You can model a universal quantum computer as a kind of probabilistic computer by starting with bits with definite values (usually all initialized to 0) which then undergo stochastic hops at each logic gate.

The stochastic matrices can be computed by starting with |U|² as the base stochastic matrix and then modifying it as little as possible such that it correctly maps |ψ(t)|² to |ψ(t+1)|², which can be done with an algorithm known as iterative proportional fitting.

For this demo, I am using the same methodology, but representing the 0s and 1s of the bits as positions on a grid. So, there are 8 qubits associated with the y-position and 9 qubits associated with the x-position, so it can be displayed on a 512x256 grid.

Then, a unitary operator is being applied on top of its qubit memory state at every discrete time step, causing the bits to hop to a new value, which since they’re being plotted on a grid, it causes the “particle” on the screen to move to a new value.

This isn’t Bohmian mechanics since the trajectories are not deterministic and there is no guiding equation. The trajectories are random.