Abstract

In addition to being of obvious practical use, classical simulations of quantum computations have interesting theoretical implications. Intuitively those computations which may be efficiently simulated by a classical computer are somehow “less quantum” while those which are prohibitively expensive to simulate classically are “more quantum”. I will discuss some ways of quantifying nonclassicality in the form of “magic” resources required to implement them. Recent work (arXiv:2307.12912, arXiv:2307.12654 and arXiv:2307.12702) has extended results known from the Clifford/stabilizer subtheory of quantum mechanics to fermionic linear optics. I will present some of these results with a particular emphasis on contrasting what is known about different classically simulable subtheories of quantum mechanics. There are many open questions but it appears that stabilizer quantum mechanics emerges as qualitatively different to the other examples which have been studied.