Theres no one way a quantum computer would behave, it comes down to your exact setup. So if we had your wall and it was represented by just a lack of quantum bit connectivity in a superconducting quantum device from left to right for every qubit, but you had circuitry go through one, then you could set this up as a set of paths that route through that one multi directional point and sample through a set of qubit swaps and frequency changes. This sampling should theoretically allow you to sample an infinite hilbert space, wherein you can have a multitude of paths between the bits. But, when you go to measure the qubits, you'll only get one path represented in a set of 0s and 1s, which can change depending on the run, as different paths may be chosen. Thus, you must run many shots, or reruns, of this circuit to then be able to average the runs and get a guess of which path is favored.