Understanding Quantum Chaos from the Perspective of Quantum Information Scrambling

Quantum technology, such as quantum computation and quantum simulation, has become a new driving force for our society. Google recently confirmed quantum supremacy in a 53-qubit system [Nature 574, 505 (2019)], demonstrating the clear advantages of quantum computers over classical computers. At the heart of these technological advances is quantum information science. Due to its importance, the 2022 Nobel Prize in Physics is awarded to Alain Aspect, John Clauser, and Anton Zeilinger “for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science.” In order to manipulate quantum information in a device, we must understand its behavior in generic chaotic quantum many-body systems. One interesting feature of such systems is that they are expected to thermalize, which results in the effective loss of quantum information. Such a process is frequently referred to as quantum information scrambling. Although substantial efforts have been devoted to understanding this subject, a unifying understanding of how quantum information scrambling occurs is still lacking. In this proposal, we propose to tackle this problem using a tool called the out-of-time-ordered correlator (OTOC), which can potentially serve as a universal diagnostic to understand quantum information scrambling in a chaotic quantum many-body system. We will study this problem from two complementary angles. First, we will focus on physical systems with unique microscopic details. We have laid out two tasks in this direction: (A) To study OTOC in a Wannier-Stark lattice and (B) To study OTOC in systems with weak ergodicity breaking. We will analyze how unique microscopic details affect quantum information scrambling. Second, we will study models defined on unitary quantum circuits. The advantage of this approach is that we can focus on extracting universal features of quantum chaos without worrying about the details of specific systems. We have laid out one task in this direction: (C) To study OTOC and the spectral form factor in unitary quantum circuits. By combining research output from these two complementary angles, our proposal will produce fundamental new insights into the mechanism of quantum information scrambling in a generic chaotic quantum many-body system. These new insights will, in turn, contribute to the design of better quantum information processing devices.