GHZ is All You Need: Quantum Sensing with VISTA

Abstract: Quantum metrology holds the potential to enhance magnetic field sensing beyond current limits. However, in the presence of realistic noise, this advantage degrades to the Standard Quantum Limit. While recent algorithmic and variational techniques attempt to recover this scaling, they are hindered by stringent control requirements on the probe state that are infeasible in the near term, or by barren plateaus and interpretability issues inherent to black-box variational quantum circuits. Here, we introduce Variational Inference and Sensing with Twin Ansätze (VISTA), a closed-loop protocol that combines passive sensing, or where the probe state is left to evolve without any active control, with physics-informed variational optimization. In the VISTA framework, a probe state evolves under a Lindbladian master-equation, and is compared, via the Swap test, to a parameterized ``quantum twin", a shallow quantum circuit designed to mimic the underlying pure-state or Lindbladian master-equation dynamics. By restricting the optimization space to the physical parameters of interest, VISTA circumvents barren plateaus. We demonstrate that by coupling the protocol with a classical optimizer and high shot counts, VISTA can temporarily achieve near-Heisenberg scaling for moderately noisy qubits over a finite range of system sizes. Furthermore, we introduce a Quasi-Normalization technique that sharpens the loss gradients, enabling simultaneous extraction of both the coherent signal $θ$ and the environmental noise rate $γ$ with low absolute error. Finally, we extend VISTA to the multi-parameter vector metrology regime, enabling simultaneous parameter extraction from a transverse-magnetic-field Hamiltonian. By eliminating the need for complex, open-loop control and processing, VISTA offers a highly practical, resource-efficient framework for near- to intermediate-term quantum sensors.