aiqbench analysis
This is theoretical quantum physics: it shows that under local quantum errors, the late-time ensemble of projected mixed states converges to a universal distribution set by the error channel's normalized Choi state. The results are analytic for several circuit models and numerically checked in qubit circuits, so the claims are concrete but remain far from hardware. For quantum readers, the practical relevance is a possible route to characterizing noise from measurement statistics, though that link is not yet demonstrated.
Mixed State Deep Thermalization under Generic Quantum Errors
arXiv:2610.31580v1 Announce Type: new Abstract: Pure-state deep thermalization predicts that, after sufficient scrambling, projected ensembles approach universal distributions that contain information beyond the reduced density matrix. In realistic quantum systems, however, noise is unavoidable and the projected states are generally mixed. Whether mixed-state deep thermalization admits an analogous universal limiting distribution has remained unclear. Here we answer this question for quantum dynamics containing local quantum channels, i.e., errors. We show that the late-time mixed-state projected ensemble is completely determined by the normalized Choi state of the error channel and is universal, independent of the microscopic details of the underlying unitary dynamics. We establish this result analytically for dual-unitary circuits, global Haar-random dynamics, and local Haar-random circuits at large local dimension, and verify it numerically in qubit circuits and kicked Ising dynamics. In a solvable setting, we further find exponentially fast convergence to the limiting ensemble. Our results extend deep thermalization to noisy quantum dynamics and establish a direct correspondence between quantum errors and universal random mixed-state ensembles.
Abstract:Pure-state deep thermalization predicts that, after sufficient scrambling, projected ensembles approach universal distributions that contain information beyond the reduced density matrix. In realistic quantum systems, however, noise is unavoidable and the projected states are generally mixed. Whether mixed-state deep thermalization admits an analogous universal limiting distribution has remained unclear. Here we answer this question for quantum dynamics containing local quantum channels, i.e., errors. We show that the late-time mixed-state projected ensemble is completely determined by the normalized Choi state of the error channel and is universal, independent of the microscopic details of the underlying unitary dynamics. We establish this result analytically for dual-unitary circuits, global Haar-random dynamics, and local Haar-random circuits at large local dimension, and verify it numerically in qubit circuits and kicked Ising dynamics. In a solvable setting, we further find exponentially fast convergence to the limiting ensemble. Our results extend deep thermalization to noisy quantum dynamics and establish a direct correspondence between quantum errors and universal random mixed-state ensembles.
Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2610.31580 [quant-ph]
(or arXiv:2610.31580v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.31580 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 265 words
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