Low overhead universality and quantum supremacy using only Z control

Abstract

We consider a model of quantum computation we call "varying Z"(VZ), defined by applying controllable Z-diagonal Hamiltonians in the presence of a uniform and constant external X field, and prove that it is universal, even in one dimension. Universality is demonstrated by construction of a universal gate set with O(1) depth overhead. We then use this construction to describe a circuit whose output distribution cannot be classically simulated unless the polynomial hierarchy collapses, with the goal of providing a low-resource method of demonstrating quantum supremacy. The VZ model can achieve quantum supremacy in O(n) depth in one dimension, equivalent to the random circuit sampling models despite a higher degree of homogeneity: it requires no individually addressed X control.