Restrictions on Transversal Encoded Quantum Gate Sets

2008/11/26 by Bryan Eastin, Emanuel Knill · 1 voice · 3 citations
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1103/physrevlett.102.110502

published as Phys. Rev. Lett. 102, 110502 (2009) · 4 pages, v2: minor changes

arxiv published 2008/11/26 · arxiv created 2009/07/09 · arxiv updated 2009/07/09

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.

Cited by

• A new approximate Eastin-Knill theorem
• Covariant quantum error correction in a three-layer quantum brain model: computational analysis of layer-specific coherence dynamics
• Efficient witnessing and testing of magic in mixed quantum states

Discussions

• The famous Eastin-Knill theorem forbids transversal (non-error-spreading) gates from achieving arbitrary logical unitary transformations. Worse, the only achievable ones can be simulated efficiently o [bsky, 2 points, 1 comments]