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Universal quantum gates. (English) Zbl 0997.81015

Chen, Goong (ed.) et al., Mathematics of quantum computation. Boca Raton, FL: Chapman & Hall/ CRC. Computational Mathematics Series. 101-116 (2002).
A collection of 1-qudit \(A_{i}\) and 2-qubit \(B_{i}\) is said to be universal when, for each \(n\) greater than 2, every \(n\)-qubit can be approximated with arbitrary accuracy by a circuit made of the \(n\)-qudit gates produced by \( A_{i}\) and \(B_{i}\). When the realisation is exact, then the collection is referred to as exactly universal. The present paper characterizes these qudit gates. In some instances universality and exact universality are equivalent. Some applications are given. Once more the key is the use of Lie groups.
For the entire collection see [Zbl 1077.81018].

MSC:

81P68 Quantum computation
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