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Designing effective quantum circuits remains a central challenge in quantum computing, as circuit structure strongly influences expressivity, trainability, and hardware feasibility. Current approaches, whether using manually designed…
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…
Parameterized quantum circuits (PQCs) play an essential role in the application of variational quantum algorithms (VQAs) in noisy intermediate-scale quantum (NISQ) devices. The PQCs are a leading candidate to achieve a quantum advantage in…
Variational quantum algorithms (VQAs) face an inherent trade-off between expressivity and trainability: deeper circuits can represent richer states but suffer from noise accumulation and barren plateaus, while shallow circuits remain…
Parametrized quantum circuits (PQCs) are crucial in variational quantum algorithms. While it is commonly believed that the optimal PQC is solely used to reproduce the target state, we here reveal that the optimal PQC can also provide…
Recurrent quantum models (RQMs) realize sequential quantum processes through repeated application of a unitary operation on a memory system coupled with a series of output registers. However, such models often rely on unnecessarily large…
Optimizing the architecture of variational quantum circuits (VQCs) is crucial for advancing quantum computing (QC) towards practical applications. Current methods range from static ansatz design and evolutionary methods to machine learned…
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…
Quantum computing has made significant progress in recent years, attracting immense interest not only in research laboratories but also in various industries. However, the application of quantum computing to solve real-world problems is…
Quantum computers have been proposed as a solution for efficiently solving non-linear differential equations (DEs), a fundamental task across diverse technological and scientific domains. However, a crucial milestone in this regard is to…
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…
The superiority of variational quantum algorithms (VQAs) such as quantum neural networks (QNNs) and variational quantum eigen-solvers (VQEs) heavily depends on the expressivity of the employed ansatze. Namely, a simple ansatze is…
Scaling quantum computers, i.e., quantum processing units (QPUs) to enable the execution of large quantum circuits is a major challenge, especially for applications that should provide a quantum advantage over classical algorithms. One…
Efficient methods for encoding and compression are likely to pave way towards the problem of efficient trainability on higher dimensional Hilbert spaces overcoming issues of barren plateaus. Here we propose an alternative approach to…
Variational quantum circuits (VQCs) are an essential tool in applying noisy intermediate-scale quantum computers to practical problems. VQCs are used as a central component in many algorithms, for example, in quantum machine learning,…
Parameterized quantum circuits (PQCs) have been broadly used as a hybrid quantum-classical machine learning scheme to accomplish generative tasks. However, whether PQCs have better expressive power than classical generative neural networks,…
Are multi-layer parameterized quantum circuits (MPQCs) more expressive than classical neural networks (NNs)? How, why, and in what aspects? In this work, we survey and develop intuitive insights into the expressive power of MPQCs in…
In the noisy intermediate-scale quantum era, variational quantum algorithms (VQAs) have emerged as a promising avenue to obtain quantum advantage. However, the success of VQAs depends on the expressive power of parameterised quantum…
Permutational Quantum Computing (PQC) [\emph{Quantum~Info.~Comput.}, \textbf{10}, 470--497, (2010)] is a natural quantum computational model conjectured to capture non-classical aspects of quantum computation. An argument backing this…
In the field of quantum machine learning (QML), parametrized quantum circuits (PQCs) -- constructed using a combination of fixed and tunable quantum gates -- provide a promising hybrid framework for tackling complex machine learning…