Tensor Network Simulations of Variational Bayesian Quantum Metrology under Correlated Noise

Variational Bayesian metrology has emerged as a promising avenue toward quantum advantage in sensing in the presence of complex noise and prior information. For the sake of practical advantage, it is important to understand how effective 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 demonstrate that this family of ansatzes can perform better than previous ansatzes despite having fewer entangling one-axis twist operators. Second, we utilize a polynomial-size tensor network algorithm to analyze realistic variational metrology beyond the symmetric subspace of the collective spin degree of freedom.