CAREER: Unlocking New Phases of Quantum Matter with Quantum Error-Correction

About This Grant

NONTECHNICAL SUMMARY Advances in quantum technologies and in our understanding of fundamental quantum phenomena are increasingly driven by synergies between two key areas of theoretical science. The first, quantum information theory, explores how quantum mechanics can enhance the storage, transmission, and processing of information, while the second, quantum many-body physics, investigates the collective behavior that can emerge in systems of many interacting quantum particles. Important developments in both fields often involve a deepening understanding of quantum entanglement, a correlation between particles which classical physics is unable to describe. Recent breakthroughs in both disciplines—new techniques for protecting quantum information and fresh insights into how complex quantum systems evolve—present an opportunity for renewed interdisciplinary focus. This project will aim to discover and characterize new phases of quantum matter that emerge from the synergy of these developments, and that may offer novel ways of storing and protecting information. Unlike traditional phases of matter, which are characterized by how particles are arranged or locally-correlated, these phases are defined by the way that their collective quantum entanglement is organized. This research has the potential to both advance an understanding of fundamental phenomena and enable the development of future quantum technologies. This research will be combined with the training of undergraduate and graduate student researchers in quantum science, an area of high national priority. The PI will partner with the Transfer Student Center (TSC) at UCSB in order to provide a pedagogical lecture series annually, with the goal of recruiting undergraduate transfer students to participate in the research. This initiative will provide students the necessary skills to begin academic research or to participate in industry efforts in quantum science. TECHNICAL SUMMARY This research project will use tools from the study of random quantum circuit evolution and from the theory of quantum codes, in order to (i) characterize novel zero-temperature phases of quantum matter which are intimately related to recently-discovered quantum low-depth parity-check codes, (ii) elucidate the universal entanglement properties of near-equilibrium, mixed-states of quantum many-body systems, and (iii) develop an understanding of regimes of far-from-equilibrium quantum many-body evolution which naturally act as emergent quantum codes. This project will advance our understanding of universal phenomena in quantum matter and strategies for quantum error-correction by bridging developments in the theory of quantum codes and quantum many-body dynamics. Quantum error-correction as a dynamical process will be used as a new paradigm in order to understand the entanglement properties of near-equilibrium mixed-states of quantum matter, and to identify universal phenomena that demarcate phases of mixed many-body states. Studies of far-from-equilibrium quantum dynamics will be used to identify error-correcting phases of matter in which open quantum dynamics acts as a robust, emergent quantum code even in the absence of feedback. Deep connections between random quantum dynamics and statistical mechanics will be used to uncover emergent quantum codes in quantum many-body evolution with measurements in higher spatial dimensions. This research will be combined with the training of undergraduate and graduate student researchers in quantum science, an area of high national priority. The PI will partner with the Transfer Student Center at UCSB in order to provide a pedagogical lecture series, with the goal of recruiting undergraduate transfer students to participate in the proposed work. This initiative will provide students the necessary skills to begin academic research or to participate in industry efforts in quantum science. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.