Supplementary Videos 2 and 3 are movies of single atoms (real pictures captured with a microscope objective and CMOS camera), showing the quantum circuit implemented in Figs. 6 to realize teleportation-based algorithms in the space and time direction. Parallel entangling gates are indicated by red ovals. Two groups of qubits, A and B, are in the readout and storage zone, respectively, with additional qubits forming the reservoir. Qubits in group A are moved into the entangling zone and encoded using a hypercube encoding circuit. Transversal gates between codes form a 1D cluster state. Next, group B (already entangled) is entangled with group A to create a 2D cluster state, across the space and time directions. Group A is moved to storage, to be entangled with the next cycle, and group B is moved to the readout zone and measured via spin-to-position conversion. For illustrative purposes, each qubit is prepared in \(| +\rangle \) and therefore imaged with equal probability in the two tweezer locations (frames are averaged over several shots). Finally, the tweezers are recombined, the atoms are re-cooled, loss is re-filled, and the qubit state is reinitialized. This is one layer. The cycle then repeats 27 times. Supplementary Video 2: Teleportation-based logical algorithm with Steane [[7,1,3]] codes. Each group consists of 16 code blocks in a 4x4 grid, which are entangled into two independent 1D cluster states (eight blocks each) and further into 2D cluster states with adjacent layers in time.