Deciding Universality of Quantum Gates

Lecturer: Gábor Ivanyos

A collection of n-qubit gates is universal if there exists N0 ≥ n such that for every N ≥ N0 every N-qubit unitary operation can be approximated with arbitrary precision by a circuit built from gates of the collection. Decidability of universality follows from an upper bound on the smallest N0 with the above property. The bound is roughly 28n. The proof is based on a recent result of Guralnick and Tiep on invariants of (finite) linear groups.

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