A Toffoli Gate Decomposition via Echoed Cross-Resonance Gates

Quantum computing has garnered significant interest for its potential to solve certain computational problems much faster than the best-known classical algorithms. A fully functional and scalable quantum computer could transform various fields such as scientific research, material science, chemistry, and drug discovery. However, in the noisy intermediate-scale quantum (NISQ) era, quantum hardware faces challenges including decoherence, gate infidelity, and restricted qubit connectivity. Efficient implementation of multi-qubit gates is critical to advancing quantum computing, especially given the constraints of near-term quantum hardware, such as the absence of all-to-all qubit connectivity. Among these gates, the Toffoli gate (or CCNOT gate) plays a pivotal role in a wide range of quantum algorithms and error correction schemes. While various decomposition strategies have been proposed, they often assume idealized all-to-all connectivity, which is not available on most NISQ hardware. This paper introduces a novel decomposition of the Toffoli gate using Echoed Cross-Resonance (ECR) gates, a native operation for many superconducting qubit architectures, including IBM Quantum's hardware. By leveraging the inherent compatibility of ECR gates with superconducting qubit technology, this approach is intended to facilitate the implementation of the Toffoli gate, potentially reducing circuit depth and enhancing the efficiency of quantum circuits implementations on near-term quantum hardware.