# Toward Physically Realizable Quantum Neural Networks

arXiv: https://arxiv.org/abs/2203.12092 · HTML: https://mlsanity.com/paper/2203.12092/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 22 Mar 2022.

## Builds on (most cited first, 7 of 7)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Advances in Quantum Deep Learning: An Overview](https://mlsanity.com/paper/2005.04316/) (2020)
- [VSQL: Variational Shadow Quantum Learning for Classification](https://mlsanity.com/paper/2012.08288/) (2020)
- [Universal discriminative quantum neural networks](https://mlsanity.com/paper/1805.08654/) (2018)
- [Transforming Bell's Inequalities into State Classifiers with Machine Learning](https://mlsanity.com/paper/1705.00813/) (2017)
- [A Theoretical Framework for Learning from Quantum Data](https://mlsanity.com/paper/2107.06406/) (2021)

## Built on by (most cited first, 8 of 8)

- [QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning](https://mlsanity.com/paper/2211.01365/) (2022)
- [SLIQ: Quantum Image Similarity Networks on Noisy Quantum Computers](https://mlsanity.com/paper/2309.15259/) (2023)
- [Expressibility-Enhancing Strategies for Quantum Neural Networks](https://mlsanity.com/paper/2211.12670/) (2022)
- [Efficient Gradient Estimation for Parameterized Quantum Systems with Lie Algebraic Symmetries](https://mlsanity.com/paper/2404.05108/) (2024)
- [Quantum Natural Stochastic Pairwise Coordinate Descent](https://mlsanity.com/paper/2407.13858/) (2024)
- [Fat Shattering, Joint Measurability, and PAC Learnability of POVM Hypothesis Classes](https://mlsanity.com/paper/2308.12304/) (2023)
- [New Bounds on Quantum Sample Complexity of Measurement Classes](https://mlsanity.com/paper/2408.12683/) (2024)
- [Towards Explainable Quantum AI: Informing the Encoder Selection of Quantum Neural Networks via Visualization](https://mlsanity.com/paper/2512.14181/) (2025)

## Abstract (arXiv)

There has been significant recent interest in quantum neural networks (QNNs), along with their applications in diverse domains. Current solutions for QNNs pose significant challenges concerning their scalability, ensuring that the postulates of quantum mechanics are satisfied and that the networks are physically realizable. The exponential state space of QNNs poses challenges for the scalability of training procedures. The no-cloning principle prohibits making multiple copies of training samples, and the measurement postulates lead to non-deterministic loss functions. Consequently, the physical realizability and efficiency of existing approaches that rely on repeated measurement of several copies of each sample for training QNNs are unclear. This paper presents a new model for QNNs that relies on band-limited Fourier expansions of transfer functions of quantum perceptrons (QPs) to design scalable training procedures. This training procedure is augmented with a randomized quantum stochastic gradient descent technique that eliminates the need for sample replication. We show that this training procedure converges to the true minima in expectation, even in the presence of non-determinism due to quantum measurement. Our solution has a number of important benefits: (i) using QPs with concentrated Fourier power spectrum, we show that the training procedure for QNNs can be made scalable; (ii) it eliminates the need for resampling, thus staying consistent with the no-cloning rule; and (iii) enhanced data efficiency for the overall training process since each data sample is processed once per epoch. We present a detailed theoretical foundation for our models and methods' scalability, accuracy, and data efficiency. We also validate the utility of our approach through a series of numerical experiments.