Constructing Three-Qubit Gate Pulse Sequences in Exchange-Only Spin System

We have developed an efficient method for constructing three-qubit gate sequences in exchange-only (EO) spin systems, which are promising for scalable quantum computing due to their all-electronic control and ability to bypass microwave-associated correlated error sources. By encoding three logical qubits into a chain of nine physical spins within a decoherence-free subspace, we applied quantum optimal control techniques to significantly optimize multi-qubit gate operations. Specifically, we implemented the Toffoli gate—a crucial component for quantum algorithms and error correction—with only 92 exchange pulses and 50 time steps, reducing the complexity by more than half compared to conventional methods. This advancement not only enhances gate fidelity by improving robustness against noise and crosstalk but also addresses key challenges in scaling EO qubit systems. Our work contributes to the development of practical, fault-tolerant quantum computers, making complex quantum computations more feasible and bringing us closer to realizing the full potential of quantum information processing.