Coherent spin-spin coupling mediated by virtual microwave photons

We report the coherent coupling of two electron spins at a distance via virtual microwave photons. Each spin is trapped in a silicon double quantum dot at either end of a superconducting resonator, achieving spin-photon couplings up to around $g_s/2\pi = 40 \ \text{MHz}$. As the two spins are brought into resonance with each other, but detuned from the photons, an avoided crossing larger than the spin linewidths is observed with an exchange splitting around $2J/2\pi = 20 \ \text{MHz}$. In addition, photon-number states are resolved from the shift $2\chi_s/2\pi = -13 \ \text{MHz}$ that they induce on the spin frequency. These observations demonstrate that we reach the strong dispersive regime of circuit quantum electrodynamics with spins. Achieving spin-spin coupling without real photons is essential to long-range two-qubit gates between spin qubits and scalable networks of spin qubits on a chip.