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Demonstration of Shor Encoding on a Trapped-Ion Quantum Computer

TitleDemonstration of Shor Encoding on a Trapped-Ion Quantum Computer
Publication TypeJournal Article
Year of Publication2021
AuthorsN. H. Nguyen, M. Li, A. M. Green, H. C. Alderete, Y. Zhu, D. Zhu, K. R. Brown, and N. M. Linke
JournalPhys. Rev. Appl.
Date PublishedAUG 30
Type of ArticleArticle

Fault-tolerant quantum error correction (QEC) is crucial for unlocking the true power of quantum computers. QEC codes use multiple physical qubits to encode a logical qubit, which is protected against errors at the physical qubit level. Here, we use a trapped-ion system to experimentally prepare m-qubit Greenberger-Horne-Zeilinger states and sample the measurement results to construct m x m logical states of the {[}{[}m(2), 1, m]] Shor code, up to m = 7. The synthetic logical fidelity shows how deeper encoding can compensate for additional gate errors in state preparation for larger logical states. However, the optimal code size depends on the physical error rate and we find that m = 5 has the best performance in our system. We further realize the direct logical encoding of the {[}{[}9, 1, 3]] Shor code on nine qubits in a 13-ion chain for comparison, with 98.8(1)% and 98.5(1)% fidelity for state vertical bar +/->(L), respectively.