Enhancing precision sensors for stochastic signals using quantum techniques is a promising emerging field of physics. Estimating a weak stochastic waveform is the core task of many fundamental physics experiments including searches for stochastic gravitational waves, quantum gravity, and axionic dark matter. Simultaneously, noise spectroscopy and characterization (e.g., estimation of various decay mechanisms in quantum devices) are relevant to a broad range of fundamental and technological applications. We consider the ultimate limit on the sensitivity of these devices for Lindblad estimation given any quantum state, fast and precise control sequence, and measurement scheme. We show that it is optimal to rapidly projectively measure and reinitialize the quantum state. We develop optimal protocols for a wide range of applications including stochastic waveform estimation, spectroscopy with qubits, and Lindblad estimation.

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• Dark matter direct detection
• Gravitational wave detection
• Measurement-based quantum computing
• Quantum control
• Quantum measurements
• Quantum metrology
• Quantum parameter estimation
• Lindblad equation