Learning quantum systems via out-of-time-order correlators

TL;DR

This paper introduces out-of-time-order correlators as a new observable to enhance the learnability of strongly-interacting quantum systems, especially under limited access or weak interactions, demonstrating robustness and exponential advantages over traditional methods.

Contribution

The work pioneers the use of out-of-time-order correlators in quantum learning, showing they improve information extraction in challenging strongly-interacting systems.

Findings

Out-of-time-order correlators improve learning in strongly-interacting systems.

They are effective under spatially-restricted access and weak interactions.

The introduced binary classification task is solvable in constant time with OTO measurements.

Abstract

Learning the properties of dynamical quantum systems underlies applications ranging from nuclear magnetic resonance spectroscopy to quantum device characterization. A central challenge in this pursuit is the learning of strongly-interacting systems, where conventional observables decay quickly in time and space, limiting the information that can be learned from their measurement. In this work, we introduce a new class of observables into the context of quantum learning -- the out-of-time-order correlator -- which we show can substantially improve the learnability of strongly-interacting systems by virtue of displaying informative physics at large times and distances. We identify two general scenarios in which out-of-time-order correlators provide a significant advantage for learning tasks in locally-interacting systems: (i) when experimental access to the system is spatially-restricted, for example via a single "probe" degree of freedom, and (ii) when one desires to characterize weak interactions whose strength is much less than the typical interaction strength. We numerically characterize these advantages across a variety of learning problems, and find that they are robust to both read-out error and decoherence. Finally, we introduce a binary classification task that can be accomplished in constant time with out-of-time-order measurements. In a companion paper, we prove that this task is exponentially hard with any adaptive learning protocol that only involves time-ordered operations.