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Deciding universality of quantum gates

Gabor Ivanyos
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Abstract

We say that collection of $n$-qudit gates is universal if there exists $N_0\geq n$ such that for every $N\geq N_0$ every $N$-qudit unitary operation can be approximated with arbitrary precision by a circuit built from gates of the collection. Our main result is an upper bound on the smallest $N_0$ with the above property. The bound is roughly $d^8 n$, where $d$ is the number of levels of the base system (the '$d$' in the term qu$d$it.) The proof is based on a recent result on invariants of (finite) linear groups.

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Gabor Ivanyos. 2006-09-08. Deciding universality of quantum gates. https://arxiv.org/abs/quant-ph/0603009

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