Measurement-only topological quantum computation without forced measurements

We investigate the measurement-only topological quantum computation (MOTQC) approach proposed by Bonderson et al (2008 Phys. Rev. Lett. 101 010501) where the braiding operation is shown to be equivalent to a series of topological charge 'forced measurements' of anyons. In a forced measurement, the charge measurement is forced to yield the desired outcome (e.g. charge 0) via repeatedly measuring charges in different bases. This is a probabilistic process with a certain success probability for each trial. In practice, the number of measurements needed will vary from run to run. We show that such an uncertainty associated with forced measurements can be removed by simulating the braiding operation using a fixed number of three measurements supplemented by a correction operator. Furthermore, we demonstrate that in practice we can avoid applying the correction operator in hardware by implementing it in software. Our findings greatly simplify the MOTQC proposal and only require the capability of performing charge measurements to implement topologically protected transformations generated by braiding exchanges without physically moving anyons.