  The intrinsic probabilistic nature of quantum systems makes error correction
or mitigation indispensable for quantum computation. While current
error-correcting strategies focus on correcting errors in quantum states or
quantum gates, these fine-grained error-correction methods can incur
significant overhead for quantum algorithms of increasing complexity. We
present a first step in achieving error correction at the level of quantum
algorithms by combining a unified perspective on modern quantum algorithms via
quantum signal processing (QSP). An error model of under- or over-rotation of
the signal processing operator parameterized by $\epsilon < 1$ is introduced.
It is shown that while Pauli $Z$-errors are not recoverable without additional
resources, Pauli $X$ and $Y$ errors can be arbitrarily suppressed by coherently
appending a noisy `recovery QSP.' Furthermore, it is found that a recovery QSP
of length $O(2^k c^{k^2} d)$ is sufficient to correct any length-$d$ QSP with
$c$ unique phases to $k^{th}$-order in error $\epsilon$. Allowing an additional
assumption, a lower bound of $\Omega(cd)$ is shown, which is tight for $k = 1$,
on the length of the recovery sequence. Our algorithmic-level error correction
method is applied to Grover's fixed-point search algorithm as a demonstration.
