Entanglement of a nuclear spin qubit register in silicon photonics

Colour centres provide an optical interface to quantum registers based on electron and nuclear spin qubits in solids. The T centre in silicon is an emerging spin-photon interface that combines telecom O-band optical transitions and an electron spin in a scalable photonics platform. Here we integrate T centres into single-mode photonic waveguides in a silicon-on-insulator platform. We demonstrate the initialization, coherent control and state read-out of a three-qubit register based on the electron spin of a T centre 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 $T_2^{*}=2.60\left(8\right)$  ms. Our results show that a T centre in silicon photonics can realize a multi-qubit register with an optical interface for quantum communication.