Improved scaling of variational quantum metrology with midcircuit adaptivity

Phase estimation with only limited prior knowledge of the value of the phase has many applications. For example, atomic clocks are operated at the largest interrogation time at which phase wraps can still be neglected and quantum algorithms based on phase estimation require the ability to estimate a phase of any value. Typically, the averaged mean squared error will decrease as a power of the system size. It was previously found that variational metrology schemes using only one or two one-axis twists exhibit a reduced scaling exponent compared to the scaling exponent associated with the variance alone. Recently, midcircuit measurements have been demonstrated in neutral atom array, superconducting qubit, and trapped ion systems. Inspired by this, we show that with only a few rounds of adaptivity variational schemes with only a single state preparation twist and no measurement twists can achieve significantly improved scaling. We further investigate the robustness of these strategies to noise and the performance of adaptive strategies utilizing more entangling resources.