Disjointness of Stabilizer Codes and Limitations on Fault-Tolerant Logical Gates
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PhysRevX.8.021047.pdf
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483.06 KB
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Checksum (MD5)
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Author(s)
Jochym-O’Connor, Tomas
Kubica, Aleksander
Yoder, Theodore James
Date Issued
May 2018
Journal
Physical Review X
Publisher
American Physical Society
Citation
Jochym-O’Connor, Tomas, et al. “Disjointness of Stabilizer Codes and Limitations on Fault-Tolerant Logical Gates.” Physical Review X, vol. 8, no. 2, May 2018.
Version
Final published version
Abstract
Stabilizer codes are among the most successful quantum error-correcting codes, yet they have important limitations on their ability to fault tolerantly compute. Here, we introduce a new quantity, the disjointness of the stabilizer code, which, roughly speaking, is the number of mostly nonoverlapping representations of any given nontrivial logical Pauli operator. The notion of disjointness proves useful in limiting transversal gates on any error-detecting stabilizer code to a finite level of the Clifford hierarchy. For code families, we can similarly restrict logical operators implemented by constant-depth circuits. For instance, we show that it is impossible, with a constant-depth but possibly geometrically nonlocal circuit, to implement a logical non-Clifford gate on the standard two-dimensional surface code. Subject Areas: Quantum Physics, Quantum Information
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/PhysRevX.8.021047
