Simulating a quantum sensor: quantum state tomography of NV-spin systems

Abstract: We employ a quantum computer to simulate the effect of spin impurities on nitrogen-vacancy (NV) centers in diamond. As these defects operate as nanoscale quantum sensors, modeling quantum noise is crucial to identify limitations in precision. The analysis is performed by means of quantum state tomography on two transmon qubits, representing respectively the NV center and a single spin impurity, modeling either a nuclear spin or an additional NV center. We demonstrate a versatile platform to simulate benchmark protocols such as Ramsey or Hahn-echo. Although we focus on a two-spin system, the same approach opens the door to using quantum processors as scalable simulators of many-spin environments, intractable in classical simulation due to the rapid exponential growth of the Hilbert space. The results reveal the effect different spin-sensor coupling regimes have on coherence, helping to identify detection schemes that maximize the sensitivity under the effect of impurities. Moreover, the role of entanglement generation is analyzed using the Peres-Horodecki criterion and CHSH inequalities. Although no violation of the latter is observed, the presence of entanglement is confirmed.