Abstract
We study quasi-exact quantum error-correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding exact codes, serving as its fixed points. The computation with a quasi-exact code cannot realize any logical gate to arbitrary accuracy. To overcome this, the notion of quasi-exact universality is proposed, which makes quasi-exact quantum computation a feasible model especially for executing moderate-size algorithms. We find that the incompatibility between universality and transversality of the set of logical gates does not persist in the quasi-exact scenario. A class of covariant quasi-exact codes is defined which proves to support a transversal and quasi-exact universal set of logical gates for . This work opens the possibility of quantum computation with quasi-exact universality, transversality, and fault tolerance.
- Received 15 October 2019
- Accepted 2 July 2020
DOI:https://doi.org/10.1103/PhysRevResearch.2.033116
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society