Measurement-Only Topological Quantum Computation

We remove the need to physically transport computational anyons around each other from the implementation of computational gates in topological quantum computing. By using an anyonic analog of quantum state teleportation, we show how the braiding transformations used to generate computational gates may be produced through a series of topological charge measurements.

Figure 1

Projective topological charge measurements of pairs of anyons (a) 1 and 2, (b) 2 and 3, and (c) 2 and 4 are used to implement anyonic state teleportation, which is used to produce braiding transformations as in Eqs. (13, 14).

Figure 2

A quasi-one-dimensional array of stationary anyons used for measurement-only topological quantum computing. Maximally entangled pairs of anyons (denoted by X’s) are situated between adjacent pairs of computational anyons (denoted by dots) to facilitate measurement induced braiding transformations used to generate computational gates.