Measurement-induced criticality as a data-structure transition
Xhek Turkeshi
Abstract
We employ unsupervised learning tools to identify the dynamical phases and their measurement-induced transitions in quantum systems subject to the combined action of unitary evolution and stochastic local measurements. Specifically, we show that the principal component analysis and the intrinsic dimension estimation provide order parameters that directly locate the transition and the critical exponents in the classical encoding data space. Finally, we test our approach on stabilizer circuits as proof of principle, finding robust agreement with previous studies.
Topics & Concepts
CriticalityUnitary stateDimension (graph theory)Statistical physicsDynamical systems theoryComputer scienceAction (physics)Space (punctuation)Critical exponentPrincipal component analysisQuantumEncoding (memory)MathematicsTheoretical computer scienceAlgorithmPhysicsArtificial intelligenceQuantum mechanicsPhase transitionPure mathematicsPolitical scienceLawNuclear physicsOperating systemProtein Structure and DynamicsQuantum many-body systemsStatistical Mechanics and Entropy