  Trapped-ion (TI) quantum computer is one of the forerunner quantum
technologies. However, TI systems can have a limited number of qubits in a
single trap. Execution of meaningful quantum algorithms requires a multiple
trap system. In such systems, the computation may frequently involve ions from
two different traps for which the qubits must be co-located in the same trap,
hence one of the ions needs to be shuttled (moved) between traps, increasing
the vibrational energy, degrading fidelity, and increasing the program
execution time. The choice of initial mapping influences the number of
shuttles. The existing Greedy policy counts the number of gates occurring
between each pair of qubits and assigns edge weight. The qubits with high edge
weights are placed close to each other. However, it neglects the stage of the
program at which the gate is occurring. Intuitively, the contribution of the
late-occurring gates to the initial mapping reduces since the ions might have
already shuttled to a different trap to satisfy other gate operations. In this
paper, we target this gap and propose a new policy especially for programs with
considerable depth and high number of qubits (valid for practical-scale quantum
programs). Our policy is program adaptive and prioritizes the gates
re-occurring at the initial stages of the program over late occurring gates.
Our technique achieves an average reduction of 9% shuttles/program (with 21.3%
at best) for 120 random circuits and enhances the program fidelity up to 3.3X
(1.41X on average).
