  A widely used method for mitigating errors in noisy quantum computers is
Richardson extrapolation, a technique in which the overall effect of noise on
the estimation of quantum expectation values is captured by a single parameter
that, after being scaled to larger values, is eventually extrapolated to the
zero-noise limit. We generalize this approach by introducing \emph{layerwise
Richardson extrapolation (LRE)}, an error mitigation protocol in which the
noise of different individual layers (or larger chunks of the circuit) is
amplified and the associated expectation values are linearly combined to
estimate the zero-noise limit. The coefficients of the linear combination are
analytically obtained from the theory of multivariate Lagrange interpolation.
LRE leverages the flexible configurational space of layerwise unitary folding,
allowing for a more nuanced mitigation of errors by treating the noise level of
each layer of the quantum circuit as an independent variable. We provide
numerical simulations demonstrating scenarios where LRE achieves superior
performance compared to traditional (single-variable) Richardson extrapolation.
