Error *mitigation* improves a noisy device's answers without correcting its errors. One method is *zero-noise extrapolation*: run the circuit at its own noise, then again with the noise deliberately scaled up by known factors, and extrapolate the measured values back to zero noise.

To scale noise without changing what a circuit computes, *fold* it: replace a gate G by G G⁻¹ G. The three gates do what G does, and carry three times its noise. Fold every two-qubit gate to scale the dominant noise by 3; fold some of them for the factors in between.

With an expectation value E(1) at the device's noise and E(3) with the gates folded, the linear (Richardson) extrapolation to zero noise is

E(0) ≈ (3·E(1) − E(3)) / 2.

The intent here is *equivalent*: the folded program must be the same circuit as the original, which the engine proves by the stabilizer tableau. The Studio's noise fields, or `--noise` on the command line, run the two versions side by side, to see ⟨Z0 Z1⟩ fall as the noise is scaled.