Hardware-Encoding Grid States in a Nonreciprocal Superconducting Circuit

Physical Review X, vol. 11

Abstract

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.

Authors 4

1. Martin Rymarz Aachen JARA-Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   JARA-Institute for Quantum Information, RWTH Aachen University, D-52056 Aachen, Germany

2. Stefano Bosco

   Forschungszentrum Jülich · University of Basel

   Affiliation as printed

   Department of Physics, University of Basel, CH-4056 Basel, Switzerland

   Peter Grünberg Institute, Theoretical Nanoelectronics, Forschungszentrum Jülich, D-52425 Jülich, Germany

3. Alessandro Ciani

   QuTech · Delft University of Technology

   Affiliation as printed

   QuTech, Delft University of Technology, 2628 CJ Delft, Netherlands

4. David Peter Divincenzo Aachen JARA-Institute for Quantum Information

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   JARA-Institute for Quantum Information, RWTH Aachen University, D-52056 Aachen, Germany

   Peter Grünberg Institute, Theoretical Nanoelectronics, Forschungszentrum Jülich, D-52425 Jülich, Germany