Efficient tensor networks for control-enhanced quantum metrology

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi><mml:mo>&amp;#x2212;</mml:mo><mml:mn>1</mml:mn></mml:math> interleaved control operations between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>100</mml:mn></mml:math> queries. In particular, our algorithm identifies a strategy that can outperform the state-of-the-art strategy when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math> is finite but large.