High-Fidelity Single-Shot Readout and Selective Nuclear Spin Control for a Spin-1/2 Quantum Register in Diamond

TL;DR

The paper demonstrates high-fidelity, single-shot readout of a germanium-vacancy center in diamond and utilizes two-dimensional correlation spectroscopy to identify and selectively control distant $^{13}$C nuclear spins, forming a scalable electro-nuclear spin register for quantum networks. The GeV center enables measurement-based initialization of nuclear spins through conditional gates, achieving a GeV SSR of $F_{SSR}^{e}=95.80\%$ and a neighboring $^{13}$C SSR of $F_{SSR}^{n}=93.66\%$, both approaching practical fault-tolerance needs. The techniques—extended CS, high-fidelity composite pulses, and optimized gate schemes—pave the way for networks with multiple spin qubits per node and compatibility with error-correction/ feed-forward operations. While demonstrated with spin-1/2 systems, the approach is general and can be extended to dozens of spins or adapted to other color centers and materials, advancing scalable quantum network nodes.

Abstract

Quantum networks offer a way to overcome the size and complexity limitations of single quantum devices by linking multiple nodes into a scalable architecture. Group-IV color centers in diamond, paired with long-lived nuclear spins, have emerged as promising building blocks demonstrating proof-of-concept experiments such as blind quantum computing and quantum-enhanced sensing. However, realizing a large-scale electro-nuclear register remains a major challenge. Here we establish the germanium-vacancy (GeV) center as a viable platform for such network nodes. Using correlation spectroscopy, we identify single nuclear spins within a convoluted spin environment, overcoming limitations imposed by the color center's spin-$1/2$ nature and thereby enabling indirect control of these nuclear spins. We further demonstrate high-fidelity single-shot readout of both the GeV center ($95.8\,\%$) and a neighboring ${}^{13}\text{C}$ nuclear spin ($93.7\,\%$), a key tool for feed-forward error correction. These critical advances position the GeV center as a compelling candidate for next-generation quantum network nodes.

Figures (8)

• Figure 1: Level scheme and single-shot readout (SSR) of the GeV center. (a) Physical structure of the GeV center and its coupling to surrounding nuclear spins. (b) Reduced energy level scheme of the GeV center showing the hyperfine splitting induced by a strongly-coupled ${}^{13}$C nuclear spin. (c) SSR pulse sequence with additional anti-correlation check. The dark state ($\ket{\downarrow_e}$, '$D$') is prepared via a laser pulse on $c_2$ while the bright state ($\ket{\uparrow_e}$, '$B$') is prepared with an additional strong microwave $\pi$ pulse on $\nu_0$ (Inv. Pop.). The anti-correlation check is done using an additional population inversion for a 'D' outcome. If the subsequent readout is not 'B', the event is classified as blinking and discarded. (d) Photon count distribution for the '$D$' state (green) and '$B$' state (blue), yielding a single-shot readout fidelity of $90.33\%$. (e) Improved SSR of the GeV center using an anti-correlation check for '$D$' outcomes and composite pulses for improving '$B$' state preparation fidelity, leading to an SSR fidelity of $\mathcal{F}_{\text{SSR}}^{\,e}=95.80\,\%$.
• Figure 2: Detection and control of ${}^{13}$C nuclear spins via dynamical decoupling (DD) and correlation spectroscopy (CS). (a) Measured XY8-1 spectrum (blue) at increasingly larger interpulse spacings $\tau_\text{DD}$, probing the GeV center's nuclear spin environment. The dotted orange line shows the simulated spectrum which includes the interaction with the strongly coupled nuclear spin ${}^{13}\text{C}_\text{A}$, capturing most features. (b) CS pulse sequence: blue blocks indicate microwave $\pi/2$ pulses on the GeV center's $\nu_0$ transition, orange blocks correspond to laser pulses and the green DD block is an XY8 sequence with fixed $\tau_{\text{DD}}$ and fixed order $N$. The sequence induces two conditional rotations of the GeV center's spin state separated by a correlation time $\text{$T_{2,e}^{\star}$}\ll\tau<T_{1,e}$ which allows for the detection of the nuclear spin's effective Larmor frequencies. (c) Power spectral density (PSD) of the CS measurement, revealing the electron spin state-dependent Larmor frequencies of surrounding ${}^{13}$C nuclear spins. The inset is a zoom-in of a measurement at an optimized $\tau_{\text{DD}}$ to better resolve the weakly-coupled spins. (d) XY8-1 spectrum (blue data points) compared with the simulated spectrum when only considering ${}^{13}\text{C}_\text{A}$ (orange dashed line) and when additionally including ${}^{13}\text{C}_\text{B}$ (green dash-dotted line). The inset showcases a resonance attributed to ${}^{13}\text{C}_\text{B}$. (e) XY8-$N$ order sweep for fixed $\tau_{\text{DD}}$ to probe the coherent interaction with ${}^{13}\text{C}_\text{B}$, which manifests as oscillations in the signal as the number of applied $\pi$ pulses $n$ is increased. Additionally, decoherence of the GeV center's electron spin leads to a decay of the signal. (f) Ramsey measurement of ${}^{13}\text{C}_\text{B}$ after its measurement-based initialization. The hyperfine interaction with the GeV center results in two distinct Larmor frequencies, $f_L^{\ket{\uparrow_e}}$ for $\ket{\uparrow_e}$ (blue) and $f_L^{\ket{\downarrow_e}}$ for $\ket{\downarrow_e}$ (green).
• Figure 3: Optimizing single-shot readout on the strongly-coupled ${}^{13}\text{C}_\text{A}$ nuclear spin. (a) Nuclear SSR fidelity for different Rabi frequencies $\Omega_e$ of the $\text{C}_{n}\text{NOT}_e$ gate. The pink dashed line marks frequencies (with index $m$) at which the $\text{C}_{n}\text{NOT}_e$ gate (i.e. a $\pi$ pulse on the GeV center at $\nu_1$ or $\nu_2$), induces an $m \cdot 2\pi$ rotation on the corresponding other hyperfine transition. The SSR of the bright ${}^{13}$C spin state is shown in blue, the dark ${}^{13}$C spin state in green and the average fidelity in orange. (b) Nuclear SSR histogram for $m=2$, yielding $\mathcal{F}_{\text{SSR}}^{\,n}=93.66\,\%$. The readout is repeated twice with an optimal photon threshold (black dashed line) of two. The resulting dark state ($\ket{\downarrow_e}$) photon counts are shown in green, and bright state ($\ket{\uparrow_e}$) in blue. (c) Optimization of $\mathcal{F}_{\text{SSR}}^{\,n}$ by repetitive nuclear spin readout. The fidelity decreases for repetitions $>2$ due to back action of the $\text{C}_{n}\text{NOT}_e$ gate on the nuclear spin state. The solid lines correspond to the optimized setting at $m=2$, while the dashed lines show the fidelity when operating at a Rabi frequency of $\Omega_e/(2\pi) = 400\,\text{kHz}$, slightly above the $T_{2,e}^{\star}$ limit. (d) Observation of quantum jumps on the nuclear spin during the repetitive readout in (c).
• Figure 4: Optical power-dependent blinking behavior of the GeV center in the absence of a magnetic field. (a) Example of blinking of the GeV center at an optical power of $7\,\text{nW}$. The 'off' state denotes the regions of low ($\sim0$) photon count rates (shaded orange) and the 'on' state denotes regions of high photon count rates (shaded green). (b) Example of a histogram of the time spent in the 'on' and 'off' states at an optical power of $42\,\text{nW}$. The histograms are obtained by binning the durations of the 'off' and 'on' states in (a). A simple exponential decay is fit (dashed lines) to the histograms to extract a characteristic 'on' and 'off' time for a specified optical power. (c) The 'on'$\rightarrow$'off' and 'off'$\rightarrow$'on' transition rates as a function of optical power, indicating a linear relation with the gradients $m_\text{'on'$\rightarrow$'off'} = (0.701\pm0.022)\,\text{nW\,/\,Hz}$ and $m_\text{'off'$\rightarrow$'on'} = (0.297\pm0.011)\,\text{nW\,/\,Hz}$. The 'on'$\rightarrow$'off' ('off'$\rightarrow$'on') transition rate is defined as the inverse of the characteristic 'on' ('off') time determined in (c). (d) The average percentage of time the GeV center spends in the ‘off’ state at different optical powers. For all other measurements presented in this work, the optical powers used were below the lowest value here of $2\,\text{nW}$.
• Figure 5: Two-dimensional correlation spectroscopy where $\tau$ is swept for 20 consecutive $\tau_{\text{DD}}$ values. The color scale indicates the power spectral density (PSD) obtained via Welch's method.