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|Title:||Leveraging automorphisms of quantum codes for fault-tolerant quantum computation|
|Authors:||Grassl, M. |
|Citation:||Grassl, M.,Roetteler, M. (2013). Leveraging automorphisms of quantum codes for fault-tolerant quantum computation. IEEE International Symposium on Information Theory - Proceedings : 534-538. ScholarBank@NUS Repository. https://doi.org/10.1109/ISIT.2013.6620283|
|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]. © 2013 IEEE.|
|Source Title:||IEEE International Symposium on Information Theory - Proceedings|
|Appears in Collections:||Staff Publications|
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