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arXiv · 1609.08188

Representations of the multi-qubit Clifford group

Jonas Helsen·Joel J. Wallman·Stephanie Wehner
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Abstract

The Clifford group is a fundamental structure in quantum information with a wide variety of applications. We discuss the tensor representations of the $q$-qubit Clifford group, which is defined as the normalizer of the $q$-qubit Pauli group in $U(2^q)$. In particular, we characterize all irreducible subrepresentations of the two-copy representation $\varphi^{\otimes2}$ of the Clifford group on the matrix space $\mathbb{C}^{d\times d}\otimes \mathbb{C}^{d\times d}$ with $d=2^q$. In an upcoming companion paper we applied this result to cut down the number of samples necessary to perform randomised benchmarking, a method for characterising quantum systems.

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Jonas Helsen, Joel J. Wallman, Stephanie Wehner. 2016-09-26. Representations of the multi-qubit Clifford group. https://doi.org/10.1063/1.4997688

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