Entanglement of a nuclear spin qubit register in silicon photonics

Color centers provide an optical interface to quantum registers based on electron and nuclear spin qubits in solids. The T center in silicon is an emerging spin-photon interface that combines telecom O-band optical transitions and an electron spin in a scalable photonics platform. In this work, we demonstrate the initialization, coherent control, and state readout of a three-qubit register based on the electron spin of a T center coupled to a hydrogen and a silicon nuclear spin. The spin register exhibits spin echo coherence times of $0.41(2)$~ms for the electron spin, $112(12)$~ms for the hydrogen nuclear spin, and $67(7)$~ms for the silicon nuclear spin. We use nuclear-nuclear two-qubit gates to generate entanglement between the two nuclear spins with a fidelity of $F=0.77(3)$ and a coherence time of $T^*_2=2.60(8)$~ms. Our results show that a T center in silicon photonics can realize a multi-qubit register with an optical interface for quantum communication.