The magic of universal quantum computing with permutations

Abstract

The role of permutation gates for universal quantum computing is investigated. The \lq magic' of computation is clarified in the permutation gates, their eigenstates, the Wootters discrete Wigner function and state-dependent contextuality (following many contributions on this subject). A first classification of main types of resulting magic states in low dimensions $d\le 9$ is performed.

12 pages, 2 figures

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• Topological Quantum Computing and 3-Manifolds
• 3D Topological Quantum Computing
• Cosine series quantum sampling method with applications in signal and image processing
• Representation matching for delegated quantum computing
• Quantum computing with Bianchi groups