# Natural Quantization of Neural Networks

arXiv: https://arxiv.org/abs/2503.15482 · HTML: https://mlsanity.com/paper/2503.15482/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 6 references that are in the map.
- First posted on arXiv 19 Mar 2025.

## Builds on (most cited first, 3 of 3)

- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Techniques for Learning Binary Stochastic Feedforward Neural Networks](https://mlsanity.com/paper/1406.2989/) (2014)
- [Neural Networks as Spin Models: From Glass to Hidden Order Through Training](https://mlsanity.com/paper/2408.06421/) (2024)

## Built on by (most cited first, 3 of 3)

- [Fermi-Dirac machines as quantizations of neurons](https://mlsanity.com/paper/2605.24386/) (2026)
- [Benchmarking a Tunable Quantum Neural Network on Trapped-Ion and Superconducting Hardware](https://mlsanity.com/paper/2507.21222/) (2025)
- [Canonical quantization of neurons](https://mlsanity.com/paper/2607.05000/) (2026)

## Abstract (arXiv)

We propose a natural quantization of a standard neural network, where the neurons correspond to qubits and the activation functions are implemented via quantum gates and measurements. The simplest quantized neural network corresponds to applying single-qubit rotations, with the rotation angles being dependent on the weights and measurement outcomes of the previous layer. This realization has the advantage of being smoothly tunable from the purely classical limit with no quantum uncertainty (thereby reproducing the classical neural network exactly) to a quantum case, where superpositions introduce an intrinsic uncertainty in the network. We benchmark this architecture on a subset of the standard MNIST dataset and find a regime of "quantum advantage," where the validation error rate in the quantum realization is smaller than that in the classical model. We also consider another approach where quantumness is introduced via weak measurements of ancilla qubits entangled with the neuron qubits. This quantum neural network also allows for smooth tuning of the degree of quantumness by controlling an entanglement angle, g, with g=fracπ 2 replicating the classical regime. We find that validation error is also minimized within the quantum regime in this approach. We also observe a quantum transition, with sharp loss of the quantum network's ability to learn at a critical point gc. The proposed quantum neural networks are readily realizable in present-day quantum computers on commercial datasets.