Title: The superconducting grid-states qubit, Theory

The Hamiltonian-based approach of hardware encoding stabilizers can protect a quantum system against errors from noisy environments, even in the absence of feedback and dissipation engineering. In particular, a superconducting circuit that is doubly nonlinear with respect to the charge and phase conjugate variables exhibit grid-like eigenstates that are resilient against common noise sources. In this talk, we present a novel realization of this platform by integrating a 4e-tunneling junction with a quantum phase-slip element embedded within a high-impedance environment. The radiofrequency spectra exhibit doubly degenerate states separated by large energy gaps, which are signatures of the Gottesman-Kitaev-Preskill (GKP) Hamiltonian. Moreover, we observe enhanced coherence times when the device operates in the protected regime, highlighting its potential as a quantum memory platform for quantum information processing. Part 1/2.