# Machine Learning Phase Transitions with a Quantum Processor

arXiv: https://arxiv.org/abs/1906.10155 · HTML: https://mlsanity.com/paper/1906.10155/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2019.

## Built on by (most cited first, 13 of 13)

- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Entangled Datasets for Quantum Machine Learning](https://mlsanity.com/paper/2109.03400/) (2021)
- [Universal Adversarial Examples and Perturbations for Quantum Classifiers](https://mlsanity.com/paper/2102.07788/) (2021)
- [Enhancing Quantum Adversarial Robustness by Randomized Encodings](https://mlsanity.com/paper/2212.02531/) (2022)
- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [Tensor networks in machine learning](https://mlsanity.com/paper/2207.02851/) (2022)
- [Quantum Model Learning Agent: characterisation of quantum systems through machine learning](https://mlsanity.com/paper/2112.08409/) (2021)
- [A simple framework for contrastive learning phases of matter](https://mlsanity.com/paper/2205.05607/) (2022)
- [Learning to Classify Quantum Phases of Matter with a Few Measurements](https://mlsanity.com/paper/2409.05188/) (2024)
- [Quantum-machine-learning channel discrimination](https://mlsanity.com/paper/2206.09933/) (2022)
- [Multi-GPU-Enabled Hybrid Quantum-Classical Workflow in Quantum-HPC Middleware: Applications in Quantum Simulations](https://mlsanity.com/paper/2403.05828/) (2024)
- [Quantum-Enhanced Neural Contextual Bandit Algorithms](https://mlsanity.com/paper/2601.02870/) (2026)
- [Quantum Phase Recognition using Quantum Tensor Networks](https://mlsanity.com/paper/2212.06207/) (2022)

## Abstract (arXiv)

Machine learning has emerged as a promising approach to study the properties of many-body systems. Recently proposed as a tool to classify phases of matter, the approach relies on classical simulation methods-such as Monte Carlo-which are known to experience an exponential slowdown when simulating certain quantum systems. To overcome this slowdown while still leveraging machine learning, we propose a variational quantum algorithm which merges quantum simulation and quantum machine learning to classify phases of matter. Our classifier is directly fed labeled states recovered by the variational quantum eigensolver algorithm, thereby avoiding the data reading slowdown experienced in many applications of quantum enhanced machine learning. We propose families of variational ansatz states that are inspired directly by tensor networks. This allows us to use tools from tensor network theory to explain properties of the phase diagrams the presented method recovers. Finally, we propose a nearest-neighbour (checkerboard) quantum neural network. This majority vote quantum classifier is successfully trained to recognize phases of matter with 99% accuracy for the transverse field Ising model and 94% accuracy for the XXZ model. These findings suggest that our merger between quantum simulation and quantum enhanced machine learning offers a fertile ground to develop computational insights into quantum systems.