Fetching the paper…
Reading the bibliography…
Despite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive.
R. A. Fisher, On the mathematical foundations of theoretical statistics, Philos. Trans. Royal Soc. A 222
1922
Earlier work this paper cites.
C. R. Rao, Information and the accuracy attainable in the estimation of statistical parameters, Bull. Calcutta Math. Soc. 37
1945
Earlier work this paper cites.
H. Cramér, Mathematical Methods of Statistics (Princeton University Press, 1946) p. 473
1946
Earlier work this paper cites.
C. W. Helstrom, Minimum mean-squared error of estimates in quantum statistics, Phys. Lett. A 25
1967
Earlier work this paper cites.
V. Berezinskii, Destruction of Long-range Order in One-dimensional and Two-dimensional Systems having a Continuous Symmetry Group I. Classical Systems, Sov. Phys. JETP 32
1971
Earlier work this paper cites.
J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C: Solid State Phys. 6
1973
Earlier work this paper cites.
N. Chentsov, Algebraic foundation of mathematical statistics, Math. Operationsforsch. statist. 9
1978
Earlier work this paper cites.
S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Phys. Rev. Lett. 72
1994
Earlier work this paper cites.
R. Jozsa, Fidelity for mixed quantum states, J. Mod. Opt. 41
1994
Earlier work this paper cites.
J. Friedman, T. Hastie, R. Tibshirani, et al. , The Elements of Statistical Learning (Springer, 2001)
2001
Earlier work this paper cites.
G. Casella and R. L. Berger, Statistical inference , 2nd ed. (Duxbury, 2002)
2002
Earlier work this paper cites.
F. Liese and I. Vajda, On divergences and informations in statistics and information theory, IEEE Trans. Inf. Theory 52
2006
Earlier work this paper cites.
W.-L. You, Y.-W. Li, and S.-J. Gu, Fidelity, dynamic structure factor, and susceptibility in critical phenomena, Phys. Rev. E 76
2007
Earlier work this paper cites.
L. Campos Venuti and P. Zanardi, Quantum critical scaling of the geometric tensors, Phys. Rev. Lett. 99
2007
Earlier work this paper cites.
P. Zanardi, P. Giorda, and M. Cozzini, Information-theoretic differential geometry of quantum phase transitions, Phys. Rev. Lett. 99
2007
Earlier work this paper cites.
M.-F. Yang, Ground-state fidelity in one-dimensional gapless models, Phys. Rev. B 76
2007
Earlier work this paper cites.
X. Nguyen, M. J. Wainwright, and M. Jordan, Estimating divergence functionals and the likelihood ratio by penalized convex risk minimization, in Adv. Neural. Inf. Process. Syst. , Vol. 20, edited by J. Platt, D. Koller, Y. Singer, and S. Roweis (Curran Associates, Inc., 2007)
2007
Earlier work this paper cites.
D. F. Abasto, A. Hamma, and P. Zanardi, Fidelity analysis of topological quantum phase transitions, Phys. Rev. A 78
2008
Earlier work this paper cites.
S. Yang, S.-J. Gu, C.-P. Sun, and H.-Q. Lin, Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model, Phys. Rev. A 78
2008
Earlier work this paper cites.
S. Garnerone, D. Abasto, S. Haas, and P. Zanardi, Fidelity in topological quantum phases of matter, Phys. Rev. A 79
2009
Earlier work this paper cites.
S.-J. Gu, Fidelity approach to quantum phase transitions, Int. J. Mod. Phys. B 24
2010
Earlier work this paper cites.
B. Wang, M. Feng, and Z.-Q. Chen, Berezinskii-Kosterlitz-Thouless transition uncovered by the fidelity susceptibility in the 𝑋𝑋𝑍 \mathit{XXZ} model, Phys. Rev. A 81
2010
Earlier work this paper cites.
M. Prokopenko, J. T. Lizier, O. Obst, and X. R. Wang, Relating fisher information to order parameters, Phys. Rev. E 84
2011
Earlier work this paper cites.
S. Sachdev, Quantum Phase Transitions (Cambridge University Press, 2011)
2011
Earlier work this paper cites.
2012
Earlier work this paper cites.
J. Liu, H.-N. Xiong, F. Song, and X. Wang, Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks, Physica A 410
2014
Cited alongside, same era.
L. Banchi, P. Giorda, and P. Zanardi, Quantum information-geometry of dissipative quantum phase transitions, Phys. Rev. E 89
2014
Cited alongside, same era.
V. Berisha and A. O. Hero, Empirical non-parametric estimation of the Fisher information, IEEE Signal Process. Lett. 22
2014
Cited alongside, same era.
D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv:1412.6980 (2014)
2014
Cited alongside, same era.
P. Bickel and K. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics , 1st ed. (Chapman and Hall/CRC, 2015)
2015
Cited alongside, same era.
E. Greplova, A. Valenti, G. Boschung, F. Schäfer, N. Lörch, and S. D. Huber, Unsupervised identification of topological phase transitions using predictive models, New J. Phys. 22
2020
Later among the works it cites.
2020
Later among the works it cites.
M. Cerezo, A. Poremba, L. Cincio, and P. J. Coles, Variational quantum fidelity estimation, Quantum 4
2020
Later among the works it cites.
M. Jarzyna and J. Kołodyński, Geometric Approach to Quantum Statistical Inference, IEEE J. Sel. Areas Inf. Theory 1
2020
Later among the works it cites.
Q. Guan and R. J. Lewis-Swan, Identifying and harnessing dynamical phase transitions for quantum-enhanced sensing, Phys. Rev. Res. 3
2021
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
K. Macieszczak, M. Guţă, I. Lesanovsky, and J. P. Garrahan, Dynamical phase transitions as a resource for quantum enhanced metrology, Phys. Rev. A 93
2016
Cited alongside, same era.
R. Rota, F. Storme, N. Bartolo, R. Fazio, and C. Ciuti, Critical behavior of dissipative two-dimensional spin lattices, Phys. Rev. B 95
2017
Cited alongside, same era.
J. Carrasquilla and R. G. Melko, Machine learning phases of matter, Nat. Phys. 13
2017
Cited alongside, same era.
E. P. Van Nieuwenburg, Y.-H. Liu, and S. D. Huber, Learning phase transitions by confusion, Nat. Phys. 13
2017
Cited alongside, same era.
K. Ch’ng, J. Carrasquilla, R. G. Melko, and E. Khatami, Machine learning phases of strongly correlated fermions, Phys. Rev. X 7
2017
Cited alongside, same era.
P. Weinberg and M. Bukov, QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains, SciPost Phys. 2
2017
Cited alongside, same era.
N. Goldenfeld, Lectures On Phase Transitions And The Renormalization Group (CRC Press, 2018)
2018
Cited alongside, same era.
Later among the works it cites.
J. Arnold, F. Schäfer, M. Žonda, and A. U. J. Lode, Interpretable and unsupervised phase classification, Phys. Rev. Res. 3
2021
Later among the works it cites.
A. Bohrdt, S. Kim, A. Lukin, M. Rispoli, R. Schittko, M. Knap, M. Greiner, and J. Léonard, Analyzing nonequilibrium quantum states through snapshots with artificial neural networks, Phys. Rev. Lett. 127
2021
Later among the works it cites.
C. Miles, A. Bohrdt, R. Wu, C. Chiu, M. Xu, G. Ji, M. Greiner, K. Q. Weinberger, E. Demler, and E.-A. Kim, Correlator convolutional neural networks as an interpretable architecture for image-like quantum matter data, Nat. Commun. 12
2021
Later among the works it cites.
K. C. Tan and T. Volkoff, Variational quantum algorithms to estimate rank, quantum entropies, fidelity, and Fisher information via purity minimization, Phys. Rev. Res. 3
2021
Later among the works it cites.
J. Singh, M. S. Scheurer, and V. Arora, Conditional generative models for sampling and phase transition indication in spin systems, SciPost Phys. 11
2021
Later among the works it cites.
2022
Later among the works it cites.
J. Arnold and F. Schäfer, Replacing neural networks by optimal analytical predictors for the detection of phase transitions, Phys. Rev. X 12
2022
Later among the works it cites.
D. Zvyagintseva, H. Sigurdsson, V. Kozin, I. Iorsh, I. Shelykh, V. Ulyantsev, and O. Kyriienko, Machine learning of phase transitions in nonlinear polariton lattices, Commun. Phys. 5
2022
Later among the works it cites.
G. O. Alves and G. T. Landi, Bayesian estimation for collisional thermometry, Phys. Rev. A 105
2022
Later among the works it cites.
N. Maskara, M. Buchhold, M. Endres, and E. van Nieuwenburg, Learning algorithm reflecting universal scaling behavior near phase transitions, Phys. Rev. Res. 4
2022
Later among the works it cites.
T. T. Duy, L. V. Nguyen, V.-D. Nguyen, N. L. Trung, and K. Abed-Meraim, Fisher information neural estimation, in 2022 30th European Signal Processing Conference (EUSIPCO) (2022) pp. 2111–2115
2022
Later among the works it cites.
J. L. Beckey, M. Cerezo, A. Sone, and P. J. Coles, Variational quantum algorithm for estimating the quantum Fisher information, Phys. Rev. Res. 4
2022
Later among the works it cites.
A. Fujiwara, Hommage to Chentsov’s theorem, Info. Geo. , 1 (2022)
2022
Later among the works it cites.
L. Zhou, J. Kong, Z. Lan, and W. Zhang, Dynamical quantum phase transitions in a spinor Bose-Einstein condensate and criticality enhanced quantum sensing, Phys. Rev. Res. 5
2023
Closest in time.
2023
Closest in time.
W.-C. Guo and L. He, Learning phase transitions from regression uncertainty: A new regression-based machine learning approach for automated detection of phases of matter, New Journal of Physics (2023)
2023
Closest in time.
H. Schlömer and A. Bohrdt, Fluctuation based interpretable analysis scheme for quantum many-body snapshots, SciPost Phys. 15
2023
Closest in time.
W.-c. Guo, B.-q. Ai, and L. He, Reveal flocking phase transition of self-propelled active particles by machine learning regression uncertainty, Acta Phys. Sin. 10.7498/aps.72.20230896 (2023)
2023
Closest in time.
2023
Closest in time.