Topological Quantum Computation and Measurement

Parsa Bonderson, Michael Hartley Freedman, Chetan Nayak

Parsa Bonderson, Michael Hartley Freedman, Chetan Nayak

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.

R. W. Ogburn, John P. Preskill

Huaixiu Zheng, Arpit Dua, Liang Jiang

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.

Jiannis K. Pachos

Keisuke Fujii

This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer formalism, and measurement-based quantum computation, are also provided in a pedagogical way. Topological quantum computation by brading the defects on the surface code is explained in both circuit-based and measurement-based models in such a way that their relation is clear. The interdisciplinary connections between quantum error correction codes and subjects in other fields such as topological order in condensed matter physics and spin glass models in statistical physics are also discussed. This manuscript will be appeared in SpringerBriefs.