Topological qubits encode quantum information not in the local state of a single particle but in the global, topological configuration of a many-body system, typically the braiding history of quasiparticles called non-Abelian anyons. The leading candidate is the Majorana zero mode, a quasiparticle predicted to appear at the ends of a topological superconducting nanowire, where a pair of spatially separated Majorana modes together form one nonlocal qubit. Because the information is stored nonlocally, it is in principle immune to local noise, the source of decoherence in every other qubit platform on this list.
This is also why topological qubits are the odd one out here: there is no simple Hamiltonian to write down for the qubit itself. The qubit's logical state isn't an eigenstate of some local Hamiltonian term the way a transmon's $\lvert 0 \rangle$ and $\lvert 1 \rangle$ are. It's a degenerate ground-space label distinguished only by a global topological invariant (the fermion parity of a pair of Majorana modes), and gates are implemented by physically braiding anyons around each other rather than by driving transitions with a control Hamiltonian.
Every other platform in this list stores its qubit state in a local degree of freedom (a junction's charge, an atom's spin, a photon's polarization) and pays for that with a Hamiltonian that couples to environmental noise the same way it couples to control fields. A topological qubit is designed so that no local operator, including noise, can distinguish its logical states, because the information a local measurement could extract is, by construction, zero. If this protection works as intended, hardware error rates could end up low enough to reduce or remove the need for the software-level error correction that all other platforms rely on.