# When Quantum Meets AI: Quantum Methods for Machine Learning and Machine Learning Methods for Quantum Systems

arXiv: https://arxiv.org/abs/2609.25641 · HTML: https://mlsanity.com/paper/2609.25641/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 156 references that are in the map.
- First posted on arXiv 22 Sep 2026.

## Builds on (most cited first, 21 of 21)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [Predicting the Generalization Gap in Deep Networks with Margin Distributions](https://mlsanity.com/paper/1810.00113/) (2018)
- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [PennyLane: Automatic differentiation of hybrid quantum-classical computations](https://mlsanity.com/paper/1811.04968/) (2018)
- [qecGPT: decoding Quantum Error-correcting Codes with Generative Pre-trained Transformers](https://mlsanity.com/paper/2307.09025/) (2023)
- [Information-theoretic generalization bounds for learning from quantum data](https://mlsanity.com/paper/2311.05529/) (2023)
- [Understanding Generalization in Quantum Machine Learning with Margins](https://mlsanity.com/paper/2411.06919/) (2024)
- [The END: An Equivariant Neural Decoder for Quantum Error Correction](https://mlsanity.com/paper/2304.07362/) (2023)
- [Scalable Neural Decoders for Practical Real-Time Quantum Error Correction](https://mlsanity.com/paper/2510.22724/) (2025)
- [Machine Learning Approaches to Decoding Topological Quantum Codes](https://mlsanity.com/paper/2608.15760/) (2026)
- [Stochastic Reconfiguration as Statistical Filtering for Overparameterized Neural Quantum States](https://mlsanity.com/paper/2609.23334/) (2026)

## Abstract (arXiv)

This thesis studies the intersection of quantum computing and artificial intelligence in two directions: quantum methods for machine learning and machine learning methods for quantum systems. For quantum machine learning, Neural Quantum Embedding learns data representations that increase the trace distance between embedded class ensembles, lowering an embedding-dependent bound on empirical risk and improving classification on noisy quantum hardware. A training objective based on the Hilbert-Schmidt inner product extends this approach to deterministic quantum computation with one qubit (DQC1) and is demonstrated on an NMR quantum processor. A margin-based generalization analysis then connects quantum neural network performance to quantum state discrimination. In the studied benchmarks, margin distributions predict generalization more reliably than parameter-count metrics. For quantum systems, a Mamba-based neural decoder for surface codes matches a reproduced Transformer baseline in memory experiments while reducing inference-cost scaling from quartic to quadratic in code distance. Under an explicit decoder-induced-noise model, it achieves lower logical error rates and a higher effective threshold. For neural quantum states, stochastic reconfiguration is interpreted as tangent-space ridge regression, with its diagonal shift controlling the bias-variance trade-off under finite Monte Carlo sampling. Multi-shift stochastic reconfiguration reduces checkpoint-local validation residuals and update variance relative to fixed-shift SR, at additional computational cost. Together, these contributions show how learned representations, statistical control, and hardware constraints shape the exchange between quantum computing and machine learning.