FET: Small: Decoding Quantum Error-Correcting Codes for Quantum Computing and Communication

University Of Southern California, Los Angeles CA

Investigators

Abstract

Quantum computers promise to solve many difficult computational tasks that strain the abilities of ordinary (classical) computers, especially in simulating quantum-mechanical systems and finding optimal solutions to a variety of mathematical problems. However, building large-scale quantum computers requires overcoming the challenge of decoherence, or quantum noise. The general answer to this is known: quantum error correction, to achieve fault-tolerant quantum computation. The current generation of noisy, intermediate scale quantum (NISQ) processors are too small and noisy to take real advantage of quantum error correction (QEC), but as they grow in size and improve in quality, this will soon become possible. Fully fault-tolerant quantum computing (FTQC) is very demanding; but some elements of fault-tolerance should be possible in the next few years. This project aims to develop methods of fault-tolerant quantum computation that will be practical in near-term machines. The approach uses quantum teleportation to process quantum bits (qubits) stored in efficient quantum codes that protect them against decoherence. his award will support Ph.D. students working towards their degrees, and will enrich the broad educational efforts at the University of Southern California. These efforts now include not only faculty, postdocs and Ph.D. students, but master's students in the MS program in Quantum Information Science, and a growing number of undergraduate students. This project will build upon an approach based on encoding logical qubits in multi-qubit block codes with high rates. In the very near term it will be possible to use quantum error-detecting codes that encode n–2 logical qubits in n physical qubits, with a universal set of encoded gates. Such a scheme cannot be fully fault-tolerant, but it can be weakly fault-tolerant, able to detect any single fault by a final (or intermediate) measurement and post-select on no error being detected. For small computations this will give an improvement over an unencoded quantum circuit. As qubit counts increase and noise rates diminish, more elements of FTQC can be added until full fault-tolerance is achieved. This project will also tackle the problem of preparing ancilla states, which are the building blocks of teleportation-based FTQC by combining state preparation and verification into a single process, using a combination of flag-based methods and error detection. The investigators will also pursue fast and accurate decoding algorithms for QEC codes that could be used in real time during a quantum computation. This project will develop decoding algorithms via machine learning methods. In addition, the project will explore applications of QEC codes to other problems in quantum information science. T 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.