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Parametric quantum circuits play a crucial role in the performance of many variational quantum algorithms. To successfully implement such algorithms, one must design efficient quantum circuits that sufficiently approximate the solution…
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…
The design of parametric quantum circuits (PQCs) for efficient use in variational quantum simulations (VQS) is subject to two competing factors. On one hand, the set of states that can be generated by the PQC has to be large enough to…
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…
Expressibility is a crucial factor of a Parameterized Quantum Circuit (PQC). In the context of Variational Quantum Algorithms (VQA) based Quantum Machine Learning (QML), a QML model composed of highly expressible PQC and sufficient number…
We characterize the expressive power of quantum circuits with the pseudo-dimension, a measure of complexity for probabilistic concept classes. We prove pseudo-dimension bounds on the output probability distributions of quantum circuits; the…
While scalable error correction schemes and fault tolerant quantum computing seem not to be universally accessible in the near sight, the efforts of many researchers have been directed to the exploration of the contemporary available…
Parameterized quantum circuits play a key role for the development of quantum variational algorithms in the realm of the NISQ era. Knowing their actual capability of performing different kinds of tasks is then of the utmost importance. By…
Variational Quantum Eigensolver is considered promising for medium-scale noisy quantum computers. Expressibility is an important metric for measuring the capability of a variational quantum Ansatz circuit. A commonly used method to increase…
With the exponentially faster computation for certain problems, quantum computing has garnered significant attention in recent years. Variational quantum algorithms are crucial methods to implement quantum computing, and an appropriate…
Hybrid quantum-classical systems make it possible to utilize existing quantum computers to their fullest extent. Within this framework, parameterized quantum circuits can be regarded as machine learning models with remarkable expressive…
Operator controllability refers to the ability to implement an arbitrary unitary in SU(N) and is a prerequisite for universal quantum computing. Controllability tests can be used in the design of quantum devices to reduce the number of…
Parameterized quantum circuits are the core of new technologies such as variational quantum algorithms and quantum machine learning, which makes studying its properties a valuable task. We implement parameterized circuits with definite and…
The expressibility of an ansatz used in a variational quantum algorithm is defined as the uniformity with which it can explore the space of unitary matrices, i.e., its covering number. The expressibility of a particular ansatz has a…
Parameterized quantum circuits have been extensively used as the basis for machine learning models in regression, classification, and generative tasks. For supervised learning, their expressivity has been thoroughly investigated and several…
Parameterized Quantum Circuits (PQCs) are essential to quantum machine learning and optimization algorithms. The expressibility of PQCs, which measures their ability to represent a wide range of quantum states, is a critical factor…
In this work, we highlight an unforeseen behavior of the expressivity of Parameterized Quantum Circuits (PQCs) for machine learning. A large class of these models, seen as Fourier Series which frequencies are derived from the encoding…
This study investigates the frame potential and expressiveness of commutative quantum circuits. Based on the Fourier series representation of these circuits, we express quantum expectation and pairwise fidelity as characteristic functions…
Sampling from a probability distribution is a core task in many quantum and classical algorithms. Variational quantum circuits provide a natural approach to generating such distributions, as measurement outcomes directly define the…
An active area of investigation in the search for quantum advantage is Quantum Machine Learning. Quantum Machine Learning, and Parameterized Quantum Circuits in a hybrid quantum-classical setup in particular, could bring advancements in…