Hybrid-Variable Topological Codes: Fundamentals and Prospective Physical Implementations

Protecting fragile quantum information from environmental noise is a central challenge in the development of scalable and transformative quantum technologies. Topological quantum error correction (QEC) provides a powerful framework for addressing this challenge by leveraging the principles of topology to suppress errors in quantum information stored in large-scale quantum systems. Most existing topological QEC architectures are based solely on digital quantum systems. However, the finite and discrete nature of digital quantum degrees of freedom imposes limitations on their flexibility, computational power, and efficiency. This project seeks to overcome these limitations by extending topological QEC to hybrid systems that combine the merits of both digital and analog quantum variables. The goal is to develop more flexible approaches to fault-tolerant quantum information storage and more efficient methods for robust quantum information processing beyond purely digital architectures. The proposed research will advance fundamental knowledge at the intersection of quantum information science and quantum many-body physics. It will also contribute to the progress of science by strengthening the future quantum workforce through rich interdisciplinary training for students. This project will advance topological QEC in hybrid-variable (HV) systems through three coordinated thrusts. The first thrust will develop new classes of two-dimensional HV topological quantum codes using analytical frameworks based on anyon condensation and symmetry gauging. The objective is to achieve greater flexibility and enhanced computational capabilities compared to architectures built solely from either digital or analog quantum variables. These developments will also introduce new models that broaden the landscape of synthetic topological quantum matter. The second thrust will develop new protocols that leverage analog quantum variables to improve the efficiency of quantum operations required for realizing existing digital QEC architectures, such as topological QEC codes based on string-net condensation that support universal quantum computation. The third thrust will translate these new models and protocols into operations native to realistic quantum platforms based on circuit quantum electrodynamics, providing potential roadmaps toward their implementation on scalable quantum devices. Together, these three thrusts aim to establish a new framework for HV topological quantum error correction and to develop new approaches for protecting and processing quantum information in scalable HV quantum systems. 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. NSF Award ID: 2609907 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Chao-Ming Jian | Institution: Cornell University, ITHACA, NY | Award Amount: $437,479 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2609907 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2609907.html