# Shallow-circuit Supervised Learning on a Quantum Processor

arXiv: https://arxiv.org/abs/2601.03235 · HTML: https://mlsanity.com/paper/2601.03235/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 6 Jan 2026.

## Builds on (most cited first, 8 of 8)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Shadows of quantum machine learning](https://mlsanity.com/paper/2306.00061/) (2023)
- [Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data](https://mlsanity.com/paper/2412.07915/) (2024)
- [Robust estimation of the intrinsic dimension of data sets with quantum cognition machine learning](https://mlsanity.com/paper/2409.12805/) (2024)
- [Quantum Cognition Machine Learning for Forecasting Chromosomal Instability](https://mlsanity.com/paper/2506.03199/) (2025)
- [Quantum Geometry of Data](https://mlsanity.com/paper/2507.21135/) (2025)

## Abstract (arXiv)

Quantum computing has long promised transformative advances in data analysis, yet practical quantum machine learning has remained elusive due to fundamental obstacles such as a steep quantum cost for the loading of classical data and poor trainability of many quantum machine learning algorithms designed for near-term quantum hardware. In this work, we show that one can overcome these obstacles by using a linear Hamiltonian-based machine learning method which provides a compact quantum representation of classical data via ground state problems for k-local Hamiltonians. We use the recent sample-based Krylov quantum diagonalization method to compute low-energy states of the data Hamiltonians, whose parameters are trained to express classical datasets through local gradients. We demonstrate the efficacy and scalability of the methods by performing experiments on benchmark datasets using up to 50 qubits of an IBM Heron quantum processor.