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In recent years, variational quantum circuits (VQCs) have been widely explored to advance quantum circuits against classic models on various domains, such as quantum chemistry and quantum machine learning. Similar to classic…

Designing quantum circuits for ground state preparation is a fundamental task in quantum information science. However, standard Variational Quantum Algorithms (VQAs) are often constrained by limited ansatz expressivity and difficult…

One of the most important properties of classical neural networks is how surprisingly trainable they are, though their training algorithms typically rely on optimizing complicated, nonconvex loss functions. Previous results have shown that…

Barren plateaus appear to be a major obstacle to using variational quantum algorithms to simulate large-scale quantum systems or replace traditional machine learning algorithms. They can be caused by multiple factors such as expressivity,…

Parameterized quantum circuits (PQCs) are crucial for quantum machine learning and circuit synthesis, enabling the practical implementation of complex quantum tasks. However, PQC learning has been largely confined to classical optimization…

Variational quantum algorithms (VQAs) are widely applied in the noisy intermediate-scale quantum era and are expected to demonstrate quantum advantage. However, training VQAs faces difficulties, one of which is the so-called barren plateaus…

Parameterized quantum circuits serve as ans\"{a}tze for solving variational problems and provide a flexible paradigm for programming near-term quantum computers. Ideally, such ans\"{a}tze should be highly expressive so that a close…

Inspired by the Fleming-Viot stochastic process, we propose a parallel implementation of variational quantum algorithms with the aim of reducing the time spent by the algorithm in barren plateaus, where optimization direction is unclear. In…

A key challenge in classical machine learning is to mitigate overparameterization by selecting sparse solutions. We translate this concept to the quantum domain, introducing quantum sparsity as a principle based on minimizing quantum…

We present a unitary-based gradient formulation for variational quantum algorithms (VQAs) that applies to general differentiable cost function defined by a parameterized quantum circuit composed of Pauli-generated rotations. The gradient is…

Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…

Optical quantum circuits can be optimized using gradient descent methods, as the gates in a circuit can be parametrized by continuous parameters. However, the parameter space as seen by the cost function is not Euclidean, which means that…

Motivated by realistic hardware considerations of the pre-fault-tolerant era, we comprehensively study the impact of uncorrected noise on quantum circuits. We first show that any noise `truncates' most quantum circuits to effectively…

Quantifying the flatness of the objective-function landscape associated with unstructured parameterized quantum circuits is important for understanding the performance of variational algorithms utilizing a "hardware-efficient ansatz",…

Variational quantum computing offers a flexible computational paradigm with applications in diverse areas. However, a key obstacle to realizing their potential is the Barren Plateau (BP) phenomenon. When a model exhibits a BP, its parameter…

Computation of observables and their gradients on near-term quantum hardware is a central aspect of any quantum algorithm. In this work, we first review standard approaches to the estimation of observables with and without quantum amplitude…

Variational Quantum Circuits are being used as versatile Quantum Machine Learning models. Some empirical results exhibit an advantage in supervised and generative learning tasks. However, when applied to Reinforcement Learning, less is…

Many near-term quantum computing algorithms are conceived as variational quantum algorithms, in which parameterized quantum circuits are optimized in a hybrid quantum-classical setup. Examples are variational quantum eigensolvers, quantum…

Variational quantum algorithms (VQAs) are among the most promising algorithms in the era of Noisy Intermediate Scale Quantum Devices. Such algorithms are constructed using a parameterization U($\pmb{\theta}$) with a classical optimizer that…

We study the problem of finding the global Riemannian center of mass of a set of data points on a Riemannian manifold. Specifically, we investigate the convergence of constant step-size gradient descent algorithms for solving this problem.…