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

Abstract

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 $\text{SWAP}$ gates and simultaneously finding efficient decomposition into native $\text{basis gates}$. 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 $\text{MIRAGE}$, a collaborative design and transpilation approach to minimize $\text{SWAP}$ gates while improving decomposition using $\text{mirror gates}$. Mirror gates utilize the same underlying physical interactions, but when their outputs are reversed, they realize a different or $\text{mirrored}$ quantum operation. Given the recent attention to $\sqrt{\text{iSWAP}}$ as a powerful basis gate with decomposition advantages over $\text{CNOT}$, we show how systems that implement the $\text{iSWAP}$ family of gates can benefit from mirror gates. Further, $\text{MIRAGE}$ uses mirror gates to reduce routing pressure and reduce true circuit depth instead of just minimizing $\text{SWAP}$s. We explore the benefits of decomposition for $\sqrt{\text{iSWAP}}$ and $\sqrt[4]{\text{iSWAP}}$ 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 $\text{iSWAP}$ systems that use square-lattice topologies, $\text{MIRAGE}$ provides an average of 29.6% reduction in circuit depth by eliminating an average of 59.9f% $\text{SWAP}$ gates, which ultimately improves the practical applicability of our algorithm.

13 pages, 13 figures. This paper is under review for the IEEE and/or ACM

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