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Single electrons trapped on solid neon surfaces (eNe) have recently emergedas a promising platform for charge qubits. Experimental results have revealedtheir exceptionally long coherence times, yet the actual quantum states ofthese trapped electrons, presumably on imperfectly flat neon surfaces, remainelusive. In this paper, we examine the electron's interactions with neonsurface topography, such as bumps and valleys. By evaluating the surfacecharges induced by the electron, we demonstrate its strong perpendicularbinding to the neon surface. The Schr\"{o}dinger equation for the electron'slateral motion on the curved 2D surface is then solved for extensivetopographical variations. Our results reveal that surface bumps can naturallybind an electron, forming unique quantum ring states that align withexperimental observations. We also show that the electron's excitation energycan be tuned using a modest magnetic field to facilitate qubit operation. Thisstudy offers a leap in our understanding of eNe qubit properties and providesstrategic insights on minimizing charge noise and scaling the system to propelforward quantum computing architectures.

Single-electron qubits based on quantum ring states on solid neon surface