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