Hardware-aware Toffoli gate decomposition via echoed cross-resonance gates

Abstract

Quantum computing promises transformative potential for solving classically intractable problems in chemistry, materials science, drug discovery, and optimization. However, current noisy intermediate-scale quantum (NISQ) devices face fundamental limitations due to decoherence, gate infidelity, and restricted qubit connectivity. Among critical quantum operations, the Toffoli gate (CCNOT)—essential for quantum algorithms and error correction—poses particular implementation challenges on near-term hardware. While various decomposition strategies have been proposed, most assume idealized all-to-all qubit connectivity, a feature unavailable on most existing NISQ architectures. We present a hardware-efficient Toffoli decomposition using native echoed cross-resonance (ECR) gates, specifically optimized for superconducting quantum architectures. Our approach leverages the natural advantages of ECR operations to reduce circuit complexity compared to CNOT-based methods, while simultaneously improving topological adaptability in constrained qubit connectivity environments. The decomposition demonstrates particular advantages in linear architectures, where it eliminates the need for SWAP operations while maintaining high operational fidelity. Experimental validation on IBM’s 127-qubit ibm_sherbrooke quantum computer demonstrates consistent high-fidelity performance across all operational regimes: target qubit activation (94.4%±0.3%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$94.4\% \pm 0.3\%$$\end{document}), deactivation (94.3%±0.3%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$94.3\% \pm 0.3\%$$\end{document}), and non-target state preservation (93.8%±0.3%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$93.8\% \pm 0.3\%$$\end{document}). The narrow 0.6% performance variation confirms the robustness of our implementation under real NISQ constraints, representing a significant advance for practical quantum circuit synthesis in real superconducting quantum hardware.