YIP Quantum Information Phases in Space-Time
Abstract
The past century has seen remarkable progress in classifying and understanding exotic phases of many-body quantum matter, leading to groundbreaking technological advancements in classical computing, communication, and sensing. Traditionally, the characterization of phases relied on studying the asymptotic behavior of spatial correlation functions in equilibrium states at low temperatures. However, in recent years, the advent of quantum simulators with unprecedented experimental capabilities for investigating quantum coherent dynamics has opened up a vast new frontier for the study quantum matter in highly-excited and far-from-equilibrium regimes. Remarkably, it has been found that the non-equilibrium many-body problem can also display rich universality, and recent discoveries like quantum scars and time-crystals have revealed qualitatively distinct dynamical phenomena with no equilibrium analog. The proposed research aims to develop an understanding of universal phases of non-equilibrium many-body quantum processes which, in full generality, are composed of unitary dynamics, controlled measurements, uncontrolled decoherence due to interactions with an environment, andthe possibility for interactive dialog between the quantum system and a classical observer for control and feedback. This significantly pushes the frontier of the study of quantum dynamics which, until recently, was mostly focused on unitary evolutions. However,measurements are fundamental in quantum theory and must be incorporated to develop a full understanding of quantum dynamics. Controlled measurements are essential for canonical information theoretic processes such as error-correction, while uncontrolled decoherence is the central challenge for modern quantum devices. This proposal explores the interplay of these ingredients with the goal of understanding dynamical phases of quantum processes through the study of quantum correlations in space-time. By causing wavefunction collapse, measurements can enable extraordinary phenomena such as teleportation, thereby breaking the "arrow of time" that is intrinsic to unitary evolution. Phases of quantum processes thereby transcend conventional paradigms for characterizing equilibrium phases, and instead must be described by the emergent organization of quantum information in space-time. Indeed, a paradigmatic recent example showed that tuning the rate of controlled local measurements in random circuit dynamics can drive a phase transition in the entanglement and teleportation properties of the dynamics. We will develop a much fuller understanding by formulating and studying new information theoretic order parameters for quantum processes, and their utility for preparing highly-entangled states and for devising novel error correcting codes. Progress on the directions discussed in the proposal will be achieved using a variety of innovative theoretical and numerical techniques. The proposed advances are synergistic with key DoD goals of understanding, controlling, and exploiting quantum phenomena for developing novel capabilities for computing, communication and simulation. In particular, the proposed research for understanding quantum information phases in space-time is not just important for fundamental theory, but also promises new approaches for controlling and preparing highly-entangled states, for characterizing dynamical regimes that yield a computational quantum advantage, and for devising new error correcting codes which exploit dynamical correlations. Approved for Public Release
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 24, 2024
- Source ID
- N000142412098
Entities
People
- Vedika Khemani
Organizations
- Office of Naval Research
- Stanford University
- United States Navy