Continuous-variable quantum neural networks

By Nathan Killoran, Thomas R. Bromley, Juan Miguel Arrazola, Maria Schuld, Nicolás Quesada, Seth Lloyd. Physical Review Research, 2018

446 citations recorded by the source corpus.

We introduce a general method for building neural networks on quantum computers. The quantum neural network is a variational quantum circuit built in the continuous-variable (CV) architecture, which encodes quantum information in continuous degrees of freedom such as the amplitudes of the electromagnetic field. This circuit contains a layered structure of continuously parameterized gates which is universal for CV quantum computation. Affine transformations and nonlinear activation functions, two key elements in neural networks, are enacted in the quantum network using Gaussian and non-Gaussian gates, respectively. The non-Gaussian gates provide both the nonlinearity and the universality of the model. Due to the structure of the CV model, the CV quantum neural network can encode highly nonlinear transformations while remaining completely unitary. We show how a classical network can be embedded into the quantum formalism and propose quantum versions of various specialized model such as convolutional, recurrent, and residual networks. Finally, we present numerous modeling experiments built with the Strawberry Fields software library. These experiments, including a classifier for fraud detection, a network which generates Tetris images, and a hybrid classical-quantum autoencoder, demonstrate the capability and adaptability of CV quantum neural networks.

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

View Paper: https://www.semanticscholar.org/paper/4e1a9a2a22913f2a5c79fba6c2e5716ee1ed20bd

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Estimating the gradient and higher-order derivatives on quantum hardware (2020, background): “Many algorithms for near-term quantum computers are based on variational circuits [1–6], i.”
Transfer learning in hybrid classical-quantum neural networks (2019, methodology): “[24], consisting of an encoding layer, 25 variational layers, and a final (Fock) measurement layer.”
General parameter-shift rules for quantum gradients (2021, background): “de tion [17, 18], and variational quantum machine learning [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31].”
Strawberry Fields: A Software Platform for Photonic Quantum Computing (2018, background): “Note that these encodings of classical continuous degress of freedom into quantum registers allows for the generalization of neural networks into the quantum regime [66].”
Challenges and opportunities in quantum machine learning (2022, background): “[44] Nathan Killoran, Thomas R Bromley, Juan Miguel Arrazola, Maria Schuld, Nicolás Quesada, and Seth Lloyd, “Continuous-variable quantum neural networks,” Physical Review Research 1, 033063 (2019).”
Quantum circuits with many photons on a programmable nanophotonic chip (2021, background): “Examples of such applications include those implementing bosonic error correction codes [10, 11], a wide class of Gaussian boson sampling applications [12–18], and other bespoke algorithms that exploit the mathematical structure of infinite-dimensional Hilbert spaces [19, 20].”
Absence of Barren Plateaus in Quantum Convolutional Neural Networks (2020, background): “[28] Nathan Killoran, Thomas R Bromley, Juan Miguel Arrazola, Maria Schuld, Nicolás Quesada, and Seth Lloyd, “Continuous-variable quantum neural networks,” Physical Review Research 1, 033063 (2019).”
Potential of quantum computing for drug discovery (2018, methodology): “Similar ideas have also been implemented by Rigetti Computing, Inc., [127] using image recognition as an example, as well as by Xanadu Quantum Technologies, Inc., on a continuous variable quantum system [128].”
PennyLane: Automatic differentiation of hybrid quantum-classical computations (2018, background): “[17] Nathan Killoran, Thomas R Bromley, Juan Miguel Arrazola, Maria Schuld, Nicolás Quesada, and Seth Lloyd, “Continuous-variable quantum neural networks,” arXiv preprint (2018), arxiv:1806.”
Effect of data encoding on the expressive power of variational quantum-machine-learning models (2020, background): “Killoran et al. [18] have shown that many neural networks can be naturally emulated on a photonic quantum computer, and point out that such quantum models therefore inherit universality.”
Neural Field Continuum Limits and the Structure–Function Partitioning of Cognitive–Emotional Brain Networks (2023, background): “Only for continuum extremes of probabilistic quantum or symmetry-associated deterministic classical behavior do synaptic or nodal clusters reach compacted densities that lead to large, sustainable, peak-degenerate structure-function map homogeneities unrepresentative of actual neural networks and he”