CIF: Medium: Iterative Quantum LDPC Decoders

University Of Arizona, Tucson AZ

Investigators

Abstract

Quantum information processing systems are far more susceptible to making errors than conventional digital computers, and error correcting is vital in protecting fragile qubits from errors. Quantum error-correction is at the heart of all applications of quantum information processing, from fault tolerant quantum computing to reconciliation in quantum key distribution, quantum sensing, and reliable optical communications. This project will contribute to the practical realization of scalable quantum computing and communications by finding structured ways of achieving the benefits afforded by quantum error-correction. This project will develop a novel class of error-correction codes and fault-tolerant decoders and apply them in architectures for quantum computing, quantum communications and networks. The project will contribute to the development of workforce skilled in quantum information processing for the growing quantum industries and quantum information programs in national laboratories. This research is an integral part of the university-wide quantum engineering initiative led by the team with a goal to establish a graduate program in quantum information science engineering at the University of Arizona. It will help the continued effort at the University of Arizona in involving under-represented students into research, whose educational experiences will be enriched by national and international collaboration. Error-correction is at the heart of all applications of quantum information processing, e.g., in realizing fault tolerant quantum computing, efficient reconciliation and privacy amplification in quantum key distribution, building fault-tolerant quantum memories for quantum repeaters used in a long distance entanglement distribution network, and for attaining quantum limits of the rate of reliable optical communications. Quantum low-density parity check (QLDPC) codes are the only known class of quantum codes in the stabilizer family that have asymptotically nonzero rates, and are an important cog in realizing scalable, fault tolerant quantum computation, but an efficient decoding solution for QLDPC codes is still lacking. In this project, the team will develop efficient and fault-tolerant decoders that employ classical-quantum messages, to harness the full potential of QLDPC codes. The approach is based on the concept of a trapping sets of quantum decoding algorithms, which allows one to characterize decoding failures combinatorially and through graph theory. This knowledge of trapping sets will be then used to develop a framework for systematic decoder design. The resulting decoder is a small fault-tolerant quantum computer built using noisy gates wherein all computations remain local at nodes, and quantum communication happens across nearest-neighbor edges on the decoding graph. The team will characterize the performance of the QLDPC codes and fault-tolerant decoders in recently developed architectures for scalable linear optical quantum computing, and coded transmission-based all-optical repeaters for long-range quantum communication. 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.