We investigate this approach to multi-qubit readout in a Type IIa polycrystalline diamond (PCD). The scanning confocal image in Fig. 1c shows NV centers in one domain of this PCD near a gold stripline for microwave delivery that cuts across a grain boundary, visible as the bright strip in the image. Despite the high strain of the PCD,24 its low nitrogen content allows for NVs with coherence times exceeding 200 µs (see Supplementary Fig. 2) at room temperature. The histogram of the NV optical transitions (Fig. 1d) indicates an inhomogeneous distribution with standard deviation of 294 GHz, nearly five times broader than what we measure in single-crystal diamond (SCD) samples.

Super-resolution localization

This broad inhomogeneous distribution allows us to spectrally distinguish NVs below the diffraction limit. Figure 1e shows a photoluminescence excitation (PLE) spectrum taken on a representative fluorescence site on the sample, labeled site 1 in the inset of Fig. 1c. The spectrum reveals several distinct zero-phonon line (ZPL) peaks, indicative of the presence of multiple NV centers within the diffraction-limited spot. Spatially scanning a narrow laser resonant with one of the transitions in Fig. 1e preferentially induces fluorescence from a single NV center, selectively imaging this defect out of the cluster. Performing this scan for each observed transition, we find that they correspond to only three spatial positions. Second-order autocorrelation and optically detected magnetic resonance measurements further confirm the presence of three NV centers in this site. The most prominent and well-isolated peaks for each NV center are labeled as A, B, and C in Fig. 1e. For these transitions, we repeat the resonant imaging experiment, each time fitting the result with a Gaussian point-spread function. The standard error on the fit centers gives a localization precision of 〈S A 〉 = 0.45 nm for the brightest and most spectrally distinct NV (see Supplementary Information for details). Figure 1f shows the reconstructed positions, with spot widths indicating 10 times the localization precision after 40 min of integration and the dashed overlay showing the full-width half-maximum size of the original diffraction-limited spot.

Readout-induced crosstalk

We next consider the crosstalk that an optical readout of one NV induces in other NVs in a diffraction-limited spot. For simplicity, we first study these dynamics in a simple spin-1 system associated with a single NV center (NV D ) in site 2 of Fig. 1c, which is initialized into state |ψ 0 〉 = |m s = 0〉 + |m s = 1〉. Suppose a laser is applied at frequency ω L for time T to perform resonant readout on a hypothetical neighboring NV. This laser non-resonantly excites NV D from ground state |i〉 into excited state |j〉, projecting its state by spontaneous emission into ground state |k〉, where i, k ∈ m s = {−1, 0, 1} and j ∈ {E 1 , E 2 , E x , E y , A 1 , A 2 }, with probability (see Supplementary Information):

$${\mathrm{\Gamma }}_{ijk} = 1 - {\mathrm{exp}}\left( { - \frac{{\gamma _{jk}{\mathrm{\Omega }}_{ij}^2T}}{{2({\mathrm{\Omega }}_{ij}^2 + {\mathrm{\Delta }}_{ij}^2)}}} \right),$$ (1)

where Δ ij is the detuning of ω L from NV D ’s |i〉 → |j〉 ground-to-excited state transition, Ω ij is the optical Rabi frequency, and γ jk is the excited state’s decay rate into |k〉. In addition to such a spontaneous-emission-induced state projection, NV D may also acquire a phase shift due to the AC stark shift of the applied laser; however, this is a weak and coherent process and can be compensated (see Supplementary Information).

We probe this laser-induced crosstalk using Ramsey interferometry, as illustrated in Fig. 2a. The application of an off-resonant laser (detuned by Δ from NV D ’s E x transition) for fixed time T during the free precession period τ projects the NV into the mixed state:

$$\rho = \left( {1 - {\mathrm{\Gamma }}} \right)|\psi \rangle \langle \psi | + \mathop {\sum}\limits_k \left( {\mathop {\sum}\limits_{ij} {\Gamma _{ijk}} |k\rangle \langle k|} \right),$$ (2)

where \(\left| \psi \right\rangle = \frac{1}{{\sqrt 2 }}\left( {\left| 0 \right\rangle + e^{ - i\theta (t)}\left| 1 \right\rangle } \right)\) is the result of the Ramsey experiment and \({\sum} {\Gamma _{ijk}} = \Gamma\). The summed terms in Eq. (2) are stationary states and provide no contrast in the Ramsey experiment, such that the fringe amplitude is directly proportional to 1 − Γ (see Supplementary Information). The final spin state (after the second π/2 pulse of the Ramsey sequence) is measured by state-dependent fluorescence F through 532 nm illumination. F is normalized to account for power fluctuations by repeating the sequence, but replacing the final π/2 gate with a 3π/2 gate and taking the contrast \(C = \frac{{(F_{3\pi /2} - F_{\pi /2})}}{{(F_{3\pi /2} + F_{\pi /2})}}\).

Fig. 2 Qubit degradation under near-resonant excitation for a single isolated nitrogen vacancy (NV). a Bloch sphere schematic for crosstalk measurement sequence. After a π/2 pulse prepares the qubit in a superposition state, it precesses around the Bloch sphere during application of a near-resonant laser. With probability (1 − Γ), the laser will not induce excitation and subsequent decay, preserving the phase built up during the precession period, which is then mapped into population by a second π/2 pulse and read out with a non-resonant readout pulse. However, the laser may also induce a spin-projecting decay event; in this scenario, the second π/2 pulse will always place the spin in an even superposition state, independent of any phase accumulated during the precessionary period, leading to a precession time-independent intensity at the final readout. b Ramsey sequences with a resonant laser of varying detunings applied during the free precession period. The fits (solid lines) have one fit parameter for the fringe amplitude relative to that of a reference Ramsey taken with no crosstalk laser. c Crosstalk probability as a function of laser detuning, taken by fixing the precession time to the fringe maximum at τ = 386 ns (dashed line in b) and sweeping the resonant laser detuning. The contrast values are normalized to the fringe amplitude from the no-laser case. In red, the model for Γ (Eq. 1) with one fit parameter for the optical Rabi frequency. Error bars in b, c show standard error Full size image

Figure 2b plots C for varying Δ. For Δ = 0, the Ramsey contrast vanishes, as expected for the laser-induced state projection. With increasing detuning, the fringe contrast recovers, approaching a control experiment without the readout laser.

We map the crosstalk as a function of Δ by fixing the precession time to the fringe maximum at 386 ns and sweeping the resonant laser over a wide range of detunings. These data are converted to a bit error probability in Fig. 2c by normalizing the fluorescence from each detuning to that from the reference “no-laser” control experiment (Fig. 2b), which gives the crosstalk-free case. The red curve represents our model from Eq. (1) with only one fit parameter for the optical Rabi frequency, which is difficult to accurately measure experimentally due to spectral diffusion of the ZPL. The optical excitation time T is fixed by our pulse generator, and the decay rate is determined by lifetime characterization. The theory shows good agreement with our data and indicates that a detuning of 16 GHz or greater keeps crosstalk errors below 1%, a regime accessible by the cluster at site 1 of Fig. 1c.

Low-crosstalk readout of individual qubits

We now demonstrate individual control and readout on this cluster. We achieve independent microwave control of the spin states by applying a magnetic field, which splits the spin levels depending on the NV center crystal orientation. In this cluster, we find that two of the NV centers (A and B) are oriented along one crystal axis and the third (C) along another, indicated by four dips in the magnetic resonance spectrum (see Supplementary Fig. 3).

We take advantage of this ground state splitting and apply the same Ramsey sequence from above to perform individual control and readout. Figure 3a shows the gate representation of our sequence. After initialization of all three NV centers with a 532 nm repump, the spin of NV C is coherently driven with a resonant microwave pulse for a time τ, inducing Rabi oscillations corresponding to a rotation of angle θ about the X-axis. Next, NVs A and B are rotated into an equal superposition state by a π/2 pulse, followed by a passive precession by angle ϕ about the Z-axis for the same time τ. While NVs A and B are in this phase-sensitive superposition state, we perform individual readout on NV C using a resonant optical pulse. After waiting a total precession time τ, a final π/2 pulse completes the Ramsey sequence on NVs A and B, and we read out these states with 532 nm light (see Supplementary Information for details). Note that while limitations in the available equipment necessitated the use of a non-resonant green readout on NVs A and B, additional lasers or modulators would allow for individual readout of each NV center in the cluster. Figure 3b shows the results of each readout window, where both gates measure the expected Rabi and Ramsey signals. Comparing these Ramsey results to that of a control Ramsey experiment on NVs A and B taken with no additional control or readout sequences on NV C, the fringe amplitudes are equal within our noise bounds (0 ± 4% bit error probability). That is, we find no detectable fringe amplitude degradation as a result of the resonant readout pulse, indicating that the states of the off-resonant NV centers are left unperturbed through this readout. This result is consistent with our model, which predicts a bit error probability of ~1%, below the 4% fit bounds.