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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.
Physical Review Letters


Quantum computation, Read-Reyazi anyons, Topological gates, Two-dimensional heterostructures


Xu, H. and Taylor, J. (2011), Unification of universal and non-universal topological quantum computation, Physical Review Letters, [online], (Accessed July 21, 2024)


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Created July 25, 2011, Updated October 12, 2021