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Abstract Training of neural networks (NNs) has emerged as a major consumer of both computational and energy resources. Quantum computers were coined as a root to facilitate training, but no experimental evidence has been presented so far. Here we demonstrate that quantum annealing platforms, such as D-Wave, can enable fast and efficient training of classical NNs, which are then deployable on conventional hardware. From a physics perspective, NN training can be viewed as a dynamical phase transition: the system evolves from an initial spin glass state to a highly ordered, trained state. This process involves eliminating numerous undesired minima in its energy landscape. The advantage of annealing devices is their ability to rapidly find multiple deep states. We found that this quantum training achieves superior performance scaling compared to classical backpropagation methods, with a clearly higher scaling exponent (1.01 vs. 0.78). It may be further increased up to a factor of 2 with a fully coherent quantum platform using a variant of the Grover algorithm. Furthermore, we argue that even a modestly sized annealer can be beneficial to train a deep NN by being applied sequentially to a few layers at a time.
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This content will become publicly available on January 7, 2027
Quantum mechanics and neural networks
Abstract We demonstrate that any Euclidean-time quantum mechanical theory may be represented as a neural network (NN), ensured by the Kosambi–Karhunen–Loève theorem, mean-square path continuity, and finite two-point functions. The additional constraint of reflection positivity, which is related to unitarity, may be achieved by a number of mechanisms, such as imposing NN parameter space splitting or the Markov property. Non-differentiability of the networks is related to the appearance of non-trivial commutators. Neural networks acting on Markov processes are no longer Markov, but still reflection positive, which facilitates the definition of deep NN quantum systems. We illustrate these principles in several examples using numerical implementations, recovering classic quantum mechanical results such as Heisenberg uncertainty, non-trivial commutators, and the spectrum.
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- Award ID(s):
- 2019786
- PAR ID:
- 10677515
- Publisher / Repository:
- IOP Publishing Ltd
- Date Published:
- Journal Name:
- Machine Learning: Science and Technology
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2632-2153
- Page Range / eLocation ID:
- 015002
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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