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We investigate the measurement-only topological quantum computation (MOTQC)approach proposed by Bonderson et al. [Phys. Rev. Lett. 101, 010501 (2008)]where the braiding operation is shown to be equivalent to a series oftopological 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 probabilisticalprocess with a certain success probability for each trial. In practice, thenumber of measurements needed will vary from run to run. We show that such anuncertainty associated with forced measurements can be removed by simulatingthe braiding operation using a fixed number of three measurements supplementedby a correction operator. Furthermore, we demonstrate that in practice we canavoid applying the correction operator in hardware by implementing it insoftware. Our findings greatly simplify the MOTQC proposal and only require thecapability of performing charge measurements to implement topologicallyprotected transformations generated by braiding exchanges without physicallymoving anyons.

Measurement-only topological quantum computation without forced measurements