Fault-tolerant gates via homological product codes
Walter Burke Institute for Theoretical Physics, Institute for Quantum Information & Matter, California Institute of Technology, Pasadena, CA 91125, USA
Published: | 2019-02-04, volume 3, page 120 |
Eprint: | arXiv:1807.09783v2 |
Doi: | https://doi.org/10.22331/q-2019-02-04-120 |
Citation: | Quantum 3, 120 (2019). |
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Abstract
A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes. In particular, it is shown that one can fault-tolerantly map between different encoded representations of a given logical state, enabling the application of different classes of transversal gates belonging to the underlying quantum codes. This allows for the circumvention of no-go results pertaining to universal sets of transversal gates and provides a general scheme for fault-tolerant computation while keeping the stabilizer generators of the code sparse.

Popular summary
We present a method to cross between different codes in a fault-tolerant manner, allowing one to exploit the desirable properties of both codes. The path between different codes may spread errors, but importantly it does so in a controlled manner that allows for the resulting code to clean up any noise that has propagated. Moreover, the method keeps the code simple and does not rely on preparing special resource states or measuring complicated objects. This provides a potential fruitful alternative to universal fault tolerance.
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