A quantum computer, quantum logic circuit, material for forming qubits, and method of operating a quantum computer is described. The material is formed from a quasicrystal or quasicrystalline approximant. In some examples, topological quantum computing is performed based on the quasicrystal or quasicrystalline approximant materials. Quasicrystals and quasicrystalline approximate materials have materials properties that can be adapted to perform quantum computing. In one example, the material is a Tsai-type quasicrystalline approximant with a material structure selected to permit qubits to be generated.