Title: Toponomic Quantum Computation

Abstract: Quantum computing is based on logical gates operating on the quantum state of a system of qbits. Being able to implement a gate in a noise-resilient way is fundamental to the robustness of the resulting quantum computation.

A proposal that promises a certain degree of resilience is that of holonomic quantum computing, in which gates are produced as holonomies (geometric phases) associated to appropriately chosen cyclic evolutions. Although such gates are immune to reparametrizations of the path taken in state space, they do change when the path is deformed.

We propose here a new scheme, toponomic quantum computing, in which logical gates are produced by cyclic rotations of a special type of subspaces of the Hilbert space called anticoherent rotosymmetric, the identification of which is facilitated by a generalization of Majorana’s stellar representation to the case of Grassmannians. We show that these gates are only dependent on topological properties of the path, and are hence immune to any continuous deformation, however large, implying a considerably improved noise resilience. We give explicit examples of implementations of NOT, CNOT, and Toffoli gates within the proposed scheme.

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