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.

Figures (16)

• Figure 1: Schematic of sensor--impurity configurations considered in the present work. (Top, red) Main NV$^{-}$ considered as the sensor, where the $\ket{0} \leftrightarrow \ket{-1}$ is exploited for sensing. (Red--green combination) NV$^{-}$--$^{13}$C coupling described by the interaction term $S'_{z}I_{z}$, representing a nuclear spin $I = 1/2$ that induces stochastic magnetic--field noise in the NV$^{-}$'s dynamics. (Red--blue combination) NV$^{-}$--NV$^{-}$ coupling described by the interaction term $S'_{z}S"_{z}$, corresponding to a coherent regime that induces quantum correlations between both NV centers.
• Figure 2: Ramsey sequence used to estimate $T_2^*$. Two $\pi /2$ pulses are separated by a free--evolution time $\tau$.
• Figure 3: Hahn echo sequence used to estimate $T_{2}$. A refocusing $\pi$ pulse is implemented between the two free--evolution intervals.
• Figure 4: Seven-qubit superconducting architecture based on transmon qubits. Each qubit is coupled to an individual resonator for control and readout, while two bus resonators (red) enable coherent two-qubit gates.
• Figure 5: Gaussian-shaped microwave pulses for coherent qubit manipulation, illustrating two rotation axes determined by the phase $\phi$. The orange solid curve corresponds to a pulse with $\phi=0$ (rotation around $X$) and the dashed blue curve corresponds to $\phi=\pi/2$ (rotation around $Y$). The shaded gray region denotes the truncated window where the pulse is applied ($\pm 3\sigma$); outside this window the pulse is assumed negligible. The pulses are characterized by amplitude ($A$), angular frequency ($\omega$), phase ($\phi$), temporal width ($\sigma$), and pulse center ($t_0$).