Training deep quantum neural networks

By Kerstin Beer, D. Bondarenko, Terry Farrelly, Tobias J. Osborne, Robert Salzmann, D. Scheiermann, Ramona Wolf. Nature Communications, 2019

740 citations recorded by the source corpus.

Neural networks enjoy widespread success in both research and industry and, with the advent of quantum technology, it is a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose a truly quantum analogue of classical neurons, which form quantum feedforward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function, providing both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing deep-network optimisation. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data. It is hard to design quantum neural networks able to work with quantum data. Here, the authors propose a noise-robust architecture for a feedforward quantum neural network, with qudits as neurons and arbitrary unitary operations as perceptrons, whose training procedure is efficient in the number of layers.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/9c8e8416bf64e592444e25e484f3f729480fd146

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In Artificial Intelligence

Citations in the corpus

Challenges and opportunities in quantum machine learning (2022, background): “4(a) we show a dissipative QNN [40] which generalizes the classical feed-forward network.”
Barren plateaus in variational quantum computing (2024, neutral): “In quantum machine learning, the input states tend to be fixed as the encoding scheme for classical data, the measurement operator and the choice of loss function are generally more flexible, offering additional design freedom.”
Noise-induced barren plateaus in variational quantum algorithms (2020, background): “[60] Kerstin Beer, Dmytro Bondarenko, Terry Farrelly, Tobias J Osborne, Robert Salzmann, Daniel Scheiermann, and Ramona Wolf, “Training deep quantum neural networks,” Nature Communications 11, 1–6 (2020).”
Absence of Barren Plateaus in Quantum Convolutional Neural Networks (2020, background): “First, let us remark that the variance for the correlated case is always larger than that of the uncorrelated case as in (32).”
Quantum variational algorithms are swamped with traps (2022, positive): “…setting of qUSQ , we can evaluate the commonly used procedure of measuring the inner product or average ﬁ delity of n -qubit states between a target unitary U * and a variationally chosen unitary V ( θ ) using statistical queries analogous to a swap test on actual quantum hardware 39,56 – 58 .”
Parameterized quantum circuits as machine learning models (2019, methodology): “[40] use separate qubit registers for input and output, and define the quantum neuron as a completely positive map between the two.”
Variational quantum algorithms (2020, neutral): “[132, 149, 150] proposed perceptron-based QNNs.”