Quantum sensors hold considerable promise for precision measurement, yet their capabilities are inherently constrained by environmental noise. A fundamental task in quantum sensing is determining the precision limit of noisy sensor devices. For continuously monitored quantum sensors, characterizing the optimal precision in the presence of environments other than the measurement channel is an outstanding open theoretical challenge, due to the infinite-dimensional nature of the sensor output field and the complex temporal correlation of the photons therein. Here, we establish a numerically efficient method to determine the quantum Cramér-Rao bound for continuously monitored quantum sensors subject to general environmental noise—Markovian or non-Markovian, and showcase its application with paradigmatic models of continuously monitored quantum sensors. Applicable to both constant-parameter and waveform estimation, our method provides a rigorous and practical framework for assessing and enhancing the sensor performance in realistic settings, with broad applications across experimental quantum physics.

Hybrid quantum architectures that integrate matter and photonic degrees of freedom present a promising pathway toward scalable fault-tolerant quantum computing. This approach needs to combine well-established entangling operations between distant registers using photonic degrees of freedom with direct interactions between matter qubits within a solid-state register. The high-fidelity control of such a register, however, poses significant challenges. In this work, we address these challenges with pulsed control sequences that modulate all interspin interactions to preserve the nearest-neighbor couplings while eliminating unwanted long-range interactions. We derive pulse sequences, including broadband and selective gates, using composite-pulse and shaped-pulse techniques as well as optimal-control methods. This ensures a general pulse sequence in the presence of spin-position bias, robustness against static offset detunings, and Rabi-frequency fluctuations of the control fields. The control techniques developed here apply well beyond the present setting to a broad range of physical platforms. We demonstrate the efficacy of our methods for the resource-state generation for fusion-based quantum computing in four- and six-spin systems encoded in the electronic ground states of nitrogen-vacancy centers or other molecular solid-state qubits. We also outline other elements of the proposed architecture, highlighting its potential for advancing quantum computing technology.