Explicit lower bounds on strong simulation of quantum circuits in terms of $T$-gate count (1902.04764v2)

Abstract: We investigate Clifford+$T$ quantum circuits with a small number of $T$-gates. Using the sparsification lemma, we identify time complexity lower bounds in terms of $T$-gate count below which a strong simulator would improve on the state-of-the-art $3$-SAT solving.