Machine learning-inspired techniques have emerged as a new paradigm for analysis of phase transitions in quantum matter. In this work, we introduce a supervised learning algorithm for studying critical phenomena from measurement data, which is based on iteratively training convolutional networks of increasing complexity, and test it on the transverse field Ising chain and q=6 Potts model. At the continuous Ising transition, we identify scaling behavior in the classification accuracy, from which we infer a characteristic classification length scale. It displays a power-law divergence at the critical point, with a scaling exponent that matches with the diverging correlation length. Our algorithm correctly identifies the thermodynamic phase of the system and extracts scaling behavior from projective measurements, independently of the basis in which the measurements are performed. Furthermore, we show the classification length scale is absent for the $q=6$ Potts model, which has a first order transition and thus lacks a divergent correlation length. The main intuition underlying our finding is that, for measurement patches of sizes smaller than the correlation length, the system appears to be at the critical point, and therefore the algorithm cannot identify the phase from which the data was drawn.
Quantum critical dynamics and emergent universality in decoherent digital quantum processors
Leibniz Universität Hannover（汉诺威莱布尼茨大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；IBM Quantum, IBM T.J. Watson Research Center（IBM量子，IBM T.J.沃森研究中心）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）
Emergent dynamical scaling in the inviscid limit of 3D stochastic Navier-Stokes equation with thermal noise
Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS, LPMMC（法国国家科学研究中心，分子与材料物理实验室）；Laboratoire de Physique de l’Ecole Normale Supérieure, CNRS, PSL Research University, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，法国国家科学研究中心，PSL研究大学，索邦大学，巴黎西岱大学）
Kinetic Turing Instability and Emergent Spectral Scaling in Chiral Active Turbulence
The European Space Agency Centre for Earth Observation（欧洲空间局地球观测中心）；Department of Physics and Engineering Physics, University of Saskatchewan（萨斯喀彻温大学物理与工程物理系）
Universal scaling of spatially extended zero modes in inhomogeneous SSH chains
Laboratoire d’Annecy de Physique Théorique (LAPTh), CNRS, Université Savoie Mont-Blanc（萨瓦蒙布朗大学）；Institut Denis-Poisson, CNRS, Université de Tours–Université d’Orléans（图尔大学与奥尔良大学）；Centre de Recherches Mathématiques, Université de Montréal（蒙特利尔大学）；Département de Physique, Université de Montréal（蒙特利尔大学）
Emergent criticality and universality class of spin and charge density wave transitions of two-component lattice Bose gases in optical cavities at finite temperature
Breakdown of Emergent Chiral Order and Defect Chaos in Nonreciprocal Flocks
Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS–Université de Montpellier（夏尔·库隆实验室）；Université de Montpellier（蒙彼利埃大学）
