  We present a quantum circuit optimization technique that takes into account
the variability in error rates that is inherent across present day noisy
quantum computing platforms. This method can be run post qubit routing or
post-compilation, and consists of computing isomorphic subgraphs to input
circuits and scoring each using heuristic cost functions derived from system
calibration data. Using an independent standard algorithmic test suite we show
that it is possible to recover on average nearly 40% of missing fidelity using
better qubit selection via efficient to compute cost functions. We demonstrate
additional performance gains by considering qubit placement over multiple
quantum processors. The overhead from these tools is minimal with respect to
other compilation steps, such as qubit routing, as the number of qubits
increases. As such, our method can be used to find qubit mappings for problems
at the scale of quantum advantage and beyond.
