To address the critical voltage stability of industrial DC microgrids serving sensitive loads, virtual capacitor control is a promising technique for inertia enhancement. However, conventional virtual capacitor control, with its fixed parameters and limited disturbance rejection capability, struggles to maintain qualified voltage quality, threatening the reliable operation of industrial equipment. This paper proposes a novel adaptive virtual capacitor control strategy based on linear active disturbance rejection control (LADRC). The key contribution is a novel control architecture where the virtual capacitor is not predetermined but is adaptively modulated by real-time disturbance estimated by LADRC. This unique feedback mechanism allows the system to proactively counteract both external load changes and internal parameter uncertainties, achieving superior voltage regulation. Furthermore, an integrated sliding time window filter ensures smooth control action by mitigating oscillations from voltage ripple. The proposed strategy's effectiveness in simultaneously enhancing voltage deviation suppression, ripple mitigation, and dynamic inertia support is validated through simulation and hardware-in the-loop (HIL) experiments.

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.

We present a Dicke state preparation scheme which uses global control of N spin qubits: our scheme is based on the standard phase estimation algorithm, which estimates the eigenvalue of a unitary operator. The scheme prepares a Dicke state nondeterministically by collectively coupling the spins to an ancilla qubit via a ZZ interaction, using log2N+1 ancilla qubit measurements. The preparation of such Dicke states can be useful if the spins in the ensemble are used for magnetic sensing: we discuss a possible realization using an ensemble of electronic spins located at diamond nitrogen-vacancy centers coupled to a single superconducting flux qubit. We also analyze the effect of noise and limitations in our scheme.