Measurement-only topological quantum computation without forced measurements

We investigate themeasurement-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 ‘forcedmeasurements’ of anyons. In a forced measurement, the chargemeasurement is forced to yield the desired outcome (e.g. charge 0) via repeatedlymeasuring charges in different bases. This is a probabilistic process with a certain success probability for each trial. In practice, the number ofmeasurements neededwill vary from run to run. We show that such an uncertainty associatedwith forcedmeasurements can be removed by simulating the braiding operation using a fixed number of threemeasurements 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. Ourfindings greatly simplify theMOTQCproposal and only require the capability of performing chargemeasurements to implement topologically protected transformations generated by braiding exchanges without physicallymoving anyons.