  The ability to manipulate coherently individual quantum objects organized in
arrays is a prerequisite to any scalable quantum information platform. For
electron spin qubits, it requires the fine tuning of large arrays of
tunnel-coupled quantum dots. The cumulated efforts in linear dot arrays have
permitted the recent realization of quantum simulators and multi-electron spin
coherent manipulation. However, the two-dimensional scaling of such
implementations remains undemonstrated while being compulsory to resolve
complex quantum matter problems or process quantum information. Here, we
demonstrate the two-dimensional coherent control of individual electron spins
in a 3x3 array of tunnel-coupled quantum dots. More specifically, we focus on
several key quantum functionalities of such control: charge deterministic
displacement, local spin readout, local coherent exchange manipulation between
two electron spins trapped in adjacent dots, and coherent multi-directional
spin shuttling over distances of several microns. This work lays the
foundations for exploiting a two-dimensional array of electron spins for
quantum simulation and information processing.
