Semiconductor qubits rely on the control of charge and spin degrees of freedom of electrons or holes confined in quantum dots (QDs). They constitute a promising approach to quantum information processing [1, 2], complementary to superconducting qubits [3]. Typically, semiconductor qubit-qubit coupling is short range [1, 2, 4, 5], effectively limiting qubit distance to the spatial extent of the wavefunction of the confined particle, which represents a significant constraint towards scaling to reach dense 1D or 2D arrays of QD qubits. Following the success of circuit quantum eletrodynamics [6], the strong coupling regime between the charge [7, 8] and spin [9, 10, 11] degrees of freedom of electrons confined in semiconducting QDs interacting with individual photons stored in a microwave resonator has recently been achieved. In this letter, we demonstrate coherent coupling between a superconducting transmon qubit and a semiconductor double quantum dot (DQD) charge qubit mediated by virtual microwave photon excitations in a tunable high-impedance SQUID array resonator acting as a quantum bus [12, 13, 14]. The transmon-charge qubit coherent coupling rate ($ sim$ 21 MHz) exceeds the linewidth of both the transmon ($ sim$ 0.8 MHz) and the DQD charge ($ sim$ 3 MHz) qubit. By tuning the qubits into resonance for a controlled amount of time, we observe coherent oscillations between the constituents of this hybrid quantum system. These results enable a new class of experiments exploring the use of the two-qubit interactions mediated by microwave photons to create entangled states between semiconductor and superconducting qubits. The methods and techniques presented here are transferable to QD devices based on other material systems and can be beneficial for spin-based hybrid systems.
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