The ability to engineer parallel, programmable operations between desired qubits within a quantum processor is central for building scalable quantum information systems [1,2]. In most stateof-the-art approaches, qubits interact locally, constrained by the connectivity associated with their fixed spatial layout. Here, we demonstrate a quantum processor with dynamic, nonlocal connectivity, in which entangled qubits are coherently transported in a highly parallel manner across two spatial dimensions, in between layers of single-and two-qubit operations. Our approach makes use of neutral atom arrays trapped and transported by optical tweezers; hyperfine states are used for robust quantum information storage, and excitation into Rydberg states is used for entanglement generation [3][4][5]. We use this architecture to realize programmable generation of entangled graph states such as cluster states and a 7-qubit Steane code state [6,7]. Furthermore, we shuttle entangled ancilla arrays to realize a surface code with 19 qubits [8] and a toric code state on a torus with 24 qubits [9]. Finally, we use this architecture to realize a hybrid analog-digital evolution [2] and employ it for measuring entanglement entropy in quantum simulations [10][11][12], experimentally observing non-monotonic entanglement dynamics associated with quantum many-body scars [13,14]. Realizing a long-standing goal, these results pave the way toward scalable quantum processing and enable new applications ranging from simulation to metrology.