Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus

Zhao, Chen; Gao, Xiao-Shan

doi:10.22331/q-2021-06-04-466

Cited by 77 publications

(86 citation statements)

References 43 publications

(52 reference statements)

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“…In general, layered-type PQCs suffer from Barren Plateaus, which makes them hard or even impossible to train for a large amount of qubits and layers. On the other hand, the absence of Barren Plateaus were shown for some PQCs with hierarchical architectures, such as Quantum Convolutional Neural Networks (QCNNs) (Pesah et al 2020) and TTNs (Zhao and Gao 2021). Because of this, comparing these two types of PQCs have great importance to better understand the behaviour of hybrid models at large scales.…”

Section: The Hybrid Neural Networkmentioning

confidence: 99%

Hybrid quantum classical graph neural networks for particle track reconstruction

Tüysüz

Rieger

Novotny³

et al. 2021

Quantum Mach. Intell.

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The Large Hadron Collider (LHC) at the European Organisation for Nuclear Research (CERN) will be upgraded to further increase the instantaneous rate of particle collisions (luminosity) and become the High Luminosity LHC (HL-LHC). This increase in luminosity will significantly increase the number of particles interacting with the detector. The interaction of particles with a detector is referred to as “hit”. The HL-LHC will yield many more detector hits, which will pose a combinatorial challenge by using reconstruction algorithms to determine particle trajectories from those hits. This work explores the possibility of converting a novel graph neural network model, that can optimally take into account the sparse nature of the tracking detector data and their complex geometry, to a hybrid quantum-classical graph neural network that benefits from using variational quantum layers. We show that this hybrid model can perform similar to the classical approach. Also, we explore parametrized quantum circuits (PQC) with different expressibility and entangling capacities, and compare their training performance in order to quantify the expected benefits. These results can be used to build a future road map to further develop circuit-based hybrid quantum-classical graph neural networks.

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Section: The Hybrid Neural Networkmentioning

confidence: 99%

Hybrid quantum classical graph neural networks for particle track reconstruction

Tüysüz

Rieger

Novotny³

et al. 2021

Quantum Mach. Intell.

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“…In classical machine learning, a notorious obstacle for training artificial neural networks concerns the barren plateau phenomenon, where the gradient of the loss function along any direction vanishes exponentially with the problem size [67]. Recently, barren plateaus have also been shown to exist for many quantum learning models based on variational quantum circuits and the related topics are still under active study at the current stage [68][69][70][71][72][73][74][75][76][77][78][79][80][81]. In this paper, we investigate the presence and absence of barren plateaus for tensor-network based machine learning models, which is a crucial but hitherto unexplored issue in the literature.…”

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confidence: 99%

The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning

Liu,

Yu,

Duan

et al. 2021

Preprint

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Tensor networks are efficient representations of high-dimensional tensors with widespread applications in quantum many-body physics. Recently, they have been adapted to the field of machine learning, giving rise to an emergent research frontier that has attracted considerable attention. Here, we study the trainability of tensor-network based machine learning models by exploring the landscapes of different loss functions, with a focus on the matrix product states (also called tensor trains) architecture. In particular, we rigorously prove that barren plateaus (i.e., exponentially vanishing gradients) prevail in the training process of the machine learning algorithms with global loss functions. Whereas, for local loss functions the gradients with respect to variational parameters near the local observables do not vanish as the system size increases. Therefore, the barren plateaus are absent in this case and the corresponding models could be efficiently trainable. Our results reveal a crucial aspect of tensor-network based machine learning in a rigorous fashion, which provide a valuable guide for both practical applications and theoretical studies in the future.

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“…The dependence of the optimization on the initial guess is well-known in quantum circuit optimization, where poor initial guesses can sometimes give rise to exponentially small gradients (the barren plateau problem [31][32][33][34][35] ). We can see a related problem in our circuits.…”

Section: Initial Guessmentioning

confidence: 99%

The Variational Power of Quantum Circuit Tensor Networks

Haghshenas,

Gray,

Potter

et al. 2021

Preprint

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We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multi-scale entanglement renormalization ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than 10 4 parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for both the energy and correlation functions of the 1D Heisenberg and Fermi-Hubbard models in the gapless regime. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of quantum advantage with respect to expressiveness in the representation of physical ground-states.

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Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus

Cited by 77 publications

References 43 publications

Hybrid quantum classical graph neural networks for particle track reconstruction

Hybrid quantum classical graph neural networks for particle track reconstruction

The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning

The Variational Power of Quantum Circuit Tensor Networks

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