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. One famous example is the Gottesman-Kitaev-Preskill (GKP) Hamiltonian, which exhibits grid-like eigenstates that are resilient against common noise sources. In this talk, we present a novel realization of this Hamiltonian by integrating a cooper-quartet tunnelling junction and a quantum phase-slip element within a high-impedance environment – a circuit which is doubly nonlinear in both charge and phase conjugate variables. When flux-biased into the protected regime and measured using microwave spectroscopy, the qubit exhibits doubly degenerate states separated by large energy gaps as is expected in a GKP qubit. Moreover, we observe enhanced coherence times as we approach protection, highlighting its potential as a quantum memory platform for quantum information processing. Part 1/2.