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Publication Citation: Restrictions on Transversal Encoded Quantum Gate Sets

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Author(s): Bryan K. Eastin; Emanuel H. Knill;
Title: Restrictions on Transversal Encoded Quantum Gate Sets
Published: March 18, 2009
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
Pages: pp. 110502-1 - 110502-4
Keywords: error detection,fault tolerance,quantum codes,transversal gates,universality,
Research Areas: Quantum Information
PDF version: PDF Document Click here to retrieve PDF version of paper (80KB)