Autonomous phase discovery

Shiyu Zhou; Yuxuan Zhang; Sebastian Wetzel; Roger Melko; Xiu-Zhe Luo

quant-phSep 27, 2026

Autonomous phase discovery

Authors: Shiyu Zhou, Yuxuan Zhang, Sebastian Wetzel, Roger Melko, Xiu-Zhe Luo

Organizations: Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada · Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA · Institute of Physics, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland · Department of Physics, Princeton University, Princeton, New Jersey, USA · Department of Physics & Astronomy, University of Waterloo, Ontario, N2L 3G1, Canada

Abstract

Understanding quantum phases of matter has long relied on physicists' intuition and mathematical tools such as symmetry and topology. Remarkably successful as these approaches have been, they provide no universal way to explore a Hamiltonian space whose organizing principle is not known in advance. In this work, we introduce a fully autonomous system combining differentiable programming and unsupervised learning for quantum phase discovery. The search evaluates ground-state data along an adaptive trajectory rather than on a predetermined parameter grid. We demonstrate the system with three different solvers and benchmark it against random sampling at equal ground-state-evaluation budgets. On a generalized cluster chain hosting up to $200$ distinct phases, the search finds up to $25$ more phases at the same budget, and matches random sampling given thirty times its budget. On a $50$ -parameter Chern insulator, it reaches sectors not obtained by the simple harmonic constructions considered here, in a family whose inverse problem remains open, while recovering all sectors found by sampling. Our results establish autonomous, gradient-driven exploration of Hamiltonian space as a practical route to discovering quantum phases without phase labels or a prescribed target phase.

Figures & tables

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

	TFIM	$\mathbb{Z}_{2}$	XXZ	cluster chain	Chern
Solver	ED	ITE ( $d\tau{=}10^{-2}$ , 150 st.)	DMRG ( $\chi{=}10$ , 10 sw.)	closed form	closed form
System	$L=10$	$2\times 3$	$L=20$	$L{=}500$ , $d{\leq}200$	$H{=}16$ , 50 couplings
Starting point	$g_{0}=-0.3,-0.5,-1.5$	$\lambda_{0}=-0.09,-0.1,-0.75$	$(\Delta_{0},h_{0}){=}(-1.5,-0.3)$	$e_{0}$ or random	mass only
AE input (dim.)	$\ket{\psi}$ ( $1024$ )	$\ket{\psi}$ ( $4096$ )	$\langle\sigma^{x,y,z}_{i}\rangle$ ( $60$ )	$g(r)$ ( $500$ )	$\hat{\mathbf{d}}(\mathbf{k})$ , $32^{2}$ ( $3072$ )
Encoder widths	$1024$ – $500$ – $d_{z}$	$4096$ – $500$ – $d_{z}$	$60$ – $20$ – $d_{z}$	$500$ – $32$ – $d_{z}$	$3072$ – $32$ – $d_{z}$
Latent dimension $d_{z}$	$10$	$30$	$15$	$16$	$16$

Appendix

Table 1: Hyperparameters and run configuration of every run in this work: the demonstrations of Sec. III and the equal-budget benchmarks of Sec. IV . The jump boost row gives the temporary learning-rate multiplier and the number of steps it is applied for; the bootstrap trigger is an EMA-smoothed gradient norm for TFIM and

\mathbb{Z}_{2}

and the maximum parameter change for XXZ, sustained over the stall window. The last three rows apply only to the long-horizon loop of Appendix C . The two benchmark families share that loop but were tuned separately, and the Chern column is the configuration returned by the successive-halving bracket.

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Discovering quantum phenomena with Interpretable Machine Learning

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Interpretable machine learning techniques are becoming essential tools for extracting physical insights from complex quantum data. We build on recent advances in variational autoencoders to demonstrate that such models can learn physically meaningful and interpretable representations from a broad class of unlabeled quantum datasets. From raw measurement data alone, the learned representation reveals rich information about the underlying structure of quantum phase spaces. We further augment the learning pipeline with symbolic methods, enabling the discovery of compact analytical descriptors that serve as order parameters for the distinct regimes emerging in the learned representations. We demonstrate the framework on experimental Rydberg-atom snapshots, classical shadows of the cluster Ising model, and hybrid discrete-continuous fermionic data, revealing previously unreported phenomena such as a corner-ordering pattern in the Rydberg arrays. These results establish a general framework for the automated and interpretable discovery of physical laws from diverse quantum datasets. All methods are available through qdisc, an open-source Python library designed to make these tools accessible to the broader community.

Abstract

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