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arXiv:2604.11340

Optimal Two-Qubit Gates for Group-IV Color-Centers in Diamond

Jurek Frey, Katharina Senkalla, Philipp J. Vetter, Fedor Jelezko, Frank K. Wilhelm, Matthias M. Müller

quant-phSubmitted Apr 13, 2026• Announced Apr 14, 2026• 0 citations
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Abstract

Color centers associated with group-IV dopants in diamond with long-lived nuclear spins have emerged as major candidates for distributed quantum computing nodes and quantum repeaters. Several proof-of-principle experiments have already been demonstrated. A key operation for long-distance entanglement-distribution protocols are fast and robust gates between the electron spin and a nuclear spin. Here, we investigate numerically for an existing experimental platform of a Germanium-vacancy (GeV) center with a strongly-coupled ${}^{13}$C spin, how such gates can be implemented via quantum optimal control. In the presence of realistic noise we investigate different parameter regimes and gate operations and obtain robust two-qubit gates with fidelities exceeding $99.9 \%$. The framework provides a scalable strategy for group-IV quantum nodes and can be adapted to related architectures.

Comments
10 pages, 8 figures

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Color centers associated with group-IV dopants in diamond with long-lived nuclear spins have emerged as major candidates for distributed quantum computing nodes and quantum repeaters. Several proof-of-principle experiments have already been demonstrated. A key operation for long-distance entanglement-distribution protocols are fast and robust gates between the electron spin and a nuclear spin. Here, we investigate numerically for an existing experimental platform of a Germanium-vacancy (GeV) center with a strongly-coupled 13{}^{13}13C spin, how such gates can be implemented via quantum optimal control. In the presence of realistic noise we investigate different parameter regimes and gate operations and obtain robust two-qubit gates with fidelities exceeding 99.9%99.9 \%99.9%. The framework provides a scalable strategy for group-IV quantum nodes and can be adapted to related architectures.
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-1/21/21/2 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 %95.8\,\%95.8%) and a neighboring 13C{}^{13}\text{C}13C nuclear spin (93.7 %93.7\,\%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.
Accurately controlling entangling gates remains a major challenge for quantum technology applications with solid-state spin qubits. Here, we study a group-IV color-center with a strongly-coupled nuclear spin and approach the problem from a quantum control perspective. We show that there are three different types of entangling gates where the entanglement is mediated by the parallel hyperfine-coupling component, the orthogonal one or both. We derive the respective quantum speed limits (QSL) and show by means of dynamical decoupling, resonant driving of single- and double-quantum transitions, quantum optimal control and algebraic gate decomposition how these gates can be realized. We finally discuss the experimental applicability.
The ability to process and store information on surrounding nuclear spins is a major requirement for group-IV color center-based repeater nodes. We demonstrate coherent control of a ^{13}C nuclear spin strongly coupled to a negatively charged germanium-vacancy center in diamond with coherence times beyond 2.5 s at mK temperatures, which is the longest reported for group-IV defects. Detailed analysis allows us to model the system's dynamics, extract the coupling parameters, and characterize noise. We estimate an achievable memory time of 18.1 s with heating limitations considered, paving the way to successful applications as a quantum repeater node.
A quantum register coupled to a spin-photon interface is a key component in quantum communication and information processing.Group-IV color centers in diamond (SiV -, GeV -, and SnV -) are promising candidates for this application, comprising an electronic spin with optical transitions coupled to a nuclear spin as the quantum register.However, the creation of a quantum register for these color centers with deterministic and strong coupling to the spin-photon interface remains challenging.Here, we make first-principles predictions of the hyperfine parameters of the group-IV color centers, which we verify experimentally with a comprehensive comparison between the spectra of spin active and spin neutral intrinsic dopant nuclei in single GeV -and SnV -emitters.In line with the theoretical predictions, detailed spectroscopy on large sample sizes reveals that hyperfine coupling causes a splitting of the optical transition of SnV -an order of magnitude larger than the optical line width and provides a magnetic field insensitive transition.This strong coupling provides access to a new regime for quantum registers in diamond color centers, opening avenues for novel spin-photon entanglement and quantum sensing schemes for these well-studied emitters.
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The germanium vacancy in diamond (GeV) is a promising candidate for color center based quantum networking. Yet, like for other group-IV vacancy defects in diamond, achieving fast, high-fidelity qubit operations using traditional magnetic resonance techniques is experimentally challenging due to a weak magnetic dipole and susceptibility to thermally induced decoherence. Here, we perform all-optical control of the GeV and realize Rabi frequencies exceeding ∼ 20 MHz. We do so by driving the two Λ -systems of the GeV simultaneously and apply this to probe the spin coherence ( T 2 * = 224 ± 14 ns, T 2 H = 11.9 ± 0.3 µ s ). Our control scheme is applicable to other color centers and particularly, other group-IV defects for which the scheme may be optimized to improve all-optical control in these systems.