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 May 10, 2026)
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
Restrictions on Transversal Encoded Quantum Gate Sets
Published
Author(s)
,
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
Pub Type
Journals
Download Paper
Keywords
error detection, fault tolerance, quantum codes, transversal gates, universality
Citation
Issues
If you have any questions about this publication or are having problems accessing it, please contact [email protected].
Created March 18, 2009, Updated February 19, 2017