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Many applications of quantum computing in the near term rely on variational quantum circuits (VQCs). They have been showcased as a promising model for reaching a quantum advantage in machine learning with current noisy intermediate scale…
Noisy intermediate scale quantum computers are useful for various tasks such as state preparation and variational quantum algorithms. However, the non-Euclidean quantum geometry of parameterized quantum circuits is detrimental for these…
In this paper, we investigate the performances of tunable quantum neural networks in the Quantum Probably Approximately Correct (QPAC) learning framework. Tunable neural networks are quantum circuits made of multi-controlled X gates. By…
We present qLEET, an open-source Python package for studying parameterized quantum circuits (PQCs), which are widely used in various variational quantum algorithms (VQAs) and quantum machine learning (QML) algorithms. qLEET enables the…
Quantum computing is transitioning from experimental prototypes to commercially available turnkey systems, making architecture-agnostic performance metrics essential for cross-platform comparison. Peaked Random Circuits (PRCs) have recently…
Parameterized quantum circuits (PQCs) are a central component of many variational quantum algorithms, yet there is a lack of understanding of how their parameterization impacts algorithm performance. We initiate this discussion by using…
In this work, we propose a generalization of the current most widely used quantum computing hardware metric known as the quantum volume. The quantum volume specifies a family of random test circuits defined such that the logical circuit…
Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These…
To harness the potential of noisy intermediate-scale quantum devices, it is paramount to find the best type of circuits to run hybrid quantum-classical algorithms. Key candidates are parametrized quantum circuits that can be effectively…
Parameterized quantum circuits play an essential role in the performance of many variational hybrid quantum-classical (HQC) algorithms. One challenge in implementing such algorithms is to choose an effective circuit that well represents the…
Variational training of parameterized quantum circuits (PQCs) underpins many workflows employed on near-term noisy intermediate scale quantum (NISQ) devices. It is a hybrid quantum-classical approach that minimizes an associated cost…
We propose a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, which we call quantum circuit learning. A quantum circuit driven by our framework learns a given task by tuning parameters implemented on…
In the Noisy Intermediate-Scale Quantum (NISQ) era, using variational quantum algorithms (VQAs) to solve optimization problems has become a key application. However, these algorithms face significant challenges, such as choosing an…
Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require…
The paradigm of measurement-based quantum computing (MBQC) starts from a highly entangled resource state on which unitary operations are executed through adaptive measurements and corrections ensuring determinism. This is set in contrast to…
Motivated by the developing mathematics of deep learning, we build universal functions approximators of continuous maps between arbitrary Polish metric spaces $\mathcal{X}$ and $\mathcal{Y}$ using elementary functions between Euclidean…
While recent breakthroughs have proven the ability of noisy intermediate-scale quantum (NISQ) devices to achieve quantum advantage in classically-intractable sampling tasks, the use of these devices for solving more practically relevant…
Very little is known about the cost landscape for parametrized Quantum Circuits (PQCs). Nevertheless, PQCs are employed in Quantum Neural Networks and Variational Quantum Algorithms, which may allow for near-term quantum advantage. Such…
We study the expressibility and learnability of convex optimization solution functions and their multi-layer architectural extension. The main results are: \emph{(1)} the class of solution functions of linear programming (LP) and quadratic…
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.…