  Optimized quantum control can enhance the performance and noise resilience of
quantum metrology. However, the optimization quickly becomes intractable when
multiple control operations are applied sequentially. In this work, we propose
efficient tensor network algorithms for optimizing strategies of quantum
metrology enhanced by a long sequence of control operations. Our approach
covers a general and practical scenario where the experimenter applies $N-1$
interleaved control operations between $N$ queries of the channel to estimate
and uses no or bounded ancilla. Tailored to different experimental
capabilities, these control operations can be generic quantum channels or
variational unitary gates. Numerical experiments show that our algorithm has a
good performance in optimizing the metrological strategy for as many as $N=100$
queries. In particular, our algorithm identifies a strategy that can outperform
the state-of-the-art strategy when $N$ is finite but large.
