Anticoherent k -planes and coding techniques for a 3-qubit scheme of universal quantum computing

Toponomic quantum computing employs rotation sequences of anticoherent k-planes to construct noise-tolerant quantum gates. In this work, we demonstrate the implementation of generalized Toffoli gates, using k-planes of spin systems with spin [Formula: see text], and of the Hadamard gate for a 3-qubit system, using a spin [Formula: see text] 8-plane. We propose a universal quantum computing scheme for 3-qubit systems (via Hadamard and Toffoli gates) based on coding techniques. A key advantage of this construction is its inherent robustness against noise: apart from reparametrization invariance, our scheme is characterized by immunity to arbitrarily large deformations of the path in (rotational) parameter space that fix its end points, so that curves in the same homotopy class give rise to identical holonomies.