This talk will describe how the geometry of the Heisenberg-Weyl group connects the world of quantum computing and the world of wireless communication. In quantum computing the Heisenberg-Weyl group appears as the Pauli group, generated by bit shifts and phase shifts. In wireless communication the Heisenberg-Weyl group is generated by shifts in delay and Doppler. In quantum computing, the geometry of commutative subgroups is used to construct quantum error-correcting codes. In wireless communication, this geometry is used to construct low-complexity signal processing algorithms that might find application in 6G wireless systems.