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Quantum dot hybrid qubits exploit an extended charge-noise sweet spot that suppresses dephasing and has enabled the experimental achievement of high-fidelity single-qubit gates. However, current proposals for two-qubit gates require tuning the qubits away from their sweet spots. Here, we propose a two-hybrid-qubit coupling scheme, based on exchange interactions, that allows the qubits to remain at their sweet spots at all times. The interaction is controlled via the inter-qubit tunnel coupling. By simulating such gates in the presence of realistic quasistatic and charge noise, we show that our scheme should enable controlled- gates of length 5~ns, and Z-CNOT gates of length 7~ns, both with fidelities 99.9%.

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