Quantum Volume Benchmark: Heavy Output Generation

Quantum Volume is the industry standard IBM introduced to grade real quantum processors with one number: run a random "square" circuit of n qubits and depth n, and check whether the machine still reproduces more probability mass in the upper half of the output distribution — the heavy outputs — than an untrained coin flip would. This simulator runs an actual complex-amplitude statevector simulation of that circuit (random SU(4) two-qubit gates over a random pairing, layer by layer), renders the circuit lattice and the resulting output-probability histogram in 3D, and then fires simulated measurement shots whose noise is driven by a gate-error slider, so you can watch the empirical heavy-output probability converge toward its theoretical value and see exactly where a device would pass or fail certification at QV = 2ⁿ.