Nuclear Spin-Assisted Protocols

• Nuclear spin-assisted protocols are hybrid methods that couple fast electronic, orbital, or Rydberg degrees of freedom with nuclear spins to extend coherence and sharpen spectral selectivity.
• They employ techniques like dynamical decoupling, Floquet engineering, and adiabatic control to implement quantum memory, entangling gates, and high-resolution spectroscopy across platforms such as diamond NV centers, donor silicon, and SiC defects.
• Practical implementations demonstrate enhanced coherence times from microseconds to milliseconds, polarization fidelities above 99%, and sub-100 Hz spectral resolution for nanoscale imaging.

Nuclear spin-assisted protocols comprise a class of control, sensing, initialization, and memory methods in which a fast electronic, orbital, or Rydberg degree of freedom is coupled to one or more nuclear spins and the resulting hybrid dynamics are used to extend coherence, sharpen spectral selectivity, polarize nuclear registers, or implement entangling gates. In diamond NV centers, the category includes SWAP-based quantum memory, dynamical-decoupling protocols extended by nuclear flips, and multi-nuclear registers used for spectroscopy and imaging (Kenny et al., 19 Jul 2025). Closely related constructions appear in donor-based silicon, transition-metal defects in SiC, rare-earth-ion crystals, and weak-field neutral-atom platforms, where hyperfine interaction, Floquet engineering, and conditional evolution provide the operative mechanism (Boross et al., 2017, Tissot et al., 2022, Ruskuc et al., 2021, Shi, 2022).

1. Physical basis and Hamiltonian structure

The unifying feature of nuclear spin-assisted protocols is the use of a hybrid Hamiltonian in which a controllable non-nuclear subsystem modulates nuclear precession or mediates effective nuclear interactions. For NV centers, a standard starting point is

$$H = D\,S_z^2 + \gamma_e\,\mathbf{B}\cdot\mathbf{S} + S\cdot A\cdot I + Q\,I_z^2 + \gamma_n\,\mathbf{B}\cdot I,$$

with $D \approx 2.87\,\mathrm{GHz}$, $Q \approx 5.04\,\mathrm{MHz}$ for ${}^{14}\mathrm N$, and a hyperfine tensor $A$ that is often treated in the secular approximation as $$A \approx \mathrm{diag}(A_\parallel,A_\perp,A_\perp)$$ (Kenny et al., 19 Jul 2025). In this setting, the electron spin supplies fast control and optical readout, while the nuclear spin supplies long-lived storage and narrow spectral response.

In dynamical-decoupling formulations, the same idea is expressed through a modulation function $F(t)=\pm 1$ that flips sign at each $\pi$-pulse. For selective addressing of nuclei surrounding an NV center, the interaction-picture Hamiltonian can be written as

$$H_{\rm int}(t)= m_s\,F(t)\,\tfrac12 \sigma_z \otimes \sum_j d_j\cdot I_j^\perp(t),$$

and after Fourier expansion of $F(t)$ and an RWA one obtains an effective resonant coupling when $D \approx 2.87\,\mathrm{GHz}$0 (Casanova et al., 2015). This recasts nuclear-spin assistance as a filter-design problem: electron control shapes the spectral window through the coefficients $D \approx 2.87\,\mathrm{GHz}$1, while the nuclei provide the sharply resolved frequencies.

A complementary formulation uses periodic Floquet dynamics. For a DD protocol of period $D \approx 2.87\,\mathrm{GHz}$2, the one-period propagator

$D \approx 2.87\,\mathrm{GHz}$3

defines quasienergies and Floquet eigenstates, and slow variation of the interpulse spacing $D \approx 2.87\,\mathrm{GHz}$4 becomes adiabatic motion in a Floquet spectrum (Whaites et al., 2021). In this picture, nuclear-spin assistance is not merely an ancillary storage resource; it is a source of avoided crossings, robust manifolds, and controllable branch-following.

Donor systems in semiconductors realize the same structure with a different microscopic mechanism. For a phosphorus donor in silicon tunnel-coupled to an interface dot, the minimal Hamiltonian contains orbital detuning, electron and nuclear Zeeman terms, contact hyperfine interaction $D \approx 2.87\,\mathrm{GHz}$5, spin-orbit or magnetic-gradient terms, and an ac electric drive $D \approx 2.87\,\mathrm{GHz}$6 (Boross et al., 2017). Here the nuclear spin is assisted not only by electron-mediated amplification of ac magnetic control, but also by electrically induced Knight fields.

2. Coherence storage and selective control

A central use of nuclear spin assistance is coherence storage. In NV centers, electron-to-nuclear SWAP or controlled-NOT gates transfer the electron superposition into a long-lived nuclear register with $D \approx 2.87\,\mathrm{GHz}$7 to several ms, and Hartmann-Hahn cross-polarization is obtained by matching the electron Rabi frequency to the nuclear Larmor frequency, $D \approx 2.87\,\mathrm{GHz}$8 (Kenny et al., 19 Jul 2025). The same review reports that memory-assisted correlation spectroscopy with $D \approx 2.87\,\mathrm{GHz}$9 achieves resolution $Q \approx 5.04\,\mathrm{MHz}$0, while an AC-field spectrum analyzer narrows linewidth from $Q \approx 5.04\,\mathrm{MHz}$1 to $Q \approx 5.04\,\mathrm{MHz}$2 by extending coherent detection from $Q \approx 5.04\,\mathrm{MHz}$3 to $Q \approx 5.04\,\mathrm{MHz}$4 (Kenny et al., 19 Jul 2025).

Selective control has been pushed further by non-equally spaced decoupling. The AXY-$Q \approx 5.04\,\mathrm{MHz}$5 family constructs each period from composite $Q \approx 5.04\,\mathrm{MHz}$6 and $Q \approx 5.04\,\mathrm{MHz}$7 pulses with symmetry constraints that cancel first- and second-order pulse errors and permit direct engineering of Fourier coefficients $Q \approx 5.04\,\mathrm{MHz}$8 (Casanova et al., 2015). This removes the geometric rigidity of standard equally spaced CPMG and XY sequences. Numerical studies on an ensemble of 736 $Q \approx 5.04\,\mathrm{MHz}$9 spins at natural abundance 1.1% with ${}^{14}\mathrm N$0 report selectivity bandwidths ${}^{14}\mathrm N$1, contrast ${}^{14}\mathrm N$2 in ${}^{14}\mathrm N$3, and negligible distortion of resonance patterns over ${}^{14}\mathrm N$4 detuning and ${}^{14}\mathrm N$5 amplitude error (Casanova et al., 2015).

State selectivity can also be built into the avoided crossings themselves. Dynamical nuclear spin state selective protocols modify CPMG by introducing a detuning ${}^{14}\mathrm N$6, which splits the Floquet crossings into

${}^{14}\mathrm N$7

with ${}^{14}\mathrm N$8 generated by pulse imperfection (Lang et al., 2018). The result is nuclear-state-dependent symmetry sectors: one crossing selectively entangles the ${}^{14}\mathrm N$9 component, the other the $A$0 component. For a weakly coupled $A$1 with $A$2 at $A$3, numerical simulation gives nuclear polarization approaching unity after $A$4 pulses, with fidelity $A$5 (Lang et al., 2018).

High-fidelity entangling control can also be optimized at the sequence level. Hybrid CPMG–UDD protocols for NV centers treat the conditional nuclear propagator as a rotation $A$6 and combine CPMG’s coarse control with UDD’s finer tuning (2002.01480). Reported benchmarks include $A$7 gates with $A$8 in roughly $A$9, together with narrower coherence dips and improved spin selectivity relative to CPMG alone (2002.01480).

At a larger scale, the NV electron can mediate arbitrary many-body nuclear gates. AXY-8-based selective electron–nuclear primitives $$A \approx \mathrm{diag}(A_\parallel,A_\perp,A_\perp)$$0 can be concatenated with fast electron rotations to synthesize $$A \approx \mathrm{diag}(A_\parallel,A_\perp,A_\perp)$$1-body operations and directly map nuclear many-body correlators to a single electronic readout channel (Casanova et al., 2017). A concrete three-qubit GHZ-type gate is simulated with fidelity $$A \approx \mathrm{diag}(A_\parallel,A_\perp,A_\perp)$$2 using 3 202 imperfect $$A \approx \mathrm{diag}(A_\parallel,A_\perp,A_\perp)$$3-pulses (Casanova et al., 2017).

3. Floquet, adiabatic, and measurement-conditioned variants

An important development is the reinterpretation of DD control as adiabatic evolution in Floquet space. In adiabatic DD-based control of nuclear spin registers around NV centers, the interpulse spacing $$A \approx \mathrm{diag}(A_\parallel,A_\perp,A_\perp)$$4 is slowly swept so that robust Floquet eigenstates are followed across avoided crossings (Whaites et al., 2021). Near a two-level crossing, the adiabaticity is quantified by the Landau-Zener formula

$$A \approx \mathrm{diag}(A_\parallel,A_\perp,A_\perp)$$5

with $$A \approx \mathrm{diag}(A_\parallel,A_\perp,A_\perp)$$6 and a protocol-dependent velocity $$A \approx \mathrm{diag}(A_\parallel,A_\perp,A_\perp)$$7 (Whaites et al., 2021). Simulations report $$A \approx \mathrm{diag}(A_\parallel,A_\perp,A_\perp)$$8 single-spin polarization in one adiabatic Ad-PolCPMG sweep, $$A \approx \mathrm{diag}(A_\parallel,A_\perp,A_\perp)$$9 for state storage with a $F(t)=\pm 1$0 sweep, and $F(t)=\pm 1$1 up to $F(t)=\pm 1$2 while the same pulses protect NV coherence (Whaites et al., 2021). This suggests that nuclear-spin assistance can be merged with coherence protection rather than appended after it.

A different route uses post-selected measurements instead of deterministic coherent transfer. In the spin-star model of measurement-induced nuclear spin polarization, a central spin-1/2 with homogeneous flip-flop couplings to $F(t)=\pm 1$3 bath spins evolves for an interval $F(t)=\pm 1$4, after which a projective measurement postselects the central spin in its ground state (Jin et al., 2022). The reduced bath map is diagonal in Dicke sectors, and in the near-resonant regime the optimal interval is

$F(t)=\pm 1$5

Unequal-time-spacing measurements obtained by updating $F(t)=\pm 1$6 after each round maintain near-maximal cooling (Jin et al., 2022). Numerically, for $F(t)=\pm 1$7 and fewer than 20 unequal-spacing measurements, the bath reaches $F(t)=\pm 1$8 and the entropy approaches zero, although the full-sequence success probability is only of order $F(t)=\pm 1$9 (Jin et al., 2022).

Hyperpolarization protocols reveal an additional Floquet effect: polarization blockade. For PulsePol-type transfer, a strongly coupled “blocking” spin with coupling $\pi$0 displaces the resonance of a weaker spin from $\pi$1 to

$\pi$2

without, in general, significant weakening of the weaker resonance (Whaites et al., 2023). In the reported NV+C3+C16 example, a two-stage schedule with 200 repetitions at the shifted weak-spin resonance and 200 at the blocker resonance increases the weaker-spin polarization from below 0.2 to above 0.3 in the same total time, corresponding to a $\pi$3 speed-up (Whaites et al., 2023). This corrects a common misinterpretation in which missing or displaced resonances are attributed only to dark states or poor coupling.

Low-power variants address a separate control bottleneck. Extended $\pi$4-pulse designs modulate the intrapulse profile so that a chosen harmonic $\pi$5 remains tunable even when $\pi$6 is long, yielding

$\pi$7

for the targeted harmonic (1901.10366). Embedded in XY-8, these sequences resolve five proton resonances with total sensing time $\pi$8 while maintaining low average microwave power (1901.10366).

4. Hyperpolarization and initialization protocols

Hyperpolarization is one of the oldest and most direct manifestations of nuclear spin assistance. In room-temperature diamond, optically induced dynamic nuclear spin polarization uses 532 nm laser pumping of the NV center, followed by either Hartmann-Hahn NOVEL spin-locking or quasi-adiabatic integrated solid-effect frequency sweeps (Scheuer et al., 2016). For bulk diamond at $\pi$9, a $$H_{\rm int}(t)= m_s\,F(t)\,\tfrac12 \sigma_z \otimes \sum_j d_j\cdot I_j^\perp(t),$$0 spin-lock with $$H_{\rm int}(t)= m_s\,F(t)\,\tfrac12 \sigma_z \otimes \sum_j d_j\cdot I_j^\perp(t),$$1 matches the $$H_{\rm int}(t)= m_s\,F(t)\,\tfrac12 \sigma_z \otimes \sum_j d_j\cdot I_j^\perp(t),$$2 Larmor frequency, while a 100 MHz-wide triangular frequency sweep at $$H_{\rm int}(t)= m_s\,F(t)\,\tfrac12 \sigma_z \otimes \sum_j d_j\cdot I_j^\perp(t),$$3 implements the angle-robust variant (Scheuer et al., 2016). The reported room-temperature $$H_{\rm int}(t)= m_s\,F(t)\,\tfrac12 \sigma_z \otimes \sum_j d_j\cdot I_j^\perp(t),$$4 NMR enhancement is $$H_{\rm int}(t)= m_s\,F(t)\,\tfrac12 \sigma_z \otimes \sum_j d_j\cdot I_j^\perp(t),$$5 over thermal, with build-up in about 5 min, and the integrated solid-effect protocol remains effective for misalignment up to $$H_{\rm int}(t)= m_s\,F(t)\,\tfrac12 \sigma_z \otimes \sum_j d_j\cdot I_j^\perp(t),$$6 (Scheuer et al., 2016).

Pulse-engineered hyperpolarization has recently been generalized into “magic” and “digital” sequential sequences. In the magic sequential protocol, the effective unitary is engineered so that the steady-state polarization

$$H_{\rm int}(t)= m_s\,F(t)\,\tfrac12 \sigma_z \otimes \sum_j d_j\cdot I_j^\perp(t),$$7

satisfies $$H_{\rm int}(t)= m_s\,F(t)\,\tfrac12 \sigma_z \otimes \sum_j d_j\cdot I_j^\perp(t),$$8 at the magic phases $$H_{\rm int}(t)= m_s\,F(t)\,\tfrac12 \sigma_z \otimes \sum_j d_j\cdot I_j^\perp(t),$$9 or $F(t)$0, independent of $F(t)$1 (Li et al., 25 Apr 2025). The comparison with PulsePol at $F(t)$2 and $F(t)$3 shows that when the half-$F(t)$4 pulse duration increases to $F(t)$5, PulsePol falls to $F(t)$6 and $F(t)$7, whereas two new magic sequences maintain $F(t)$8 and $F(t)$9, with $D \approx 2.87\,\mathrm{GHz}$00 and $D \approx 2.87\,\mathrm{GHz}$01, respectively (Li et al., 25 Apr 2025). The significance of this result lies in high-field operation, where finite pulse duration is no longer a perturbative nuisance.

Transition-metal defects in SiC provide an all-optical initialization route. For $D \approx 2.87\,\mathrm{GHz}$02 in 4H-SiC, the optical drive and Lindblad decay generate a ratchet-type pumping process with suppressed backward nuclear steps, driving the system into the dark steady state $D \approx 2.87\,\mathrm{GHz}$03 (Tissot et al., 2022). Full master-equation simulations at $D \approx 2.87\,\mathrm{GHz}$04, $D \approx 2.87\,\mathrm{GHz}$05, $D \approx 2.87\,\mathrm{GHz}$06, and $D \approx 2.87\,\mathrm{GHz}$07 give $D \approx 2.87\,\mathrm{GHz}$08, and the summary states deterministic polarization in $D \approx 2.87\,\mathrm{GHz}$09 with $D \approx 2.87\,\mathrm{GHz}$10 fidelity (Tissot et al., 2022). Once polarized, neighboring $D \approx 2.87\,\mathrm{GHz}$11-levels form a ZEFOZ-like qubit with $D \approx 2.87\,\mathrm{GHz}$12 extrapolated to milliseconds to seconds and Hahn-echo $D \approx 2.87\,\mathrm{GHz}$13 extending to seconds at cryogenic temperature (Tissot et al., 2022).

Dense nuclear hosts can also be polarized collectively. In $D \approx 2.87\,\mathrm{GHz}$14, the engineered exchange Hamiltonian called ZenPol couples the Yb qubit to a four-spin $D \approx 2.87\,\mathrm{GHz}$15 register and polarizes the register by alternating resonances at $D \approx 2.87\,\mathrm{GHz}$16 and $D \approx 2.87\,\mathrm{GHz}$17 (Ruskuc et al., 2021). Saturation in about 10 cycles indicates $D \approx 2.87\,\mathrm{GHz}$18 polarization into the collective ground configuration, with overall polarization fidelity estimated at $D \approx 2.87\,\mathrm{GHz}$19 (Ruskuc et al., 2021).

5. Electrically and optically assisted nuclear-spin gates

Not all nuclear spin-assisted protocols rely on repeated microwave decoupling. In donor-based silicon, hyperfine interaction can directly amplify magnetic driving and convert electric fields into efficient nuclear control. For an isolated phosphorus donor driven by an ac magnetic field $D \approx 2.87\,\mathrm{GHz}$20, the electron adiabatically follows the total field and generates an additional Knight field so that the effective nuclear drive becomes

$D \approx 2.87\,\mathrm{GHz}$21

with Rabi frequency

$D \approx 2.87\,\mathrm{GHz}$22

(Boross et al., 2017). In a single-electron dot-donor setup at the tipping point, the electric-drive Rabi frequency obeys

$D \approx 2.87\,\mathrm{GHz}$23

whereas in the two-electron configuration

$D \approx 2.87\,\mathrm{GHz}$24

in the limit $D \approx 2.87\,\mathrm{GHz}$25 (Boross et al., 2017). With $D \approx 2.87\,\mathrm{GHz}$26, $D \approx 2.87\,\mathrm{GHz}$27, $D \approx 2.87\,\mathrm{GHz}$28, and $D \approx 2.87\,\mathrm{GHz}$29, the one-electron tipping-point configuration gives $D \approx 2.87\,\mathrm{GHz}$30, hence $D \approx 2.87\,\mathrm{GHz}$31 (Boross et al., 2017). The two-electron version has comparable MHz-scale Rabi rate but far stronger charge-noise resilience: numerical averaging over Gaussian noise destroys one-electron Rabi oscillations for $D \approx 2.87\,\mathrm{GHz}$32, whereas the two-electron protocol remains coherent for $D \approx 2.87\,\mathrm{GHz}$33 (Boross et al., 2017).

Optically assisted nuclear-spin logic extends even to weak-field neutral atoms. For $D \approx 2.87\,\mathrm{GHz}$34, Rydberg-mediated protocols implement arbitrary nuclear-spin controlled-phase gates using global addressing only (Shi, 2022). A two-pulse Stark-shift-assisted gate realizes $D \approx 2.87\,\mathrm{GHz}$35 in total time $D \approx 2.87\,\mathrm{GHz}$36, while a three-pulse scheme implements the same gate in $D \approx 2.87\,\mathrm{GHz}$37; the stated net fidelities are $D \approx 2.87\,\mathrm{GHz}$38 and $D \approx 2.87\,\mathrm{GHz}$39, respectively (Shi, 2022). The same framework generates a two-atom “Super Bell State” with $D \approx 2.87\,\mathrm{GHz}$40 and a three-atom state combining an electronic $D \approx 2.87\,\mathrm{GHz}$41 state with a nuclear GHZ state at $D \approx 2.87\,\mathrm{GHz}$42 (Shi, 2022). These results show that nuclear spin assistance is not restricted to long-time storage or narrowband sensing; it can also support fast entangling logic in regimes where both nuclear-spin qubit states are Rydberg-excited.

6. Applications, performance envelope, and unresolved issues

The most mature application domain is quantum sensing with NV centers. The review literature states that by mapping electron coherence onto a nuclear memory, the effective interrogation time $D \approx 2.87\,\mathrm{GHz}$43 can be extended from $D \approx 2.87\,\mathrm{GHz}$44 for a bare NV to $D \approx 2.87\,\mathrm{GHz}$45 with $D \approx 2.87\,\mathrm{GHz}$46 memory, improving sensitivity from the $D \approx 2.87\,\mathrm{GHz}$47 scale to $D \approx 2.87\,\mathrm{GHz}$48 (Kenny et al., 19 Jul 2025). The same family of protocols supports nuclear-spin spectroscopy, atomic imaging, magnetic-field sensing, and gyroscopy. Reported examples include a 27-spin cluster resolved with sub-100 Hz spectral resolution, 3D positioning of carbons around the NV with $D \approx 2.87\,\mathrm{GHz}$49 precision, a 50-spin network graph reconstructed at cryogenic temperature, and $D \approx 2.87\,\mathrm{GHz}$50 nuclear-Ramsey gyroscopes tracking rotation rates $D \approx 2.87\,\mathrm{GHz}$51 with $D \approx 2.87\,\mathrm{GHz}$52 (Kenny et al., 19 Jul 2025).

Nuclear-spin assistance also changes the spatial-resolution limit of nanoscale MRI. In the NV-plus-$D \approx 2.87\,\mathrm{GHz}$53 memory imaging protocol, repeated modules of spin-locking, SWAP to nuclear memory, gradient evolution, and inverse SWAP create a Bragg-grating-like frequency filter with linewidth $D \approx 2.87\,\mathrm{GHz}$54 (Ajoy et al., 2014). With $D \approx 2.87\,\mathrm{GHz}$55 and $D \approx 2.87\,\mathrm{GHz}$56, the paper gives $D \approx 2.87\,\mathrm{GHz}$57, compared with $D \approx 2.87\,\mathrm{GHz}$58 without filtering, and translates this to a spatial discrimination $D \approx 2.87\,\mathrm{GHz}$59 in the idealized estimate, with practical volume uncertainties $D \approx 2.87\,\mathrm{GHz}$60 (Ajoy et al., 2014). This is the sense in which nuclear memory is used not merely to preserve a quantum state, but to synthesize a much narrower spectroscopic aperture.

Magnetic-field angle sensing provides another nontrivial application. Near $D \approx 2.87\,\mathrm{GHz}$61, direct NV magnetic sensitivity vanishes, yet electron–nuclear entanglement restores an angle-dependent signal through ESEEM (Qiu et al., 2020). The protocol uses the $D \approx 2.87\,\mathrm{GHz}$62 nuclear spin and yields an effective angle-response coefficient $D \approx 2.87\,\mathrm{GHz}$63, so that the sensor remains responsive exactly where the bare electron Zeeman shift is first-order insensitive (Qiu et al., 2020). The review characterizes the resulting performance as sub-millidegree resolution of field orientation near $D \approx 2.87\,\mathrm{GHz}$64 (Kenny et al., 19 Jul 2025). The same angle dependence makes $D \approx 2.87\,\mathrm{GHz}$65 asymmetric in anisotropic noise, thereby exposing directional structure in the local magnetic environment (Qiu et al., 2020).

Characterization protocols show that not all nuclear spin-assisted methods are equally universal. For color centers with different electronic spin multiplicities and mixed-isotope baths, a recent comparison using Fisher information matrices and Cramér-Rao bounds concludes that conventional DD works best for $D \approx 2.87\,\mathrm{GHz}$66 in the weakly coupled, high-field regime, but fails for $D \approx 2.87\,\mathrm{GHz}$67 because the first-order $D \approx 2.87\,\mathrm{GHz}$68 shift cancels (Zahedian et al., 2024). In contrast, 5-pulse correlation ESEEM works for both $D \approx 2.87\,\mathrm{GHz}$69 and $D \approx 2.87\,\mathrm{GHz}$70, is limited by $D \approx 2.87\,\mathrm{GHz}$71 rather than $D \approx 2.87\,\mathrm{GHz}$72, and in a 23-spin cluster resolves roughly 17–18 nuclei in 1 s total measurement time; DD-ESEEM can raise this to approximately 20–22 (Zahedian et al., 2024). A plausible implication is that “nuclear spin-assisted” should not be understood as a single protocol family, but as a design principle whose optimal implementation depends strongly on sensor spin, coupling regime, and control bandwidth.

Persistent limitations are well defined. Control errors and pulse infidelity remain a bottleneck: the review cites current CNOT/SWAP fidelities of about $D \approx 2.87\,\mathrm{GHz}$73 and single-shot nuclear readout fidelities of roughly $D \approx 2.87\,\mathrm{GHz}$74 (Kenny et al., 19 Jul 2025). AXY-based addressing requires accurate knowledge of $D \approx 2.87\,\mathrm{GHz}$75 and becomes harder in very dense spectra (Casanova et al., 2015). Measurement-induced polarization is nondeterministic and typically requires hundreds of repeats for a single fully polarized bath (Jin et al., 2022). In SiC, spectral diffusion on the order of 400 MHz linewidth is identified as a principal noise source, even though ZEFOZ points and echo sequences suppress much of its impact (Tissot et al., 2022). For engineered devices, the review identifies scaling from single NV centers to dense arrays or ensembles, and ensemble control of $D \approx 2.87\,\mathrm{GHz}$76 NV centers with nuclear registers, as outstanding engineering tasks (Kenny et al., 19 Jul 2025).