Universal Fault-Tolerant Gates on Concatenated Stabilizer Codes
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PhysRevX.6.031039.pdf
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942.08 KB
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Author(s)
Yoder, Theodore James
Takagi, Ryuji
Chuang, Isaac
Date Issued
September 2016
Journal
Physical Review X
Publisher
American Physical Society
Citation
Yoder, Theodore J., Ryuji Takagi, and Isaac L. Chuang. “Universal Fault-Tolerant Gates on Concatenated Stabilizer Codes.” Physical Review X 6.3 (2016): n. pag.
Version
Final published version
Abstract
It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions including magic state distillation. Widely overlooked, however, is the possibility of nontransversal, yet still fault-tolerant, gates that work directly on small quantum codes. Here, we demonstrate precisely the existence of such gates. In particular, we show how the limits of nontransversality can be overcome by performing rounds of intermediate error correction to create logical gates on stabilizer codes that use no ancillas other than those required for syndrome measurement. Moreover, the logical gates we construct, the most prominent examples being Toffoli and controlled-controlled-Z, often complete universal gate sets on their codes. We detail such universal constructions for the smallest quantum codes, the 5-qubit and 7-qubit codes, and then proceed to generalize the approach. One remarkable result of this generalization is that any nondegenerate stabilizer code with a complete set of fault-tolerant single-qubit Clifford gates has a universal set of fault-tolerant gates. Another is the interaction of logical qubits across different stabilizer codes, which, for instance, implies a broadly applicable method of code switching.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevX.6.031039
