Quantum metrology using quantum combs and tensor network formalism

We develop an efficient algorithm for determining optimal adaptive quantum estimation protocols with arbitrary quantum control operations between subsequent uses of a probed channel. We introduce a tensor network representation of an estimation strategy, which drastically reduces the time and memory consumption of the algorithm, and allows us to analyze metrological protocols involving up to $N=50$ qubit channel uses, whereas the state-of-the-art approaches are limited to $N<5$. The method is applied to study the performance of the optimal adaptive metrological protocols in presence of various noise types, including correlated noise.