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Parameterized quantum circuits (PQCs) have emerged as a foundational element in the development and applications of quantum algorithms. However, when initialized with random parameter values, PQCs often exhibit barren plateaus (BP). These…

Quantum Physics · Physics 2025-07-02 Muhammad Kashif , Muhammad Rashid , Saif Al-Kuwari , Muhammad Shafique

Parametrized quantum circuits initialized with random initial parameter values are characterized by barren plateaus where the gradient becomes exponentially small in the number of qubits. In this technical note we theoretically motivate and…

Quantum Physics · Physics 2019-12-11 Edward Grant , Leonard Wossnig , Mateusz Ostaszewski , Marcello Benedetti

Parameterized quantum circuits (PQCs) are crucial for quantum machine learning and circuit synthesis, enabling the practical implementation of complex quantum tasks. However, PQC learning has been largely confined to classical optimization…

Quantum Physics · Physics 2024-10-01 Keren Li , Yuanfeng Wang , Pan Gao , Shenggen Zheng

There has been intensive research on increasing the utility and performance of Parameterized Quantum Circuits (PQCs) in the past couple of years. Owing to this research, there are now several inductive biases available to a quantum…

Quantum Physics · Physics 2026-04-24 Ankit Kulshrestha , Sarvagya Upadhyay

Parameterized Quantum Circuits (PQC) are drawing increasing research interest thanks to its potential to achieve quantum advantages on near-term Noisy Intermediate Scale Quantum (NISQ) hardware. In order to achieve scalable PQC learning,…

Quantum Physics · Physics 2025-01-29 Hanrui Wang , Zirui Li , Jiaqi Gu , Yongshan Ding , David Z. Pan , Song Han

Variational quantum algorithms (VQAs) have emerged as the leading strategy to obtain quantum advantage on the current noisy intermediate-scale devices. However, their entanglement-trainability correlation, as the major reason for the barren…

Quantum Physics · Physics 2025-05-07 Shikun Zhang , Yang Zhou , Zheng Qin , Rui Li , Chunxiao Du , Zhisong Xiao , Yongyou Zhang

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…

Quantum Physics · Physics 2022-02-28 Tobias Haug , Kishor Bharti , M. S. Kim

In the era of noisy intermediate-scale quantum (NISQ), variational quantum circuits (VQCs) have been widely applied in various domains, demonstrating the potential advantages of quantum circuits over classical models. Similar to classic…

Quantum Physics · Physics 2025-08-26 Jun Zhuang , Jack Cunningham , Chaowen Guan

When compared to fault-tolerant quantum computational strategies, variational quantum algorithms stand as one of the candidates with the potential of achieving quantum advantage for real-world applications in the near term. However, the…

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…

Quantum Physics · Physics 2026-03-24 Iosif Sakos , Antonios Varvitsiotis , Georgios Korpas , Wayne Lin

Quantum algorithms based on parameterized quantum circuits (PQCs) have enabled a wide range of applications on near-term quantum devices. However, existing PQC architectures face several challenges, among which the ``barren plateaus"…

Quantum Physics · Physics 2026-01-09 Zhenyu Chen , Yuguo Shao , Zhengwei Liu , Zhaohui Wei

Quantum Computing aims to streamline machine learning, making it more effective with fewer trainable parameters. This reduction of parameters can speed up the learning process and reduce the use of computational resources. However, in the…

Quantum Physics · Physics 2024-05-22 Michael Kölle , Timo Witter , Tobias Rohe , Gerhard Stenzel , Philipp Altmann , Thomas Gabor

Whether parameterized quantum circuits (PQCs) can be systematically constructed to be both trainable and expressive remains an open question. Highly expressive PQCs often exhibit barren plateaus, while several trainable alternatives admit…

Quantum Physics · Physics 2026-03-17 Peter Röseler , Dennis Willsch , Kristel Michielsen

Parameterized quantum circuits (PQC, aka, variational quantum circuits) are among the proposals for a computational advantage over classical computation of near-term (not fault tolerant) digital quantum computers. PQCs have to be "trained"…

Quantum Physics · Physics 2019-04-01 Evgenii Dolzhkov , Bahman Ghandchi , Dirk Oliver Theis

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…

Quantum Physics · Physics 2025-10-10 Joona V. Pankkonen , Matti Raasakka , Andrea Marchesin , Ilkka Tittonen

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…

Quantum Physics · Physics 2024-10-10 Zhan Yu , Qiuhao Chen , Yuling Jiao , Yinan Li , Xiliang Lu , Xin Wang , Jerry Zhijian Yang

The public access to noisy intermediate-scale quantum (NISQ) computers facilitated by IBM, Rigetti, D-Wave, etc., has propelled the development of quantum applications that may offer quantum supremacy in the future large-scale quantum…

Emerging Technologies · Computer Science 2019-03-22 Mahabubul Alam , Abdullah Ash-Saki , Swaroop Ghosh

In the current noisy intermediate-scale quantum (NISQ) era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parametrized,…

Quantum Physics · Physics 2022-06-15 Osvaldo Simeone

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…

Quantum Physics · Physics 2023-01-31 Tobias Haug , M. S. Kim

In recent years, neural networks (NNs) have driven significant advances in machine learning. However, as tasks grow more complex, NNs often require large numbers of trainable parameters, which increases computational and energy demands.…

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