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Universal quantum gates

Jean-Luc Brylinski·Ranee Brylinski
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Abstract

In this paper we study universality for quantum gates acting on qudits.Qudits are states in a Hilbert space of dimension d where d is at least two. We determine which 2-qudit gates V have the properties (i) the collection of all 1-qudit gates together with V produces all n-qudit gates up to arbitrary precision, or (ii) the collection of all 1-qudit gates together with V produces all n-qudit gates exactly. We show that (i) and (ii) are equivalent conditions on V, and they hold if and only if V is not a primitive gate. Here we say V is primitive if it transforms any decomposable tensor into a decomposable tensor. We discuss some applications and also relations with work of other authors.

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Jean-Luc Brylinski, Ranee Brylinski. 2001-08-13. Universal quantum gates. https://arxiv.org/abs/quant-ph/0108062

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