@inproceedings{grassl2013leveraging,
author = {Grassl, Markus and Roetteler, Martin},
title = {Leveraging automorphisms of quantum codes for fault-tolerant quantum computation},
booktitle = {Proceedings of the 2013 IEEE International Symposium on Information Theory (ISIT'13), Istanbul, Turkey},
year = {2013},
month = {January},
abstract = {Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal set of quantum gates that act on the code space of an underlying quantum code. To implement such a universal gate set fault-tolerantly is an expensive task in terms of physical operations, and any possible shortcut to save operations is potentially beneficial and might lead to a reduction in overhead for fault-tolerant computations. We show how the automorphism group of a quantum code can be used to implement some operators on the encoded quantum states in a fault-tolerant way by merely permuting the physical qubits. We derive conditions that a code has to satisfy in order to have a large group of operations that can be implemented transversally when combining transversal CNOT with automorphisms. We give several examples for quantum codes with large groups, including codes with parameters [[8,3,3]], [[15,7,3]], [[22,8,4]], and [[31,11,5]].},
url = {http://approjects.co.za/?big=en-us/research/publication/leveraging-automorphisms-of-quantum-codes-for-fault-tolerant-quantum-computation/},
pages = {534-538},
edition = {Proceedings of the 2013 IEEE International Symposium on Information Theory (ISIT'13), Istanbul, Turkey},
note = {See also arXiv preprint arXiv:1302.1035},
}