The power of quantum neural networks

By Amira Abbas, David Sutter, Christa Zoufal, Aurélien Lucchi, Alessio Figalli, Stefan Woerner. Nature Computational Science, 2020

1,167 citations recorded by the source corpus.

It is unknown whether near-term quantum computers are advantageous for machine learning tasks. In this work we address this question by trying to understand how powerful and trainable quantum machine learning models are in relation to popular classical neural networks. We propose the effective dimension—a measure that captures these qualities—and prove that it can be used to assess any statistical model’s ability to generalize on new data. Crucially, the effective dimension is a data-dependent measure that depends on the Fisher information, which allows us to gauge the ability of a model to train. We demonstrate numerically that a class of quantum neural networks is able to achieve a considerably better effective dimension than comparable feedforward networks and train faster, suggesting an advantage for quantum machine learning, which we verify on real quantum hardware. A class of quantum neural networks is presented that outperforms comparable classical feedforward networks. They achieve a higher capacity in terms of effective dimension and at the same time train faster, suggesting a quantum advantage.

Subfields: Artificial Intelligence, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/adebb037521cf2b49208098f4179dd3ed635ccab

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Citations in the corpus

Variational quantum algorithms (2020, background): “For instance, it has been shown that quantum neural networks can achieve a significantly better effective dimension than comparable classical neural networks [258].”
Absence of Barren Plateaus in Quantum Convolutional Neural Networks (2020, background): “…forward to analyze the trainability of the cost functions of VQAs and QNNs, as it has been shown that the optimization landscape can exhibit the so-called barren plateau phenomenon where the cost function gradients of a randomly initialized ansatz vanish exponentially with the problem size [35–44].”
Barren plateaus in variational quantum computing (2024, neutral): “In fact, equation (7) precludes any type of non-exponentially suppressed features in the landscape.”
Noise-induced barren plateaus in variational quantum algorithms (2020, methodology): “Our results also generalize to settings that allow for multiple input states or training data, as in machine learning applications, often called quantum neural networks [58–62].”
QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits (2021, background): “[1] shows that from an information geometry point of view, if carefully designed, QNNs have higher effective dimensions and faster training convergence speed over classical NNs.”
Connecting ansatz expressibility to gradient magnitudes and barren plateaus (2021, background): “Recently, it was shown that VQAs can exhibit barren plateaus, where under certain conditions the gradient of the cost function vanishes exponentially with the size of the system [27–36].”
Challenges and opportunities in quantum machine learning (2022, background): “Local minima are not the only issue facing QML, as it has been shown that quantum landscapes can exhibit a fascinating property known as a barren plateau [58, 77– 89].”