Hardware-Encoding Grid States in a Nonreciprocal Superconducting Circuit

Martin Rymarz*, Stefano Bosco, Alessandro Ciani, David P. Divincenzo

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)
42 Downloads (Pure)


We present a circuit design composed of two Josephson junctions coupled by a nonreciprocal element, the gyrator, whose ground space is doubly degenerate. The ground states are approximate code words of the Gottesman-Kitaev-Preskill code. We determine the low-energy dynamics of the circuit by working out the equivalence of this system to the problem of a single electron in a crystal, confined to a two-dimensional plane, and subjected to a strong, homogeneous magnetic field. We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux noise, implying that it can be used for passive quantum error correction. We also propose realistic design parameters for an experimental realization, and we describe possible protocols to perform logical one- and two-qubit gates, state preparation, and readout.

Original languageEnglish
Article number011032
Number of pages25
JournalPhysical Review X
Issue number1
Publication statusPublished - 2021


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