Seeking quantum advantage is a crucial goal in quantum technology, encompassing quantum sensing, quantum communication, quantum simulation, and quantum computing. Solid-state defect centers, such as nitrogen-vacancy (NV) centers in diamond, are promising platforms due to their excellent optical and spin properties, along with long coherence times. The abundant nuclear spins surrounding these centers serve as quantum qubits, providing substantial computational resources. A key challenge is harnessing these latent nuclear spin resources to achieve quantum advantage. 

To study the system Hamiltonian, firstly a generic Hamiltonian estimation method from random-shaped-pulses driven trajectories is introduced. Estimating the parameters of a Hamiltonian is crucial in quantum information processing with several advantages: minimizing system errors, enabling optimal control of the system, and enhancing metrology and sensing. The approach utilizes randomly shaped pulses to continuously drive qubit states, allowing for efficient exploration of Hamiltonian dynamics in the system’s Hilbert space. 

Following this, by exploring the quantum nature of the quantum targets, a novel approach for the detection of quantum signals free of classical noise via quantum correlation is developed. Conventional noise filtering methods rely on different patterns of signal and noise in frequency or time domains, thus limiting their scope of application. Here, we propose a signal-nature-based approach which singles out a quantum signal from its classical noise background by employing the intrinsic quantum nature of the system. Utilizing quantum correlated signals, a parallel state readout of multiple nuclear spins is achieved. 

Finally, we demonstrate a variational quantum eigensolver with a solid-state spin system under ambient conditions. Quantum simulators exploit the quantum nature of one physical system to study another, thus  showcasing quantum advantage. This demonstration marks a crucial step toward achieving a scalable quantum simulator in solid-state spin systems.