The realization of a coherent interface between distant charge or spin qubits in semiconductor quantum dots is an open challenge for quantum information processing. Here we demonstrate both resonant and non-resonant photon-mediated coherent interactions between double quantum dot charge qubits separated by several tens of micrometers. We present clear spectroscopic evidence of the collective enhancement of the resonant coupling of two qubits. With both qubits detuned from the resonator we observe exchange coupling between the qubits mediated by virtual photons. In both instances pronounced bright and dark states governed by the symmetry of the qubit-field interaction are found. Our observations are in excellent quantitative agreement with masterequation simulations. The extracted two-qubit coupling strengths significantly exceed the linewidths of the combined resonator-qubit system. This indicates that this approach is viable for creating photon-mediated twoqubit gates in quantum dot based systems.Semiconductor nanostructure based systems are one of the promising contenders for quantum information processing since they offer flexibility in tuning, long coherence times and well-established fabrication techniques [1,2]. However, scaling to larger numbers of qubits remains a challenge, since many coupling mechanisms for realizing two-qubit gates are short range, i.e. limited to nearest neighbors. For scaling to larger systems and eventually to a full scale quantum computer, a combination of short and longer range interactions seems promising [3].So far, short range (∼ 100 nm) qubit-qubit interaction has been realized via capacitive or exchange coupling between charge [4-6] and spin qubits [7-10], which was expanded by making use of interactions mediated by additional qubits (∼ 400 nm) [11] or electronic cavities (∼ 1.7 µm) [12]. However, it is predicted that the range of interaction between semiconductor qubits can be increased significantly using microwave photons [3,13,14]. A key ingredient, the strong coupling of individual charges [15,16] or spins [17][18][19] to individual microwave photons, has recently been realized in semiconductor implementations of circuit quantum electrodynamics (QED) [20].Here, we present experiments in which the coherent photon-mediated coupling between two spatially separated semiconductor qubits is realized both in the resonant and the dispersive regime using high impedance SQUID array resonators. The high Josephson inductance of the SQUID array increases the strength of the vacuum fluctuations of the electric field, enhancing the coupling strength of the individual qubits to the resonator [16] and consequently the qubitqubit coupling, which allows us to overcome the limitations of prior experiments [17,21,22]. This key step holds the strong promise that two-qubit gates based on photon-mediated interactions, which are a corner-stone in quantum information processing with superconducting circuits [23], are implementable with semiconductor qubits based on a variety of material systems. ...
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