In a recent breakthrough, Bravyi, Gosset and König (Science, 2018) proved an unconditional separation between the complexity classes of constant-depth quantum circuits QNC⁰, also called shallow quantum circuits, and their classical counterparts NC⁰. This result has since then been extended to a number of different computational problems. In this talk, we introduce so-called higher-dimensional generalised GHZ states, which are multipartite entangled states in a superposition of pure GHZ-like states, and explore their non-local properties. We further discuss the main ideas behind proving a separation in the setting of arithmetic problems, which generalise the Parity Halving problem, previously introduced by Watts, Kothari, Schaeffer and Tal (STOC 2019).