Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit

By taking advantage of the gyrator [1] as a source of non-reciprocity in electrical networks, we propose a superconducting circuit [2], whose effective low-energy dynamics is engineered to approximate the GKP stabilizer Hamiltonian [3]. Thus, the doubly degenerate ground space of this system coincides with the code space of the continuous variable GKP code, which constitutes grid states as codewords.
Consequently, our particular qubit design benefits not only from the excellent error-correcting properties of the GKP code but also from its passive implementation, which waives the necessity of frequent hardware-expensive active error-correcting protocols. This suggests that our system might be a suitable candidate for future large-scale quantum processors.
We present ideas for single- and two-qubit gates and discuss protocols for state preparation and readout. Finally, we demonstrate the resilience against common types of noise in superconducting circuits and evaluate challenges of an experimental realization.

[1] B. Tellegen, Philips Res. Rep. 3, 81-101 (1948)
[2] M. Rymarz, S. Bosco, A. Ciani, D. P. DiVincenzo, arXiv:2002.07718 (2020)
[3] D. Gottesman, A. Kitaev, J. Preskill, Phys. Rev. A 64, 012310 (2001)