Quantum Volume Benchmark: Heavy-Output Sampling

Quantum Volume is the industry-standard way to answer "how good is this quantum computer, really?" — not just how many qubits it has, but how deep a genuinely random circuit it can run before noise wins. This simulator runs the real protocol: it builds a random square model circuit of width m and depth m out of random two-qubit entangling blocks, computes the exact ideal output distribution on a full state-vector simulator to identify the "heavy" outcomes, then re-runs the same circuit through a stochastic per-gate noise model and checks whether at least two-thirds of noisy measurement samples still land in the heavy set. Sweep across qubit counts to find the largest width that still passes, and watch how quickly a higher per-gate error rate collapses the achievable Quantum Volume — the same trade-off that defines the real race between IBM, Google, Quantinuum and Rigetti hardware.