  Achieving near-term quantum advantage will require effective methods for
mitigating hardware noise. Data-driven approaches to error mitigation are
promising, with popular examples including zero-noise extrapolation (ZNE) and
Clifford data regression (CDR). Here we propose a novel, scalable error
mitigation method that conceptually unifies ZNE and CDR. Our approach, called
variable-noise Clifford data regression (vnCDR), significantly outperforms
these individual methods in numerical benchmarks. vnCDR generates training data
first via near-Clifford circuits (which are classically simulable) and second
by varying the noise levels in these circuits. We employ a noise model obtained
from IBM's Ourense quantum computer to benchmark our method. For the problem of
estimating the energy of an 8-qubit Ising model system, vnCDR improves the
absolute energy error by a factor of 33 over the unmitigated results and by
factors 20 and 1.8 over ZNE and CDR, respectively. For the problem of
correcting observables from random quantum circuits with 64 qubits, vnCDR
improves the error by factors of 2.7 and 1.5 over ZNE and CDR, respectively.
