on noisy intermediate-scale quantum devices. However, both empirical and theoretical results exhibit that the deployed ansatz heavily affects the…