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

Toponomic quantum computing (TQC) 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 s ≥ k + 1, and of the Hadamard gate for a 3-qubit system, using a spin $s \!= \! 15$ 8-plane. We propose a universal quantum computing scheme for 3-qubit systems (via Hadamard + 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.