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Building efficient large-scale quantum computers is a significant challengedue to limited qubit connectivities and noisy hardware operations.Transpilation is critical to ensure that quantum gates are on physically linkedqubits, while minimizing $\texttt{SWAP}$ gates and simultaneously findingefficient decomposition into native $\textit{basis gates}$. The goal of thismultifaceted optimization step is typically to minimize circuit depth and toachieve the best possible execution fidelity. In this work, we propose$\textit{MIRAGE}$, a collaborative design and transpilation approach tominimize $\texttt{SWAP}$ gates while improving decomposition using$\textit{mirror gates}$. Mirror gates utilize the same underlying physicalinteractions, 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 advantagesover $\texttt{CNOT}$, we show how systems that implement the $\texttt{iSWAP}$family of gates can benefit from mirror gates. Further, $\textit{MIRAGE}$ usesmirror gates to reduce routing pressure and reduce true circuit depth insteadof just minimizing $\texttt{SWAP}$s. We explore the benefits of decompositionfor $\sqrt{\texttt{iSWAP}}$ and $\sqrt[4]{\texttt{iSWAP}}$ using mirror gates,including both expanding Haar coverage and conducting a detailed fault rateanalysis trading off circuit depth against approximate gate decomposition. Wealso describe a novel greedy approach accepting mirror substitution atdifferent aggression levels within MIRAGE. Finally, for $\texttt{iSWAP}$systems that use square-lattice topologies, $\textit{MIRAGE}$ provides anaverage of 29.6% reduction in circuit depth by eliminating an average of 59.9f%$\texttt{SWAP}$ gates, which ultimately improves the practical applicability ofour algorithm.

MIRAGE: Quantum Circuit Decomposition and Routing Collaborative Design using Mirror Gates