This study investigates the exponential protection of zero-energy Majorana modes in Majorana islands, which are promising candidates for fault-tolerant quantum computing. The research focuses on InAs nanowires with epitaxial Al shells, forming superconducting Coulomb islands (Majorana islands) that are isolated from normal-metal leads by tunnel barriers. The team uses Coulomb-blockade spectroscopy to measure the splitting of near-zero-energy Majorana modes in these devices. They observe exponential suppression of energy splitting with increasing wire length, with a characteristic length scale of 260 nm. For short devices, subgap state energies oscillate with magnetic field, consistent with hybridized Majorana modes. For longer devices, transport occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. The results help explain the trivial-to-topological transition in finite systems and quantify the scaling of topological protection with end-mode separation. The study shows that the energy splitting of Majorana modes decreases exponentially with increasing wire length, demonstrating exponential protection of zero-energy modes. The observed energy splitting is consistent with the expected topological protection of Majorana modes. The results also show that the zero-energy state is robust over many successive Coulomb peaks and that the energy of the sub-gap state can be measured using bias spectroscopy. The study provides experimental support for electron teleportation via Majorana modes and highlights the importance of topological protection in quantum computing. The findings are consistent with known parameters for InAs nanowires and the emergence of topological superconductivity. The results demonstrate the potential of Majorana islands as a platform for quantum computing and highlight the importance of topological protection in quantum systems.This study investigates the exponential protection of zero-energy Majorana modes in Majorana islands, which are promising candidates for fault-tolerant quantum computing. The research focuses on InAs nanowires with epitaxial Al shells, forming superconducting Coulomb islands (Majorana islands) that are isolated from normal-metal leads by tunnel barriers. The team uses Coulomb-blockade spectroscopy to measure the splitting of near-zero-energy Majorana modes in these devices. They observe exponential suppression of energy splitting with increasing wire length, with a characteristic length scale of 260 nm. For short devices, subgap state energies oscillate with magnetic field, consistent with hybridized Majorana modes. For longer devices, transport occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes. The results help explain the trivial-to-topological transition in finite systems and quantify the scaling of topological protection with end-mode separation. The study shows that the energy splitting of Majorana modes decreases exponentially with increasing wire length, demonstrating exponential protection of zero-energy modes. The observed energy splitting is consistent with the expected topological protection of Majorana modes. The results also show that the zero-energy state is robust over many successive Coulomb peaks and that the energy of the sub-gap state can be measured using bias spectroscopy. The study provides experimental support for electron teleportation via Majorana modes and highlights the importance of topological protection in quantum computing. The findings are consistent with known parameters for InAs nanowires and the emergence of topological superconductivity. The results demonstrate the potential of Majorana islands as a platform for quantum computing and highlight the importance of topological protection in quantum systems.