  Precision measurement plays a crucial role in all fields of science. The use
of entangled sensors in quantum metrology improves the precision limit from the
standard quantum limit (SQL) to the Heisenberg limit (HL). To date, most
experiments beating the SQL are performed on the sensors which are well
isolated under extreme conditions. However, it has not been realized in
solid-state spin systems at ambient conditions, owing to its intrinsic
complexity for the preparation and survival of pure and entangled quantum
states. Here we show a full interferometer sequence beating the SQL by
employing a hybrid multi-spin system, namely the nitrogen-vacancy (NV) defect
in diamond. The interferometer sequence starts from a deterministic and joint
initialization, undergoes entanglement and disentanglement of multiple spins,
and ends up with projective measurement. In particular, the deterministic and
joint initialization of NV negative state, NV electron spin, and two nuclear
spins is realized at room temperature for the first time. By means of optimal
control, non-local gates are implemented with an estimated fidelity above the
threshold for fault-tolerant quantum computation. With these techniques
combined, we achieve two-spin interference with a phase sensitivity of 1.79 \pm
0.06 dB beyond the SQL and three-spin 2.77 \pm 0.10 dB. Moreover, the
deviations from the HL induced by experimental imperfections are completely
accountable. The techniques used here are of fundamental importance for quantum
sensing and computing, and naturally applicable to other solid-state spin
systems.
