Solid-state quantum registers consisting of optically active electron spins with nearby nuclear spins are promising building blocks for future quantum technologies. For electron spin-1 registers, dynamical decoupling (DD) quantum gates have been developed that enable the precise control of multiple nuclear spin qubits. However, for the important class of electron spin-1/2 systems, this control method suffers from intrinsic selectivity limitations, resulting in reduced nuclear spin gate fidelities. Here, we demonstrate improved control of single nuclear spins by an electron spin-1/2 using dynamically decoupled radio-frequency (DDRF) gates. We make use of the electron spin-1/2 of a diamond tin-vacancy center, showing high-fidelity single-qubit gates, single-shot readout, and spin coherence beyond a millisecond. The DD control is used as a benchmark to observe and control a single 31C nuclear spin. Using the DDRF control method, we demonstrate improved control on that spin. In addition, we find and control an additional nuclear spin that is insensitive to the DD control method. Using these DDRF gates, we show entanglement between the electron and the nuclear spin with 72(3)% state fidelity. Our extensive simulations indicate that DDRF gate fidelities well in excess are feasible. Finally, we employ time-resolved photon detection during readout to quantify the hyperfine coupling for the electron's optically excited state. Our work provides key insights into the challenges and opportunities for nuclear spin control in electron spin-1/2 systems, opening the door to multiqubit experiments on these promising qubit platforms.

The goal of future quantum networks is to enable new internet applications that are impossible to achieve using only classical communication1, 2–3. Up to now, demonstrations of quantum network applications4, 5–6 and functionalities7, 8, 9, 10, 11–12 on quantum processors have been performed in ad hoc software that was specific to the experimental setup, programmed to perform one single task (the application experiment) directly into low-level control devices using expertise in experimental physics. Here we report on the design and implementation of an architecture capable of executing quantum network applications on quantum processors in platform-independent high-level software. We demonstrate the capability of the architecture to execute applications in high-level software by implementing it as a quantum network operating system—QNodeOS—and executing test programs, including a delegated computation from a client to a server13 on two quantum network nodes based on nitrogen-vacancy (NV) centres in diamond14,15. We show how our architecture allows us to maximize the use of quantum network hardware by multitasking different applications. Our architecture can be used to execute programs on any quantum processor platform corresponding to our system model, which we illustrate by demonstrating an extra driver for QNodeOS for a trapped-ion quantum network node based on a single 40Ca+ atom16. Our architecture lays the groundwork for computer science research in quantum network programming and paves the way for the development of software that can bring quantum network technology to society.

The ability to sense and control nuclear spins near solid-state defects might enable a range of quantum technologies. Dynamically decoupled radio-frequency (DDrf) control offers a high degree of design flexibility and long electron-spin coherence times. However, previous studies have considered simplified models and little is known about optimal gate design and fundamental limits. Here, we develop a generalized DDrf framework that has important implications for spin sensing and control. Our analytical model, which we corroborate by experiments on a single NV center in diamond, reveals the mechanisms that govern the selectivity of gates and their effective Rabi frequencies, and enables flexible detuned gate designs. We apply these insights to numerically show a 60× sensitivity enhancement for detecting weakly coupled spins and study the optimization of quantum gates in multiqubit registers. These results advance the understanding for a broad class of gates and provide a toolbox for application-specific design, enabling improved quantum control and sensing.

The decoherence of a central electron spin due to the dynamics of a coupled electron-spin bath is a core problem in solid-state spin physics. Ensemble experiments have studied the central spin coherence in detail, but such experiments average out the underlying quantum dynamics of the bath. Here, we show the coherent back-action of an individual NV center on an electron-spin bath and use it to detect, prepare, and control the dynamics of a pair of bath spins. We image the NV-pair system with subnanometer resolution and reveal a long dephasing time [T2∗=44(9) ms] for a qubit encoded in the electron-spin pair. Our experiment reveals the microscopic quantum dynamics that underlie the central spin decoherence and provides new opportunities for controlling and sensing interacting spin systems.

Spins associated to solid-state color centers are a promising platform for investigating quantum computation and quantum networks. Recent experiments have demonstrated multiqubit quantum processors, optical interconnects, and basic quantum error-correction protocols. One of the key open challenges towards larger-scale systems is to realize high-fidelity universal quantum gates. In this work, we design and demonstrate a complete high-fidelity gate set for the two-qubit system formed by the electron and nuclear spin of a nitrogen-vacancy center in diamond. We use gate set tomography (GST) to systematically optimize the gates and demonstrate single-qubit gate fidelities of up to 99.999⁢(1)% and a two-qubit gate fidelity of 99.93⁢(5)%. Our gates are designed to decouple unwanted interactions and can be extended to other electron-nuclear spin systems. The high fidelities demonstrated provide opportunities towards larger-scale quantum processing with color-center qubits.

Solid-state single-photon emitters provide a versatile platform for exploring quantum technologies such as optically connected quantum networks. A key challenge is to ensure the optical coherence and spectral stability of the emitters. Here, we introduce a high-bandwidth ‘check-probe’ scheme to quantitatively measure (laser-induced) spectral diffusion and ionisation rates, as well as homogeneous linewidths. We demonstrate these methods on single V2 centres in commercially available bulk-grown 4H-silicon carbide. Despite observing significant spectral diffusion under laser illumination (≳GHz s−1), the optical transitions are narrow (~35 MHz), and remain stable in the dark (≳1 s). Through Landau-Zener-Stückelberg interferometry, we determine the optical coherence to be near-lifetime limited (T2 = 16.4(4) ns), hinting at the potential for using bulk-grown materials for developing quantum technologies. These results advance our understanding of spectral diffusion of quantum emitters in semiconductor materials, and may have applications for studying charge dynamics across other platforms.

We realize high-fidelity gates for the two-qubit system formed by NV center. Using gate set tomography, we report gate fidelities exceeding 99%, and analyze the origin of the errors.

Spins associated to optically accessible solid-state defects have emerged as a versatile platform for exploring quantum simulation, quantum sensing and quantum communication. Pioneering experiments have shown the sensing, imaging, and control of multiple nuclear spins surrounding a single electron spin defect. However, the accessible size of these spin networks has been constrained by the spectral resolution of current methods. Here, we map a network of 50 coupled spins through high-resolution correlated sensing schemes, using a single nitrogen-vacancy center in diamond. We develop concatenated double-resonance sequences that identify spin-chains through the network. These chains reveal the characteristic spin frequencies and their interconnections with high spectral resolution, and can be fused together to map out the network. Our results provide new opportunities for quantum simulations by increasing the number of available spin qubits. Additionally, our methods might find applications in nano-scale imaging of complex spin systems external to the host crystal.

We discuss measurements on single NV centers in isotopically purified diamond and show coherent optical transitions combined with enhanced electron and carbon spin coherence. These results open avenues for new quantum network applications.

In the search for scalable, fault-tolerant quantum computing, distributed quantum computers are promising candidates. These systems can be realized in large-scale quantum networks or condensed onto a single chip with closely situated nodes. We present a framework for numerical simulations of a memory channel using the distributed toric surface code, where each data qubit of the code is part of a separate node, and the error-detection performance depends on the quality of four-qubit Greenberger-Horne-Zeilinger (GHZ) states generated between the nodes. We quantitatively investigate the effect of memory decoherence and evaluate the advantage of GHZ creation protocols tailored to the level of decoherence. We do this by applying our framework for the particular case of color centers in diamond, employing models developed from experimental characterization of nitrogen-vacancy centers. For diamond color centers, coherence times during entanglement generation are orders of magnitude lower than coherence times of idling qubits. These coherence times represent a limiting factor for applications, but previous surface code simulations did not treat them as such. Introducing limiting coherence times as a prominent noise factor makes it imperative to integrate realistic operation times into simulations and incorporate strategies for operation scheduling. Our model predicts error probability thresholds for gate and measurement reduced by at least a factor of three compared to prior work with more idealized noise models. We also find a threshold of 4 × 10 2 in the ratio between the entanglement generation and the decoherence rates, setting a benchmark for experimental progress.

Striving toward a scalable quantum processor, this article presents the first cryo-CMOS quantum bit (qubit) controller targeting color centers in diamond. Color-center qubits enable a modular architecture that allows for the 3-D integration of photonics, cryo-CMOS control electronics, and qubits in the same package. However, performing quantum operations in a scalable manner requires large currents in the driving coils due to low coil-to-qubit coupling. Moreover, active calibration of the qubit Larmor frequency is required to compensate inhomogeneities of the bias magnetic field. To overcome these challenges, this work proposes both a cryo-CMOS alternating current (AC) controller consisting of a class-DE series-resonant driver and a DC current regulator (DC CR) that uses a triode-biased H-bridge for scalable low-power qubit operations. By experimentally validating the cryo-CMOS performance with a nitrogen-vacancy (NV) color-center qubit, the AC controller can drive a Rabi oscillation up to 2.5 MHz with a supply draw of 6.5 mA, and the DC CR can tune the Larmor frequency by ±9 MHz while driving up to ±20 mA in the bias coil. T ^∗ ₂ coherence times up to 5.3μs and single-qubit gate fidelities above 98% are demonstrated with the cryo-CMOS control using Ramsey experiments and gate set tomography (GST), respectively. The results demonstrate the efficacy of the proposed cryo-CMOS chips and enable the development of a modular quantum processor based on color centers.

Color-center quantum bits (qubits), such as the Nitrogen-Vacancy center (NV) in diamond, have demonstrated entanglement between remote (>1.3km) qubits and excellent coherence times [1], all while operating at a few Kelvins. Compared to other qubit technologies typically operating at mK temperatures, the higher operating temperature of NVs enables scalable 3D integration with cryo-CMOS control electronics [2], provides significantly more cooling power, and removes the interconnect bottleneck between the qubits and the electronics in prior art [3-5]. Yet, no cryo-CMOS controller for NV-based quantum computers (QC) has been demonstrated.

The field of nanoscale magnetic resonance imaging (NanoMRI) was started 30 years ago. It was motivated by the desire to image single molecules and molecular assemblies, such as proteins and virus particles, with near-atomic spatial resolution and on a length scale of 100 nm. Over the years, the NanoMRI field has also expanded to include the goal of useful high-resolution nuclear magnetic resonance (NMR) spectroscopy of molecules under ambient conditions, including samples up to the micron-scale. The realization of these goals requires the development of spin detection techniques that are many orders of magnitude more sensitive than conventional NMR and MRI, capable of detecting and controlling nanoscale ensembles of spins. Over the years, a number of different technical approaches to NanoMRI have emerged, each possessing a distinct set of capabilities for basic and applied areas of science. The goal of this roadmap article is to report the current state of the art in NanoMRI technologies, outline the areas where they are poised to have impact, identify the challenges that lie ahead, and propose methods to meet these challenges. This roadmap also shows how developments in NanoMRI techniques can lead to breakthroughs in emerging quantum science and technology applications.

Nuclear quadrupolar resonance (NQR) spectroscopy reveals chemical bonding patterns in materials and molecules through the unique coupling between nuclear spins and local fields. However, traditional NQR techniques require macroscopic ensembles of nuclei to yield a detectable signal, which obscures molecule-to-molecule variations. Solid-state spin qubits, such as the nitrogen-vacancy (NV) center in diamond, facilitate the detection and control of individual nuclei through their local magnetic couplings. Here, we use NV centers to perform NQR spectroscopy on their associated nitrogen-14 (¹⁴N) nuclei at room temperature. In mapping the nuclear quadrupolar Hamiltonian, we resolve minute variations between individual nuclei. The measurements reveal correlations between the Hamiltonian parameters associated with the NV center’s electronic and nuclear spin states, as well as a previously unreported symmetry-breaking quadrupolar term. We further design pulse sequences to initialize, read out, and control the quantum evolution of the ¹⁴N nuclear state using the nuclear quadrupolar Hamiltonian.

Efficient hyperpolarization of nuclear spins via optically active defect centers, such as the nitrogen vacancy (NV) center in diamond, has great potential for enhancing NMR-based quantum information processing and nanoscale magnetic resonance imaging. Recently, pulse-based protocols have been shown to efficiently transfer optically induced polarization of the electron defect spin to surrounding nuclear spins - at particular resonant pulse intervals. In this work, we investigate the performance of these protocols, both analytically and experimentally, with the electronic spin of a single NV defect. We find that whenever polarization resonances of nuclear spins are near degenerate with a "blocking"spin, which is single spin with stronger off-diagonal coupling to the electronic central spin, they are displaced out of the central resonant region - without, in general, significant weakening in the rate of polarization. We analyze the underlying physical mechanism and obtain a closed-form expression for the displacement. We propose that spin blocking represents a common but overlooked effect in hyperpolarization of nuclear spins and suggest solutions for improved protocol performance in the presence of (naturally occurring) blocking nuclear spins.

We demonstrate interference of photons emitted by remote, spectrally distinct NV-centers. Quantum frequency conversion at the nodes brings the photons to the same wavelength in the telecom L-band, compatible with entanglement generation at metropolitan scale.

Solid-state spin qubits is a promising platform for quantum computation and quantum networks^1,2. Recent experiments have demonstrated high-quality control over multi-qubit systems^3–8, elementary quantum algorithms^8–11 and non-fault-tolerant error correction^12–14. Large-scale systems will require using error-corrected logical qubits that are operated fault tolerantly, so that reliable computation becomes possible despite noisy operations^15–18. Overcoming imperfections in this way remains an important outstanding challenge for quantum science^15,19–27. Here, we demonstrate fault-tolerant operations on a logical qubit using spin qubits in diamond. Our approach is based on the five-qubit code with a recently discovered flag protocol that enables fault tolerance using a total of seven qubits^28–30. We encode the logical qubit using a new protocol based on repeated multi-qubit measurements and show that it outperforms non-fault-tolerant encoding schemes. We then fault-tolerantly manipulate the logical qubit through a complete set of single-qubit Clifford gates. Finally, we demonstrate flagged stabilizer measurements with real-time processing of the outcomes. Such measurements are a primitive for fault-tolerant quantum error correction. Although future improvements in fidelity and the number of qubits will be required to suppress logical error rates below the physical error rates, our realization of fault-tolerant protocols on the logical-qubit level is a key step towards quantum information processing based on solid-state spins.

Understanding and protecting the coherence of individual quantum systems is a central challenge in quantum science and technology. Over the past decades, a rich variety of methods to extend coherence have been developed. A complementary approach is to look for naturally occurring systems that are inherently protected against decoherence. Here, we show that pairs of identical nuclear spins in solids form intrinsically long-lived qubits. We study three carbon-13 pairs in diamond and realize high-fidelity measurements of their quantum states using a single nitrogen-vacancy center in their vicinity. We then reveal that the spin pairs are robust to external perturbations due to a combination of three phenomena: a decoherence-free subspace, a clock transition, and a variant on motional narrowing. The resulting inhomogeneous dephasing time is T2∗=1.9(3) min, the longest reported for individually controlled qubits. Finally, we develop complete control and realize an entangled state between two spin pairs through projective parity measurements. These long-lived qubits are abundantly present in diamond and other solids and provide new opportunities for ancilla-enhanced quantum sensing and for robust memory qubits for quantum networks.

Entanglement distribution over quantum networks has the promise of realizing fundamentally new technologies. Entanglement between separated quantum processing nodes has been achieved on several experimental platforms in the past decade. To move toward metropolitan-scale quantum network test beds, the creation and transmission of indistinguishable single photons over existing telecom infrastructure is key. Here, we report the interference of photons emitted by remote spectrally detuned NV-center-based network nodes, using quantum frequency conversion to the telecom L band. We find a visibility of 0.79±0.03 and an indistinguishability between converted NV photons around 0.9 over the full range of the emission duration, confirming the removal of the spectral information present. Our approach implements fully separated and independent control over the nodes, time multiplexing of control and quantum signals, and active feedback to stabilize the output frequency. Our results demonstrate a working principle that can be readily employed on other platforms and shows a clear path toward generating metropolitan-scale solid-state entanglement over deployed telecom fibers.

Quantum networks can enable quantum communication and modular quantum computation. A powerful approach is to use multi-qubit nodes that provide quantum memory and computational power. Nuclear spins associated with defects in diamond are promising qubits for this role. However, dephasing during optical entanglement distribution hinders scaling to larger systems. Here, we show that a ¹³C-spin quantum memory in isotopically engineered diamond is robust to the optical link operation of a nitrogen-vacancy centre. The memory lifetime is improved by two orders-of-magnitude upon the state-of-the-art, surpassing reported times for entanglement distribution. Additionally, we demonstrate that the nuclear-spin state can survive ionisation and recapture of the nitrogen-vacancy electron. Finally, we use simulations to show that combining this memory with previously demonstrated entanglement links and gates can enable key network primitives, such as deterministic non-local two-qubit gates, paving the way for test-bed quantum networks capable of investigating complex algorithms and error correction.