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Variational quantum algorithms (VQAs) are expected to become a practical application of near-term noisy quantum computers. Although the effect of the noise crucially determines whether a VQA works or not, the heuristic nature of VQAs makes…
We present a hardware-validated reference dataset for variational ground-state energy calculations of the hydrogen molecule H\(_2\) on several IBM Quantum processors available in 2026. Using a standardized workflow, we benchmark the impact…
Variational quantum circuits have recently gained much interest due to their relevance in real-world applications, such as combinatorial optimizations, quantum simulations, and modeling a probability distribution. Despite their huge…
Many optimization methods for training variational quantum algorithms are based on estimating gradients of the cost function. Due to the statistical nature of quantum measurements, this estimation requires many circuit evaluations, which is…
Quantum neural networks (QNNs) offer a powerful paradigm for programming near-term quantum computers and have the potential to speedup applications ranging from data science to chemistry to materials science. However, a possible obstacle to…
Barren plateaus present a major challenge in the training of variational quantum algorithms (VQAs), particularly for large-scale discretizations of nonlinear partial differential equations. In this work, we introduce a domain decomposition…
We establish essentially optimal bounds on the complexity of initial-value problems in the randomized and quantum settings. For this purpose we define a sequence of new algorithms whose error/cost properties improve from step to step. These…
Within the context of hybrid quantum-classical optimization, gradient descent based optimizers typically require the evaluation of expectation values with respect to the outcome of parameterized quantum circuits. In this work, we explore…
We propose an algorithm for variational quantum algorithms (VQAs) to optimize the structure of parameterized quantum circuits (PQCs) efficiently. The algorithm optimizes the PQC structure on-the-fly in VQA by sequentially replacing a…
While Quantum Convolutional Neural Networks (QCNNs) offer a theoretical paradigm for quantum machine learning, their practical implementation is severely bottlenecked by barren plateaus -- the exponential vanishing of gradients -- and poor…
Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their scalability. One known scaling result for VQAs is…
Second-order optimization uses curvature information about the objective function, which can help in faster convergence. However, such methods typically require expensive computation of the Hessian matrix, preventing their usage in a…
With rapid advances in quantum hardware, a central question is whether quantum devices with or without full error correction can outperform classical computers on practically relevant problems. Variational Quantum Algorithms (VQAs) have…
Variational quantum algorithms are of special importance in the research on quantum computing applications because of their applicability to current Noisy Intermediate-Scale Quantum (NISQ) devices. The main building blocks of these…
Variational quantum algorithms (VQAs), which classically optimize a parametrized quantum circuit to solve a computational task, promise to advance our understanding of quantum many-body systems and improve machine learning algorithms using…
Two main challenges preventing efficient training of variational quantum algorithms and quantum machine learning models are local minima and barren plateaus. Typically, barren plateaus are associated with deep circuits, while shallow…
Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient…
Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order…
The optimization of Variational Quantum Eigensolver is severely challenged by finite-shot sampling noise, which distorts the cost landscape, creates false variational minima, and induces statistical bias called winner's curse. We…
We develop quantum algorithms for pricing Asian and barrier options under the Heston model, a popular stochastic volatility model, and estimate their costs, in terms of T-count, T-depth and number of logical qubits, on instances under…