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Variational Bayesian quantum metrology is a promising avenue toward quantumadvantage in sensing which optimizes both the state preparation (or encoding)and measurement (or decoding) procedures and takes prior information intoaccount. For the sake of practical advantage, it is important to understand howeffective various parametrized protocols are as well as how robust they are tothe effects of complex noise, such as spatially correlated noise. First, wepropose a new family of parametrized encoding and decoding protocols calledarbitrary-axis twist ansatzes, and show that it can lead to a substantialreduction in the number of one-axis twists needed to achieve a targetestimation error. Second, using a polynomial-size tensor network algorithm, weanalyze practical variational metrology beyond the symmetric subspace of acollective spin, and find that quantum advantage persists for shallow-depthansatzes under realistic noise level.

Optimizing one-axis twists for realistic variational Bayesian quantum metrology