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arXiv · 1302.1035

Leveraging Automorphisms of Quantum Codes for Fault-Tolerant Quantum Computation

Markus Grassl·Martin Roetteler
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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]].

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Markus Grassl, Martin Roetteler. 2013-02-05. Leveraging Automorphisms of Quantum Codes for Fault-Tolerant Quantum Computation. https://doi.org/10.1109/isit.2013.6620283

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