CAREER: Design and Analysis of Low-Overhead Fault-Tolerant Quantum Circuits

Quantum computers have the potential to revolutionize the paradigm of computing by offering a substantial advantage compared to classical computers for certain high-impact computational tasks. The main obstacle to unleashing the full power of quantum computers is their extreme susceptibility to noise and decoherence. Despite the significant progress in designing fault-tolerant protocols over the last two decades, the fundamental limits of the permissible noise on quantum devices and the required overhead to correct the errors are not fully understood. This project aims to develop mathematical frameworks to design and analyze low-overhead fault-tolerant quantum computing schemes. In addition, the project also explores the minimum requirements for reliable quantum computation. The multidisciplinary nature of the research provides a unique educational environment for both graduate and undergraduate students who will be trained and mentored during this project. The goal of this project is to develop mathematical models to describe error propagation in quantum circuits and use them to construct resource-efficient computing subroutines. The approach will enable the application of classical data compression and error correction codes in designing low-overhead reliable quantum computers. The developed framework will be used to understand the minimum resources required for reliable computation and to discover resource-efficient protocols by directly incorporating the hardware constraints of quantum processors. The systematic approach will provide an opportunity to perform computer-assisted search to find optimized constructions. The applications of the developed procedures to protect key fault-tolerant quantum operations such as code-switching will be investigated. The successful completion of this effort will make progress in lowering the hardware requirements to build reliable quantum processors capable of accurate large-scale quantum computation. This project is jointly funded by the Foundations of Emerging Technologies core research program in the Computing and Communication Foundations Division and the Established Program to Stimulate Competitive Research (EPSCoR). 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.