APA 7: TWs Editor. (2023, November 24). Quantum Information Scrambling in Open Systems: A General Description. PerEXP Teamworks. [News Link]
In open systems, where there is an exchange of both energy and matter with their surroundings, scrambling is subject to various additional factors such as noise and errors. Although the impacts of these additional influences are well-documented, contributing, for instance, to decoherence, their specific effects on the process of scrambling remain inadequately comprehended.
A novel framework has been presented by researchers from the University of California Berkeley (UC Berkeley) and Harvard University. Published in Physical Review Letters, this framework offers a universal perspective on the mechanisms behind information scrambling in open quantum systems. The framework provides a notably straightforward viewpoint for comprehending and modeling the propagation of errors within an open quantum system. Furthermore, it holds promise for elucidating previously perplexing observations recorded in magnetic resonance experiments.
Thomas Schuster, one of the researchers involved in the study, shared that he and Norm, presumably a collaborator, have previously collaborated on various projects centered around quantum information scrambling.
Thomas Schuster explained that in their previous collaborative works, they explored aspects such as measuring scrambling and understanding the potential applications of scrambling. Throughout these projects, a recurring question revolved around how scrambling is influenced by errors, specifically in the context of “open-system” dynamics inherent in real-life experiments. Despite recognizing the significance of this question, they lacked a comprehensive framework to provide satisfactory answers.
During their investigation into this question, Schuster and Yao recognized the potential utility of adopting an experimental perspective. This insight ultimately became the driving force behind their recent study.
Schuster elaborated on the consideration of errors in open-system dynamics, emphasizing the need to understand how the system is perturbed by these errors and the impact on experimental outcomes. The notion that the sensitivity of an experiment to errors is linked to the process of information scrambling guided their approach. They endeavored to refine this connection between errors and scrambling, examining its specific implications for physical systems and experiments that are of interest.
In the recent study by Schuster and Yao, a crucial concept is that information scrambling within an open system is not heavily reliant on the specific microscopic nature of the errors. Instead, the determining factor lies in how these errors influence the “operator size distributions,” which characterize the complexity of the operator under time evolution.
Schuster clarified that the dynamics of the operator size distribution play a pivotal role in dictating the precise spread of errors. In simpler terms, this is encapsulated in a set of two coupled differential equations. The input for these equations is the alteration in the distribution of operator sizes, while the output can be envisioned as a precise prediction of how errors propagate within the system.
Although earlier research had provided glimpses of this connection, Schuster and Yao were the first to articulate it clearly and precisely. Through their formulation, they discovered that the relationship between errors and scrambling is more nuanced than previously anticipated.
In their study, Schuster and Yao uncovered a novel finding: errors not only influence the system’s response to perturbations but also alter the behavior of information scrambling. This introduces an intriguing interplay between errors and scrambling, as elucidated by the aforementioned equations. The outcome of this interplay becomes a distinctive characterization of the dynamics, offering predictions for various properties of experiments.
The framework developed by Schuster and Yao holds significant promise, especially in experiments involving “Ergodic” many-body dynamics. Further exploration and validation of this framework in future studies could yield valuable insights and applications.
In the course of their research, Schuster and Yao made a noteworthy discovery: their framework is not only applicable to their original focus but also extends to a substantial class of experiments known as the “Loschmidt echo.” This includes experiments of interest to the nuclear magnetic resonance (NMR) and quantum chaos communities, with historical roots dating back to Josef Loschmidt and the foundation of thermodynamics in the 1800s.
Despite advancements in experimental techniques related to the Loschmidt echo, which have been particularly notable in quantum simulation experiments and solid-state magnetic resonance studies, deciphering these signals, especially in the context of interacting Hamiltonians, remains a persistent challenge.
In the realm of experimental investigations involving the Loschmidt echo, researchers traditionally employed various functional forms (such as Gaussians, exponentials, or sigmoids) to fit their data. However, there was a lack of a comprehensive explanation for why a specific experiment exhibited one functional form over another. In the early 2000s, a framework emerged for describing the Loschmidt echo in few-body quantum systems, but the application of this framework to many-body systems has remained an unanswered question. The researchers believe that their newly proposed framework may offer insights into addressing this lingering question.
Beyond elucidating the dynamics of error propagation in open many-body quantum systems, the recent study also implies that data obtained from Loschmidt echo experiments may harbor more information than initially apparent.
Schuster stated that the functional form of the Loschmidt echo is shaped by the interplay between errors and operator size distribution dynamics. He expressed confidence in this assertion based on numerical studies of toy models. Future work aims to conduct a more detailed analysis of Loschmidt echo experimental data to substantiate the applicability of the framework in real-world scenarios. Indications strongly suggest its relevance, an aspect that Schuster finds particularly exciting.
In the future, Schuster and Yao intend to extend their novel framework to various experiments and delve into the ramifications of their findings for the classical simulation of open quantum systems.
Yao expressed curiosity about the potential insights their understanding of information spreading in open systems might offer regarding the harnessing of quantum advantage. Additionally, he is interested in exploring whether this understanding could lead to the design of new algorithms for the efficient simulation of open quantum systems.
Resources
- ONLINE NEWS Fadelli, I. & Phys.org. (2023, November 23). A universal framework describing the scrambling of quantum information in open systems. Phys.org. [Phys.org]
- JOURNAL Schuster, T., & Yao, N. Y. (2023). Operator growth in open quantum systems. Physical Review Letters, 131(16). [Physical Review Letters]
