# From Classical to Quantum: Extending Prometheus for Unsupervised Discovery of Phase Transitions in Three Dimensions and Quantum Systems

arXiv: https://arxiv.org/abs/2602.14928 · HTML: https://mlsanity.com/paper/2602.14928/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 31 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Builds on (most cited first, 4 of 4)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Discovering Phase Transitions with Unsupervised Learning](https://mlsanity.com/paper/1606.00318/) (2016)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Learning hard quantum distributions with variational autoencoders](https://mlsanity.com/paper/1710.00725/) (2017)

## Abstract (arXiv)

We extend the Prometheus framework for unsupervised phase transition discovery from two-dimensional classical systems to three-dimensional classical systems and quantum many-body systems. Building upon preliminary observations from a 2D Ising model student abstract [Yee et al., 2026], we address two fundamental questions: (1) Does the framework scale to higher dimensions where exact solutions are unavailable? (2) Can it generalize to quantum phase transitions driven by quantum fluctuations rather than thermal fluctuations? For the 3D Ising model on lattices up to L=32, we achieve critical temperature detection within 0.01% of literature values (Tc/J = 4.511 ± 0.005) and extract critical exponents with ≥70% accuracy, with statistical analysis correctly identifying the 3D Ising universality class (p = 0.72). For quantum systems, we develop quantum-aware VAE (Q-VAE) architectures operating on complex-valued wavefunctions with fidelity-based loss functions, achieving 2% accuracy in quantum critical point detection for the transverse field Ising model. For the disordered TFIM, we perform a consistency check of activated dynamical scaling ln xi ~ |h - hc|-psi, extracting tunneling exponent psi = 0.48 ± 0.08 consistent with theoretical predictions (psi = 0.5, Deltachi2 = 12.3, p < 0.001). This demonstrates that unsupervised learning can identify qualitatively different types of critical behavior, serving as a consistency check on known IRFP physics.