**(SyncedReview)** In the paper *The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning,* a team from Qualcomm AI proposes a direct mapping of a deep neural network onto an optical quantum computer through the language of quantum field theory, an approach that could pave the way for the future development of novel quantum neural network architectures.

The “Hintons” in the paper title is an homage to Geoffrey Hinton — the researchers coined the term to refer to “the elementary excitation of the quantum field from which optical quantum neural networks are made.”

The researchers begin by reviewing the frameworks of probabilistic numeric neural networks, which classify input signals with missing data using Gaussian processes (GP) to interpolate the signal and use GP representations to define the neural network.

Then they introduce a series of quantum operations that generalize the classical layers of a probabilistic numeric neural network. First, they show how to perform Bayesian inference with Gaussian states in such a way as to allow quantum entanglement to represent an agent’s uncertainty about discretization errors. In the next step, they show how to perform the quantum equivalent of a linear layer that acts on the quantum fields in the same way as a classical linear layer acts on a classical field.

Finally, the researchers explain how to embed classical neural networks in the quantum model. They interpret the resulting model as a semi-classical limit of the quantum model. Specifically, the proposed model uses elements (uncertainty relation for the covariance) of quantum mechanics and classical mechanics for the non-linearity (similar to classical non-linearities, a quantum non-linearity acts pointwise on the quantum fields).

The team also proposes exciting possible future directions in this field, such as studying approximate solutions that get closer to the full quantum model, finding efficient ways to do quantum GP inference on quantum hardware, and developing further quantum non-linearities and a quantum formalism for classical models.