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
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
Z2
XXZ
cluster chain
Chern
Solver
ED
ITE ( dτ=10−2 , 150 st.)
DMRG ( χ=10 , 10 sw.)
closed form
closed form
System
L=10
2×3
L=20
L=500 , d≤200
H=16 , 50 couplings
Starting point
g0=−0.3,−0.5,−1.5
λ0=−0.09,−0.1,−0.75
(Δ0,h0)=(−1.5,−0.3)
e0 or random
mass only
AE input (dim.)
∣ψ⟩ ( 1024 )
∣ψ⟩ ( 4096 )
⟨σix,y,z⟩ ( 60 )
g(r) ( 500 )
d^(k) , 322 ( 3072 )
Encoder widths
1024 – 500 – dz
4096 – 500 – dz
60 – 20 – dz
500 – 32 – dz
3072 – 32 – dz
Latent dimension dz
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 Z2 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.
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.
Paulin de Schoulepnikoff, Hendrik Poulsen Nautrup, Hans J. Briegel +1
University of Innsbruck, Department for Theoretical Physics, Technikerstr. 21a, A-6020 Innsbruck, Austria
Rare-regime discovery in parameterized dynamical systems is an active-search problem: find one verified parameter at which a scientifically defined qualitative threshold is crossed, even when acceptable candidates are rare, nonconvex, or fragmented. We introduce Quantum-Classical Phase-space and Stability-Threshold Search (QC-PHAST), an evidence-gated decision protocol and query-accounting framework for finite candidate libraries. A candidate induces a dynamical object, simulator-derived criticality score, and verified first-hit predicate. Scientific metadata and charged pilot evidence are used to assess whether equation-aware search, scalar-score active search, predicate-only search, or only a query-model comparison is admissible. The quantum row is the inherited Grover/Boyer--Brassard--Hoyer--Tapp (BBHT) unknown-M marked-set query reference; it is not a new quantum-search theorem, materialized circuit, or hardware-speedup claim. The result is a regime map. Direct boundary constructions, geometry controls, online simulator loops, and learned-label accounting further identify when classical structure, false positives, calibration cost, or state preparation erases the query-model margin. QC-PHAST is therefore an auditable protocol for deciding when a finite-pool marked-set reference is informative and when classical or resource-aware search should dominate.
Harsh Milind Tirhekar, Chandrajit Bajaj
Department of Computer Science College of Natural Sciences The University of Texas at Austin Austin, TX, USA · Department of Computer Science Oden Institute for Computational Engineering and Sciences The University of Texas at Austin Austin, TX, USA
Characterizing quantum topological phases requires measuring non-local string order parameters, demanding access to the full system, which is often experimentally unfeasible. In this work, we introduce a data-efficient supervised learning framework that circumvents this limitation by recognizing quantum phases from small subsystems. Our protocol utilizes a quantum kernel constructed from the reduced density matrices of these subsystems, which can be efficiently estimated experimentally. We benchmark our framework with the classification of the phase diagrams of two spin models on one-dimensional lattices, namely the generalized cluster-Ising spin-1/2 chain and the anisotropic Haldane spin-1 chain. Remarkably, our approach achieves high accuracy in phase classification when operations are limited to as few as one to four sites, and it also generalizes to longer chains even when trained on moderate system sizes. These findings demonstrate that local reduced density matrices preserve vital signatures of global topological phases, offering a practical route to characterize rich phase diagrams of quantum many-body systems.
Department of Physics and Astronomy, University of Florence, via G. Sansone 1, I-50019 Sesto Fiorentino (FI), Italy · Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom · INFN Sezione di Firenze, via G. Sansone 1, I-50019, Sesto Fiorentino (FI), Italy +2