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Restrictions on Transversal Encoded Quantum Gate Sets

Published

Author(s)

Bryan K. Eastin, Emanuel H. Knill

Abstract

Transversal gates play an important role in the theory of fault-tolerant quantum computation due to their simplicity and robustness to noise. By definition, transversal operators do not couple physical subsystems within the same code block. Consequently, such operators do not spread errors within code blocks and are, therefore, fault tolerant. Nonetheless, other methods of ensuring fault tolerance are required, as it is invariably the case that some encoded gates cannot be implemented transversally. This observation has led to a long-standing conjecture that transversal encoded gate sets cannot be universal. Here we show that the ability of a quantum code to detect an arbitrary error on any single physical subsystem is incompatible with the existence of a universal, transversal encoded gate set for the code.
Citation
Physical Review Letters
Volume
102

Keywords

error detection, fault tolerance, quantum codes, transversal gates, universality

Citation

Eastin, B. and Knill, E. (2009), Restrictions on Transversal Encoded Quantum Gate Sets, Physical Review Letters, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=900210 (Accessed July 24, 2024)

Issues

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Created March 18, 2009, Updated February 19, 2017