Article
Physics, Multidisciplinary
Zidu Liu, Li-Wei Yu, L. -M. Duan, Dong-Ling Deng
Summary: This study investigates the trainability of tensor-network based machine learning models and discovers that gradients of global loss functions vanish, while gradients of local loss functions do not vanish, which is proven. These findings provide valuable insights for future practical applications and theoretical studies.
PHYSICAL REVIEW LETTERS
(2022)
Article
Quantum Science & Technology
Jacob L. Cybulski, Thanh Nguyen
Summary: This paper investigates four countermeasures for dealing with barren plateaus in the training of quantum neural networks and demonstrates their impact on model training, generalization ability, and effective dimension through experiments. The findings are of great significance for guiding the development of quantum models.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Optics
Lucas Friedrich, Jonas Maziero
Summary: This paper proposes a method to mitigate the barren plateaus (BPs) problem in variational quantum algorithms (VQAs) by using a classical neural network (CNN) to generate parameters. The experiments demonstrate that this method can alleviate the impact of BPs during startup and training.
Article
Multidisciplinary Sciences
Samson Wang, Enrico Fontana, M. Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, Patrick J. Coles
Summary: The study demonstrates that local Pauli noise can render VQAs untrainable. It shows that noise-induced barren plateaus cause the gradient to exponentially vanish during the training process.
NATURE COMMUNICATIONS
(2021)
Article
Multidisciplinary Sciences
M. Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, Patrick J. Coles
Summary: In this study, the authors rigorously prove that defining cost functions with local observables can avoid the barren plateau problem, while defining them with global observables leads to exponentially vanishing gradients. The results indicate a connection between locality and trainability in variational quantum algorithms (VQAs).
NATURE COMMUNICATIONS
(2021)
Article
Quantum Science & Technology
Andrew Arrasmith, M. Cerezo, Piotr Czarnik, Lukasz Cincio, Patrick J. Coles
Summary: Barren plateau landscapes are shown to significantly impact gradient-based optimizers, and this study confirms that gradient-free optimizers are also unable to solve the barren plateau problem. The research reveals the limitations of gradient-free optimization and sheds light on the challenges of training quantum neural networks in barren plateaus.
Article
Physics, Multidisciplinary
Zoe Holmes, Andrew Arrasmith, Bin Yan, Patrick J. Coles, Andreas Albrecht, Andrew T. Sornborger
Summary: In this paper, the authors investigate the possibility of using quantum machine learning to study scrambling processes, and demonstrate the difficulty of learning unknown scrambling processes. The study shows that there are limitations in learning unitaries without prior information.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Multidisciplinary
Huan-Yu Liu, Tai-Ping Sun, Yu-Chun Wu, Yong-Jian Han, Guo-Ping Guo
Summary: In this paper, a parameter initialization method is proposed to mitigate barren plateaus (BPs) phenomenon in training Variational Quantum Algorithms (VQAs). The method utilizes transfer learning by solving a smaller-sized task first and transferring the ansatz and optimum parameters to larger-sized tasks. Numerical simulations show that this method can mitigate BPs and improve training efficiency. This work provides a reference for mitigating BPs, enabling VQAs to be applied to more practical problems.
NEW JOURNAL OF PHYSICS
(2023)
Article
Quantum Science & Technology
Zoe Holmes, Kunal Sharma, M. Cerezo, Patrick J. Coles
Summary: Parametrized quantum circuits are a flexible paradigm for solving variational problems and programming near-term quantum computers. By extending the barren plateau phenomenon to arbitrary ansatze, we establish a fundamental relationship between expressibility and trainability, showing that highly expressive ansatze are more difficult to train.
Article
Physics, Multidisciplinary
A. Uvarov, J. D. Biamonte
Summary: The text discusses variational quantum algorithms and the phenomenon of barren plateaus in parametrized quantum circuits, where gradients vanish exponentially. By deriving a lower bound on the variance of the gradient, researchers clarify the conditions under which barren plateaus can occur. The onset of a barren plateau regime is shown to depend on the cost function and the width of the circuit causal cone.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
Article
Optics
Antonio A. Mele, Glen B. Mbeng, Giuseppe E. Santoro, Mario Collura, Pietro Torta
Summary: This paper discusses the scalability of variational quantum algorithms in terms of the number of qubits and proposes a solution to circumvent the barren plateau phenomenon by employing iterative search schemes.
Article
Quantum Science & Technology
Stefan H. Sack, Raimel A. Medina, Alexios A. Michailidis, Richard Kueng, Maksym Serbyn
Summary: Variational quantum algorithms show promise for achieving quantum advantage on near-term devices. However, the presence of barren plateaus, with vanishing gradients, in the optimization landscape hinders efficient optimization. In this work, a general algorithm is proposed to avoid barren plateaus by introducing the concept of weak barren plateaus (WBPs) and utilizing shadow tomography with classical computers. The study demonstrates that avoiding WBPs ensures non-negligible gradients during initialization and can be further achieved during the optimization process by decreasing the gradient step size based on entropies.
Article
Quantum Science & Technology
Enrique Cervero Martin, Kirill Plekhanov, Michael Lubasch
Summary: We analyze the barren plateau phenomenon in the variational optimization of quantum circuits inspired by qMPS, qTTN, and qMERA. The variance of the cost function gradient decreases exponentially with the distance of a Hamiltonian term from the canonical centre in the quantum tensor network. The calculation of these gradients is exponentially more efficient on a classical computer than on a quantum computer.
Article
Quantum Science & Technology
Chen Zhao, Xiao-Shan Gao
Summary: This paper proposes a general scheme to analyze the gradient vanishing phenomenon in training quantum neural networks using the ZX-calculus. By representing integrations as ZX-diagrams and computing them with the ZX-calculus, the barren plateau phenomenon is studied on four concrete quantum neural networks with different structures. It is found that there are barren plateaus for hardware efficient ansatz and MPS-inspired ansatz, while no barren plateau exists for QCNN ansatz and tree tensor network ansatz.
Article
Computer Science, Artificial Intelligence
Muhammad Kashif, Saif Al-Kuwari
Summary: This paper empirically analyzes the locality and globality of the cost function in hybrid quantum neural networks. The results show that for multiclass classification, the local cost function does not solve the problem of the flat loss function, and the overall performance of the global cost function is significantly better. However, for binary classification, the local cost function can solve the problem of the flat loss function, but the global cost function still performs slightly better.
MACHINE LEARNING-SCIENCE AND TECHNOLOGY
(2023)
Article
Multidisciplinary Sciences
Shui-Jiong Wang, Wenzhong Wang, Jian-Ming Zhu, Zhongqing Wu, Jingao Liu, Guilin Han, Fang-Zhen Teng, Shichun Huang, Hongjie Wu, Yujian Wang, Guangliang Wu, Weihan Li
Summary: During Earth's late-stage accretion, impactors delivered most of the volatiles, with nickel serving as an important tracer. Research has found that the BSE has a lighter nickel isotopic composition compared to chondrites, suggesting that this sub-chondritic signature was established during the Moon-forming giant impact.
NATURE COMMUNICATIONS
(2021)
Article
Multidisciplinary Sciences
M. Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, Patrick J. Coles
Summary: In this study, the authors rigorously prove that defining cost functions with local observables can avoid the barren plateau problem, while defining them with global observables leads to exponentially vanishing gradients. The results indicate a connection between locality and trainability in variational quantum algorithms (VQAs).
NATURE COMMUNICATIONS
(2021)
Article
Physics, Multidisciplinary
Kunal Sharma, M. Cerezo, Zoe Holmes, Lukasz Cincio, Andrew Sornborger, Patrick J. Coles
Summary: The NFL theorem limits one's ability to learn a function with a training dataset. Researchers show that entangled datasets in the quantum environment can lead to a violation of the NFL theorem, and that entanglement can reduce the fundamental limit on the learnability of a unitary.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Kunal Sharma, M. Cerezo, Lukasz Cincio, Patrick J. Coles
Summary: This article analyzes the gradient scaling performance of a recently proposed architecture called dissipative quantum neural networks (DQNNs), and finds that DQNNs can exhibit gradient vanishing. Moreover, we quantitatively bound the scaling of the gradient for DQNNs under different conditions and demonstrate that trainability is not always guaranteed.
PHYSICAL REVIEW LETTERS
(2022)
Article
Quantum Science & Technology
Andrew Arrasmith, Zoe Holmes, M. Cerezo, Patrick J. Coles
Summary: This research investigates the relationship between cost function landscapes of parameterized quantum circuits (PQCs). It is analytically proven that the phenomena of exponentially vanishing gradients, exponential cost concentration about the mean, and the exponential narrowness of minima occur together. The key implication of this result is that BPs can be diagnosed numerically through cost differences instead of computationally expensive gradients.
QUANTUM SCIENCE AND TECHNOLOGY
(2022)
Article
Physics, Multidisciplinary
C. Huerta Alderete, Max Hunter Gordon, Frederic Sauvage, Akira Sone, Andrew T. Sornborger, Patrick J. Coles, M. Cerezo
Summary: This article presents an inference-based scheme for quantum sensing, which allows accurate estimation of unknown parameters and determination of the scheme's sensitivity through measurements of the system response. The scheme is applicable to arbitrary probe states and measurement schemes, and remains effective in the presence of quantum noise.
PHYSICAL REVIEW LETTERS
(2022)
Article
Quantum Science & Technology
M. Cerezo, Kunal Sharma, Andrew Arrasmith, Patrick J. Coles
Summary: In this study, we introduce the variational quantum state eigensolver (VQSE) method for dealing with exponentially large matrices of density matrix. By exploiting the connection between diagonalization and majorization, VQSE can accurately calculate the largest eigenvalues of the density matrix rho and the corresponding eigenvectors gate sequence V, with lower computational complexity.
NPJ QUANTUM INFORMATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Martin Larocca, Nathan Ju, Diego Garcia-Martin, Patrick J. Coles, Marco Cerezo
Summary: A theoretical framework for quantum neural network (QNN) overparametrization and its impact on QNN design is established. The prospect of achieving quantum advantage with QNNs is exciting. Understanding how QNN properties, such as the number of parameters, affect the loss landscape is crucial for designing scalable QNN architectures.
NATURE COMPUTATIONAL SCIENCE
(2023)
Article
Quantum Science & Technology
Martin Larocca, Piotr Czarnik, Kunal Sharma, Gopikrishnan Muraleedharan, Patrick J. Coles, M. Cerezo
Summary: Variational Quantum Algorithms (VQAs) have received attention for their potential quantum advantage, but more research is needed on their scalability. This study proposes a framework using quantum optimal control to diagnose the presence of barren plateaus in problem-inspired ansatzes and proves that avoiding barren plateaus is not guaranteed for these ansatzes. The results provide a framework for trainability-aware ansatz design strategies without extra quantum resources and establish a link between barren plateaus and the scaling of the dimension of g.
Article
Computer Science, Interdisciplinary Applications
M. Cerezo, Guillaume Verdon, Hsin-Yuan Huang, Lukasz Cincio, Patrick J. Coles
Summary: Quantum machine learning, positioned at the intersection of machine learning and quantum computing, shows great potential in accelerating data analysis for quantum data and has wide applications. Challenges still remain regarding the trainability of quantum machine learning models, but through continuous research and exploration, the development potential in this field is evident.
NATURE COMPUTATIONAL SCIENCE
(2022)
Article
Quantum Science & Technology
Enrico Fontana, M. Cerezo, Andrew Arrasmith, Ivan Rungger, Patrick J. Coles
Summary: This paper analyzes the cost landscape for Parametrized Quantum Circuits (PQCs) and proves the exponential symmetry and resilience of these symmetries under noise. Based on these findings, the paper introduces an optimization method called Symmetry-based Minima Hopping (SYMH) which improves the optimizer performance in the presence of non-unital noise. Numerical simulations show that SYMH achieves performance comparable to current hardware.
Article
Quantum Science & Technology
Martin Larocca, Frederic Sauvage, Faris M. Sbahi, Guillaume Verdon, Patrick J. Coles, M. Cerezo
Summary: This study proposes a framework for designing quantum machine learning models based on underlying invariances, which can create models that adhere to symmetries. The effectiveness of the framework is demonstrated through theoretical results and examples, as well as the discovery of new algorithms.
Article
Quantum Science & Technology
Max Hunter Gordon, M. Cerezo, Lukasz Cincio, Patrick J. Coles
Summary: Principal component analysis (PCA) is a dimensionality reduction method that involves diagonalizing the covariance matrix of a dataset. Recently, quantum algorithms for PCA based on diagonalizing a density matrix have been proposed. However, a concrete protocol for encoding the covariance matrix as a density matrix has been lacking. In this study, we address this gap by providing a simple means for preparing the covariance matrix for arbitrary quantum datasets or centered classical datasets. We also propose a method for uncentered classical datasets, which we interpret as PCA on a symmetrized dataset. We demonstrate the effectiveness of our method through numerical experiments on the MNIST handwritten digit dataset and molecular ground-state datasets.
Article
Physics, Multidisciplinary
Jacob L. Beckey, M. Cerezo, Akira Sone, Patrick J. Coles
Summary: This paper presents a variational quantum algorithm, VQFIE, for estimating the quantum Fisher information (QFI) of a mixed state. By estimating the lower and upper bounds on the QFI, VQFIE outputs a range in which the actual QFI lies, and can be used to prepare the state that maximizes the QFI for quantum sensing applications. Unlike previous approaches, VQFIE does not require knowledge of the explicit form of the sensor dynamics.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Quantum Science & Technology
Zoe Holmes, Kunal Sharma, M. Cerezo, Patrick J. Coles
Summary: Parametrized quantum circuits are a flexible paradigm for solving variational problems and programming near-term quantum computers. By extending the barren plateau phenomenon to arbitrary ansatze, we establish a fundamental relationship between expressibility and trainability, showing that highly expressive ansatze are more difficult to train.