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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., Comment: 9 pages, 6 figures

Electron spins hold great promise for quantum computation due to their long coherence times. An approach to realize interactions between distant spin-qubits is to use photons as carriers of quantum information. We demonstrate strong coupling between single microwave photons in a NbTiN high impedance cavity and a three-electron spin-qubit in a GaAs triple quantum dot. We resolve the vacuum Rabi mode splitting with a coupling strength of $g/2\pi\simeq31$ MHz and a qubit decoherence of $\gamma_2/2\pi\simeq 20$ MHz. We can tune the decoherence electrostatically and obtain a minimal $\gamma_2/2\pi\simeq 10$ MHz for $g/2\pi\simeq 23$ MHz. The dependence of the qubit-photon coupling strength on the tunable electric dipole moment of the qubit is measured directly using the ac Stark effect. Our demonstration of strong spin-photon interaction is an important step towards coherent long-distance coupling of spin-qubits.

We report the strong coupling of a single electron spin and a single microwave photon. The electron spin is trapped in a silicon double quantum dot and the microwave photon is stored in an on-chip high-impedance superconducting resonator. The electric field component of the cavity photon couples directly to the charge dipole of the electron in the double dot, and indirectly to the electron spin, through a strong local magnetic field gradient from a nearby micromagnet. This result opens the way to the realization of large networks of quantum dot based spin qubit registers, removing a major roadblock to scalable quantum computing with spin qubits.

We present a microscopic theory of the optical properties of self-assembled quantum dots doped with a single magnetic manganese (Mn) impurity and containing a controlled number of electrons. The single-particle electron and heavy-hole electronic shells are described by two-dimensional harmonic oscillators. The electron-electron, electron-hole Coulomb as well as the short-range electron spin-Mn spin and hole spin-Mn spin contact exchange interactions are included. The electronic states of the photo-excited electron-hole-Mn complex and of the final electron-Mn complex are expanded in a finite number of configurations and the full interacting Hamiltonian is diagonalized numerically. The emission spectrum is predicted as a function of photon energy for a given number of electrons and different number of confined electronic quantum dot shells. We show how emission spectra allow to identify the number of electronic shells, the number of electrons populating these shells and, most importantly, their spin. We show that electrons not interacting directly with the spin of Mn ion do so via electron-electron interactions. This indirect interaction is a strong effect even when Mn impurity is away from the quantum dot center., Comment: 12 pages, 10 figures