Realization of self-protected grid states in a superconducting qubit

A central pursuit in quantum science is to safeguard encoded information from noise, through active quantum error correction and through Hamiltonian-engineered intrinsic protection. Motivated by the Gottesman–Kitaev–Preskill code, theoretical proposals over the past decades have envisioned low-overhead approaches to fault-tolerance using devices in which grid states arise as eigenstates of the Hamiltonian itself, yet a physical implementation has remained elusive. Here we realize a superconducting circuit where dual nonlinearities from coherent quantum phase-slip and charge-4e tunneling generate a Hamiltonian whose eigenstates form intrinsically protected grids in phase space with emergent degeneracies. The encoded states exhibit enhanced robustness against environmental noise and device disorder as the grid support expands, fulfilling a crucial criterion for device-level fault tolerance. Our findings establish a hardware-efficient avenue toward scalable, fault-tolerant quantum computing and set the stage for the development of solid-state devices with dual nonlinearities.