Abstract: Disclosed herein are efficient geometries for dynamical topology changing (DTC), together with protocols to incorporate DTC into quantum computation. Given an Ising system, twisted depletion to implement a logical gate T, anyonic state teleportation into and out of the topology altering structure, and certain geometries of the (1,?2)-bands, a classical computer can be enabled to implement a quantum algorithm.

Abstract: A method for changing qubit encoding for implementation of a quantum computational gate is disclosed. Such a method may include providing first and second qubits encoded in a plurality of non-abelian anyons according to a first encoding scheme. The first encoding scheme may not be suitable for implementing a certain topologically protected quantum computational gate, such as an entangling gate, for example. Successive topological charge measurements may be performed on at least a subset of the anyons until the qubits are encoded according to a second encoding scheme. The second encoding scheme may be different from the first encoding scheme, and may be suitable for implementing the gate.

Abstract: An implementation of a single qubit phase gate for use in a quantum information processing scheme based on the ?=5/2 fractional quantum Hall (FQH) state is disclosed. Using sack geometry, a qubit consisting of two ?-quasiparticles. which may be isolated on respective antidots, may be separated by a constriction from the bulk of a two-dimensional electron gas in the ?=5/2 FQH state. An edge quasiparticle may induce a phase gate on the qubit. The number of quasiparticles that are allowed to traverse the edge path defines which gate is induced. For example, if a certain number of quasiparticles are allowed to traverse the path, then a ?/8 gate may be effected.

Abstract: Measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge is described. Various issues that would arise when realizing it in fractional quantum Hall systems are discussed.