# Work on "quantum homeopathy" in the Communications of Mathematical Physics

Unitary designs are important tools in quantum information theory, as collections of unitaries that resemble averages over the Haar measure. So-called k-designs recover k-th moments exactly. They have a wealth of applications in technology-oriented fields such as benchmarking, certification as well as in fundamental quantum physics. Random Clifford operations are 3-designs, but just not 4-designs, which constitutes a roadblock in some applications. Adding (expensive) T-gates will uplift such random circuits to k-designs of arbitrary order. But the question arises how of those many one needs? It turns out that strikingly, a non-extensive number is sufficient: One will still arrive at a design of arbitrary order. This technical and mathematically minded work - that jokingly can be explained as quantum homeopathy actually working - goes to press in the Communications of Mathematical Physics, the most prestigious venue for mathematical physics.

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News from Sep 21, 2022