  To run a quantum program in the real device, the compiler maps the logical
qubits to physical qubits. This is the most crucial step of compiling a quantum
circuit. Because the fidelity of a quantum circuit depends heavily on this
mapping process. However, this qubit mapping problem is NP-complete. Therefore,
we should resort to heuristics to find high-fidelity mappings. In this paper,
we focused on finding efficient heuristic techniques to incorporate real-time
error feedback and device connectivity information in order to achieve high
fidelity mapping of the quantum circuits. We performed extensive analysis and
experimental study based on two baseline algorithms. We performed our
experimentation on various combinations of different error rates and heuristic
techniques. Consequently, we designed very elegant techniques to consider both
all types of real-time error feedback and connectivity information. We showed
that our best heuristic approach performs \textbf{1.62x} ( on average) better
than one baseline and \textbf{1.934x} ( on average ) better than the other
baseline on random benchmarks. Finally, we compared our best heuristic ( CAES )
with the state-of-the-art heuristic-based mapping algorithm on representative
benchmarks. We found that CAES performed \textbf{1.7x} ( on average ) better
than the state of the art in terms of success rate.
