Apparatus, methods, and systems are disclosed for robust scalable topological quantum computing. Quantum dots are fabricated as van der Waals heterostructures, supporting localized topological phases and non-Abelian anyons (quasiparticles). Large bandgaps provide noise immunity. Three-dot structures include an intermediate quantum dot between two computational quantum dots. With the intermediate quantum dot in an OFF state, quasiparticles at the computational quantum dots can be isolated, with long lifetimes. Alternatively, the intermediate quantum dot can be controlled to decrease the quasiparticle tunneling barrier, enabling fast computing operations. A computationally universal suite of operations includes quasiparticle initialization, braiding, fusion, and readout of fused quasiparticle states, with, optionally, transport or tunable interactions—all topologically protected. Robust qubits can be operated without error correction. Quasilinear arrays of quantum dots or qubits can be scaled arbitrarily, up to resource limits, and large-scale topological quantum computers can be realized. Extensive two-dimensional arrays can also be used.