Imaginary components of out-of-time correlators and information scrambling for navigating the learning landscape of a quantum machine learning model

Abstract

We introduce and analytically illustrate that hitherto unexplored imaginary components of out-of-time correlators can provide unprecedented insight into the information scrambling capacity of a graph neural network. Furthermore, we demonstrate that it can be related to conventional measures of correlation like quantum mutual information and rigorously establish the inherent mathematical bounds (both upper and lower bound) jointly shared by such seemingly disparate quantities. To consolidate the geometrical ramifications of such bounds during the dynamical evolution of training we thereafter construct an emergent convex space. This newly designed space offers much surprising information including the saturation of lower bound by the trained network even for physical systems of large sizes, transference, and quantitative mirroring of spin correlation from the simulated physical system across phase boundaries as desirable features within the latent sub-units of the network (even though the latent units are directly oblivious to the simulated physical system) and the ability of the network to distinguish exotic spin connectivity(volume-law vs area law). Such an analysis demystifies the training of quantum machine learning models by unraveling how quantum information is scrambled through such a network introducing correlation surreptitiously among its constituent sub-systems and open a window into the underlying physical mechanism behind the emulative ability of the model.

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• Quantifying imaginarity in terms of pure-state imaginarity
• Phase-Sensitive Quantum Measurement without Controlled Operations
• Magnetic Phases of Spatially-Modulated Spin-1 Chains in Rydberg Excitons: Classical and Quantum Simulations
• Subsystem Information Capacity in Random Circuits and Hamiltonian Dynamics
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• Quantum-imaginarity-based quantum speed limit
• Random Projection using Random Quantum Circuits
• Imaginarity measures induced by real part states and the complementarity relations
• Analyzing the free states of one quantum resource theory as resource states of another
• Non-stabilizerness and entanglement from cat-state injection
• Analogy between Boltzmann machines and Feynman path integrals
• Out-of-time-order correlators bridge classical transport and quantum dynamics
• Measure of set imaginarity
• Experimental certification of the nonlocal advantages of quantum imaginarity