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Parameterized quantum circuits (PQCs) have emerged as a promising approach for quantum neural networks. However, understanding their expressive power in accomplishing machine learning tasks remains a crucial question. This paper…
Parametrized quantum circuits (PQC) are quantum circuits which consist of both fixed and parametrized gates. In recent approaches to quantum machine learning (QML), PQCs are essentially ubiquitous and play the role analogous to classical…
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…
We consider random quantum circuits (RQC) on arbitrary connected graphs whose edges determine the allowed $2$-qudit interactions. Prior work has established that such $n$-qudit circuits with local dimension $q$ on 1D, complete, and…
Parameterised quantum circuits (PQCs) hold great promise for demonstrating quantum advantages in practical applications of quantum computation. Examples of successful applications include the variational quantum eigensolver, the quantum…
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…
Parameterized quantum circuits (PQCs) are fundamental to quantum machine learning (QML), quantum optimization, and variational quantum algorithms (VQAs). The expressibility of PQCs is a measure that determines their capability to harness…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
Loading functions into quantum computers represents an essential step in several quantum algorithms, such as quantum partial differential equation solvers. Therefore, the inefficiency of this process leads to a major bottleneck for 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…
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…
In the absence of error correction, noisy intermediate-scale quantum devices are operated by training parametrized quantum circuits (PQCs) so as to minimize a suitable loss function. Finding the optimal parameters of those circuits is a…
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…
Parametrized Quantum Circuits (PQCs) enable a novel method for machine learning (ML). However, from a computational point of view they present a challenge to existing eXplainable AI (xAI) methods. On the one hand, measurements on quantum…
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…
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…
Numerous quantum algorithms operate under the assumption that classical data has already been converted into quantum states, a process termed Quantum State Preparation (QSP). However, achieving precise QSP requires a circuit depth that…
The feasibility of variational quantum algorithms, the most popular correspondent of neural networks on noisy, near-term quantum hardware, is highly impacted by the circuit depth of the involved parametrized quantum circuits (PQCs). Higher…
Quantum computers can be used for supervised learning by treating parametrised quantum circuits as models that map data inputs to predictions. While a lot of work has been done to investigate practical implications of this approach, many…