  We propose a general framework for quantum error mitigation that combines and
generalizes two techniques: probabilistic error cancellation (PEC) and
zero-noise extrapolation (ZNE). Similarly to PEC, the proposed method
represents ideal operations as linear combinations of noisy operations that are
implementable on hardware. However, instead of assuming a fixed level of
hardware noise, we extend the set of implementable operations by noise scaling.
By construction, this method encompasses both PEC and ZNE as particular cases
and allows us to investigate a larger set of hybrid techniques. For example,
gate extrapolation can be used to implement PEC without requiring knowledge of
the device's noise model, e.g., avoiding gate set tomography. Alternatively,
probabilistic error reduction can be used to estimate expectation values at
intermediate virtual noise strengths (below the hardware level), obtaining
partially mitigated results at a lower sampling cost. Moreover, multiple
results obtained with different noise reduction factors can be further
post-processed with ZNE to better approximate the zero-noise limit.
