Zero-Noise Extrapolation (2D): NISQ Error Mitigation Chart

Real quantum processors are noisy, so every circuit's measured expectation value is biased toward zero the deeper the circuit runs. Zero-noise extrapolation (ZNE) doesn't fix the hardware — it runs the same circuit deliberately stretched to 1×, 2× and 3× its gate count (unitary folding), samples the shot-noise expectation value at each stretch, and fits a curve back through the unphysical zero-noise point to estimate what a perfect processor would have measured. This 2D companion plots every individually sampled ±1 measurement shot as a scattered point on a flat noise-scale-vs-expectation-value chart, draws the true depolarizing decay curve ⟨O(c)⟩ = ⟨O⟩_ideal·(1−p)^cG underneath it, and lets you compare linear, Richardson and exponential extrapolation against the unmitigated raw reading and the known ideal value.