Magic: a new perspective on quantum chaos

Magic in quantum states is the resource that allows quantum computers to attain the quantum computational advantage over classical computers. Without magic, a quantum computer cannot do anything that a classical computer cannot do. In this work, we show that the resource theory of magic is closely connected to the theory of quantum chaos: we provide a measure of non-Cliffordness for unitary operators based on high order OTOCs and, as a consequence, only those quantum evolutions that attain a quantum computational advantage over classical computation can be considered chaotic.