Passive Error Correction with Grid States in a Non-Reciprocal Superconducting Circuit

Non-reciprocal circuit elements play an essential role for the practical realization of a solid-state quantum computer, independent of the chosen implementation. For that matter, non-reciprocal circuit elements often constitute the interface between the classical and quantum description of an electrical network.
In electrical network theory, the gyrator proposed by Tellegen [1] in 1948 is considered to be the most fundamental non-reciprocal circuit element. The miniaturization of the actual device allows for the description of the gyrator within the lumped element model.
Besides the incorporation of the gyrator into the theory of circuit quantum electrodynamics [2], we propose a non-reciprocal superconducting circuit comprising a gyrator, whose effective dynamics is described by the Hofstadter Hamiltonian [3]. Thus, the eigenstates of the system constitute grid states, which can be used for passive error correction in terms of the continuous variable code proposed in 2001 by Gottesman, Kitaev and Preskill [4].

[1] B. Tellegen, Philips Res. Rep. 3, 81-101 (1948)
[2] U. Vool, M. Devoret, arXiv:1610.03438v2 (2017)
[3] D. Hofstadter, Phys. Rev. B 14, 2239 (1976)
[4] D. Gottesman, A. Kitaev, J. Preskill, Phys. Rev. A 64, 012310 (2001)