We probe dephasing mechanisms within a quantum network node consisting of a single nitrogen-vacancy center electron spin that is hyperfine coupled to surrounding C13 nuclear-spin quantum memories. Previous studies have analyzed memory dephasing caused by the stochastic electron-spin reset process, which is a component of optical internode entangling protocols. Here, we find, by using dynamical decoupling techniques and exploiting phase matching conditions in the electron-nuclear dynamics, that control infidelities and quasistatic noise are the major contributors to memory dephasing induced by the entangling sequence. These insights enable us to demonstrate a 19-fold improved memory performance which is still not limited by the electron reinitialization process. We further perform pump-probe studies to investigate the spin-flip channels during the optical electron spin reset. We find that spin flips occur via decay from the metastable singlet states with a branching ratio of 8(1):1:1, in contrast with previous work. These results allow us to formulate straightforward improvements to diamond-based quantum networks and similar architectures.

Large-scale quantum networks promise to enable secure communication, distributed quantum computing, enhanced sensing and fundamental tests of quantum mechanics through the distribution of entanglement across nodes ^1-7. Moving beyond current two-node networks ^8-13 requires the rate of entanglement generation between nodes to exceed the decoherence (loss) rate of the entanglement. If this criterion is met, intrinsically probabilistic entangling protocols can be used to provide deterministic remote entanglement at pre-specified times. Here we demonstrate this using diamond spin qubit nodes separated by two metres. We realize a fully heralded single-photon entanglement protocol that achieves entangling rates of up to 39 hertz, three orders of magnitude higher than previously demonstrated two-photon protocols on this platform ¹⁴. At the same time, we suppress the decoherence rate of remote-entangled states to five hertz through dynamical decoupling. By combining these results with efficient charge-state control and mitigation of spectral diffusion, we deterministically deliver a fresh remote state with an average entanglement fidelity of more than 0.5 at every clock cycle of about 100 milliseconds without any pre-or post-selection. These results demonstrate a key building block for extended quantum networks and open the door to entanglement distribution across multiple remote nodes.

Quantum key distribution allows for the generation of a secret key between distant parties connected by a quantum channel such as optical fibre or free space. Unfortunately, the rate of generation of a secret key by direct transmission is fundamentally limited by the distance. This limit can be overcome by the implementation of so-called quantum repeaters. Here, we assess the performance of a specific but very natural setup called a single sequential repeater for quantum key distribution. We offer a fine-grained assessment of the repeater by introducing a series of benchmarks. The benchmarks, which should be surpassed to claim a working repeater, are based on finite-energy considerations, thermal noise and the losses in the setup. In order to boost the performance of the studied repeaters we introduce two methods. The first one corresponds to the concept of a cut-off, which reduces the effect of decoherence during the storage of a quantum state by introducing a maximum storage time. Secondly, we supplement the standard classical post-processing with an advantage distillation procedure. Using these methods, we find realistic parameters for which it is possible to achieve rates greater than each of the benchmarks, guiding the way towards implementing quantum repeaters.

Single electron spins coupled to multiple nuclear spins provide promising multi-qubit registers for quantum sensing and quantum networks. The obtainable level of control is determined by how well the electron spin can be selectively coupled to, and decoupled from, the surrounding nuclear spins. Here we realize a coherence time exceeding a second for a single nitrogen-vacancy electron spin through decoupling sequences tailored to its microscopic nuclear-spin environment. First, we use the electron spin to probe the environment, which is accurately described by seven individual and six pairs of coupled carbon-13 spins. We develop initialization, control and readout of the carbon-13 pairs in order to directly reveal their atomic structure. We then exploit this knowledge to store quantum states in the electron spin for over a second by carefully avoiding unwanted interactions. These results provide a proof-of-principle for quantum sensing of complex multi-spin systems and an opportunity for multi-qubit quantum registers with long coherence times.

The impact of future quantum networks hinges on high-quality quantum entanglement shared between network nodes. Unavoidable imperfections necessitate a means to improve remote entanglement by local quantum operations. We realize entanglement distillation on a quantum network primitive of distant electron-nuclear two-qubit nodes. The heralded generation of two copies of a remote entangled state is demonstrated through single-photon-mediated entangling of the electrons and robust storage in the nuclear spins. After applying local two-qubit gates, single-shot measurements herald the distillation of an entangled state with increased fidelity that is available for further use. The key combination of generating, storing, and processing entangled states should enable the exploration of multiparticle entanglement on an extended quantum network.

Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be compatible with universal fault-tolerant computations, it is essential that states remain encoded at all times and that errors are actively corrected. Here we demonstrate such active error correction on a continuously protected logical qubit using a diamond quantum processor. We encode the logical qubit in three long-lived nuclear spins, repeatedly detect phase errors by non-destructive measurements, and apply corrections by real-time feedback. The actively error-corrected qubit is robust against errors and encoded quantum superposition states are preserved beyond the natural dephasing time of the best physical qubit in the encoding. These results establish a powerful platform to investigate error correction under different types of noise and mark an important step towards fault-tolerant quantum information processing.

Repeated observations inhibit the coherent evolution of quantum states through the quantum Zeno effect. In multi-qubit systems this effect provides opportunities to control complex quantum states. Here, we experimentally demonstrate that repeatedly projecting joint observables of multiple spins creates quantum Zeno subspaces and simultaneously suppresses the dephasing caused by a quasi-static environment. We encode up to two logical qubits in these subspaces and show that the enhancement of the dephasing time with increasing number of projections follows a scaling law that is independent of the number of spins involved. These results provide experimental insight into the interplay between frequent multi-spin measurements and slowly varying noise and pave the way for tailoring the dynamics of multi-qubit systems through repeated projections.

The realization of a network of quantum registers is an outstanding challenge in quantum science and technology. We experimentally investigate a network node that consists of a single nitrogen-vacancy center electronic spin hyperfine coupled to nearby nuclear spins. We demonstrate individual control and readout of five nuclear spin qubits within one node. We then characterize the storage of quantum superpositions in individual nuclear spins under repeated application of a probabilistic optical internode entangling protocol. We find that the storage fidelity is limited by dephasing during the electronic spin reset after failed attempts. By encoding quantum states into a decoherence-protected subspace of two nuclear spins, we show that quantum coherence can be maintained for over 1000 repetitions of the remote entangling protocol. These results and insights pave the way towards remote entanglement purification and the realization of a quantum repeater using nitrogen-vacancy center quantum-network nodes.