  Building efficient large-scale quantum computers is a significant challenge
due to limited qubit connectivities and noisy hardware operations.
Transpilation is critical to ensure that quantum gates are on physically linked
qubits, while minimizing $\texttt{SWAP}$ gates and simultaneously finding
efficient decomposition into native $\textit{basis gates}$. The goal of this
multifaceted optimization step is typically to minimize circuit depth and to
achieve the best possible execution fidelity. In this work, we propose
$\textit{MIRAGE}$, a collaborative design and transpilation approach to
minimize $\texttt{SWAP}$ gates while improving decomposition using
$\textit{mirror gates}$. Mirror gates utilize the same underlying physical
interactions, but when their outputs are reversed, they realize a different or
$\textit{mirrored}$ quantum operation. Given the recent attention to
$\sqrt{\texttt{iSWAP}}$ as a powerful basis gate with decomposition advantages
over $\texttt{CNOT}$, we show how systems that implement the $\texttt{iSWAP}$
family of gates can benefit from mirror gates. Further, $\textit{MIRAGE}$ uses
mirror gates to reduce routing pressure and reduce true circuit depth instead
of just minimizing $\texttt{SWAP}$s. We explore the benefits of decomposition
for $\sqrt{\texttt{iSWAP}}$ and $\sqrt[4]{\texttt{iSWAP}}$ using mirror gates,
including both expanding Haar coverage and conducting a detailed fault rate
analysis trading off circuit depth against approximate gate decomposition. We
also describe a novel greedy approach accepting mirror substitution at
different aggression levels within MIRAGE. Finally, for $\texttt{iSWAP}$
systems that use square-lattice topologies, $\textit{MIRAGE}$ provides an
average of 29.6% reduction in circuit depth by eliminating an average of 59.9f%
$\texttt{SWAP}$ gates, which ultimately improves the practical applicability of
our algorithm.
