Unification of universal and non-universal topological quantum computation
Haitan Xu, Jacob Taylor
Approaches for implementing primitives for quantum computation using Read-Reyazi anyons remain computational difficult to find. We demonstrate how recently discovered approaches, including composition of anyons and deconstruction of many-qubit operations into effective single-qubit gates can be used for both effective mapping between dense and sparse representations of qubits, the construction of two- qubit gate, and the construction of the Toffoli gate (CCPHASE) for the universal class of Read-Reyazi anyons, k=3, k > 4. In the process, we show how the constructions for quantum memory in non-universal anyon classes connect naturally to the construction of quantum bits for computation in the universal class, unifying these two concepts in a simple framework.
and Taylor, J.
Unification of universal and non-universal topological quantum computation, Physical Review Letters, [online], https://doi.org/10.1103/PhysRevA.84.012332
(Accessed February 28, 2024)