  Quantum computation promises to advance a wide range of computational tasks.
However, current quantum hardware suffers from noise and is too small for error
correction. Thus, accurately utilizing noisy quantum computers strongly relies
on noise characterization, mitigation, and suppression. Crucially, these
methods must also be efficient in terms of their classical and quantum
overhead. Here, we efficiently characterize and mitigate crosstalk noise, which
is a severe error source in, e.g., cross-resonance based superconducting
quantum processors. For crosstalk characterization, we develop a simplified
measurement experiment. Furthermore, we analyze the problem of optimal
experiment scheduling and solve it for common hardware architectures. After
characterization, we mitigate noise in quantum circuits by a noise-aware qubit
routing algorithm. Our integer programming algorithm extends previous work on
optimized qubit routing by swap insertion. We incorporate the measured
crosstalk errors in addition to other, more easily accessible noise data in the
objective function. Furthermore, we strengthen the underlying integer linear
model by proving a convex hull result about an associated class of polytopes,
which has applications beyond this work. We evaluate the proposed method by
characterizing crosstalk noise for a complete 27 qubit chip and leverage the
resulting data to improve the approximation ratio of the Quantum Approximate
Optimization Algorithm by up to 10 % compared to other established noise-aware
routing methods. Our work clearly demonstrates the gains of including noise
data when mapping abstract quantum circuits to hardware native ones.
