Optimizing one-axis twists for realistic variational Bayesian quantum metrology*

Variational Bayesian quantum metrology is a promising avenue toward quantum advantage in sensing which optimizes both the state preparation (or encoding) and measurement (or decoding) procedures and takes prior information into account. For the sake of practical advantage, it is important to understand how effective various parametrized protocols are as well as how robust they are to the effects of complex noise, such as spatially correlated noise. First, we propose a new family of parametrized encoding and decoding protocols called arbitrary-axis twist ansatzes, and show that it can lead to a substantial reduction in the number of one-axis twists needed to achieve a target estimation error. Second, using a polynomial-size tensor network algorithm, we analyze practical variational metrology beyond the symmetric subspace of a collective spin, and find that quantum advantage persists for shallow-depth ansatzes under realistic noise level.