Random Circuit Sampling Lab (2D)

A from-scratch, 2D-canvas companion to the 3D Random Circuit Sampling Lab: the same real random-circuit-sampling protocol — random single-qubit rotations plus CZ entangling gates applied layer by layer to an exact complex statevector of dimension 2^N — is simulated exactly for N = 2 to 8 qubits, small enough to track every one of the D basis-state amplitudes directly. Beyond watching a single circuit's output distribution scramble live, this version runs a statistical batch of many independent random circuit instances, pools every resulting probability, and overlays the pooled histogram against the theoretical Porter–Thomas exponential curve P(x) = e^−x — a direct numerical check that random quantum circuits really do produce the chaotic "speckle" statistics that real quantum-supremacy experiments are benchmarked against.