Entanglement Induced Barren Plateaus

By Carlos Ortiz Marrero, Mária Kieferová, Nathan Wiebe. PRX Quantum, 2020

359 citations recorded by the source corpus.

We argue that an excess in entanglement between the visible and hidden units in a Quantum Neural Network can hinder learning. In particular, we show that quantum neural networks that satisfy a volume-law in the entanglement entropy will give rise to models not suitable for learning with high probability. Using arguments from quantum thermodynamics, we then show that this volume law is typical and that there exists a barren plateau in the optimization landscape due to entanglement. More precisely, we show that for any bounded objective function on the visible layers, the Lipshitz constants of the expectation value of that objective function will scale inversely with the dimension of the hidden-subsystem with high probability. We show how this can cause both gradient descent and gradient-free methods to fail. We note that similar problems can happen with quantum Boltzmann machines, although stronger assumptions on the coupling between the hidden/visible subspaces are necessary. We highlight how pretraining such generative models may provide a way to navigate these barren plateaus.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c0a1b887aefcec5570d4894c8eac054ddd0f06d1

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Citations in the corpus

Connecting ansatz expressibility to gradient magnitudes and barren plateaus (2021, background): “[33]. where σ = | 0 (cid:105)(cid:104) 0 | − 1 /d .”
Variational quantum algorithms (2020, methodology): “In addition, the BP phenomenon has been studied when training randomly initialized perceptron-based quantum neural networks [171, 172].”
Barren plateaus in variational quantum computing (2024, neutral): “Interestingly, one can still bound how much the variance will deviate from that in equation (8) when the circuit is not a two-design (see Box 4 and the results in refs.”
Diagnosing Barren Plateaus with Tools from Quantum Optimal Control (2021, background): “In addition, it has been shown that circuits that generate large amounts of entanglement [41, 45, 44] are prone to suffer from barren plateaus.”
Challenges and opportunities in quantum machine learning (2022, background): “[86] Carlos Ortiz Marrero, Maria Kieferova, and Nathan Wiebe, “Entanglement induced barren plateaus,” arXiv preprint arXiv:2010.”
Absence of Barren Plateaus in Quantum Convolutional Neural Networks (2020, background): “Additionally, recent studies have shown that more general perceptron-based dissipative QNNs [32] can also show barren plateau land-scapes [37, 43], proving that this is a general phenomenon in many quantum machine learning applications.”
Noise-induced barren plateaus in variational quantum algorithms (2020, background): “[35] Carlos Ortiz Marrero, Mária Kieferová, and Nathan Wiebe, “Entanglement induced barren plateaus,” arXiv preprint arXiv:2010.”