Efficient tensor networks for control-enhanced quantum metrology

Qiushi Liu; Yuxiang Yang

doi:10.22331/q-2024-12-18-1571

Efficient tensor networks for control-enhanced quantum metrology

QICI Quantum Information and Computation Initiative, Department of Computer Science, School of Computing and Data Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China

Published:	2024-12-18, volume 8, page 1571
Eprint:	arXiv:2403.09519v3
Doi:	https://doi.org/10.22331/q-2024-12-18-1571
Citation:	Quantum 8, 1571 (2024).

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Abstract

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.

Featured image: Control-enhanced sequential strategy for estimating the parameter $\theta$. One can choose to use identical or different control at each step, tailored to experimental requirements.

Popular summary

A focus of research in quantum metrology is using quantum control to enhance the estimation precision. On the other hand, theoretical tools for optimizing the quantum control in realistic setups are lacking. Most of the existing work makes unrealistic assumptions, such as using unbounded ancilla and an infinitely long sequence of control operations.

For practical experimental demonstration of quantum sensors, we develop a highly efficient approach to optimizing the protocol for quantum metrology with a long sequence of quantum control with bounded ancilla, by leveraging the power of tensor networks. Our algorithm exihibits a robust performance under various types of noise.

► BibTeX data

@article{Liu2024efficienttensor,
  doi = {10.22331/q-2024-12-18-1571},
  url = {https://doi.org/10.22331/q-2024-12-18-1571},
  title = {Efficient tensor networks for control-enhanced quantum metrology},
  author = {Liu, Qiushi and Yang, Yuxiang},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1571},
  month = dec,
  year = {2024}
}

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Cited by

[1] Stanisław Kurdziałek, Piotr Dulian, Joanna Majsak, Sagnik Chakraborty, and Rafał Demkowicz-Dobrzański, "Quantum metrology using quantum combs and tensor network formalism", New Journal of Physics 27 1, 013019 (2025).

[2] Arpan Das and Rafał Demkowicz-Dobrzański, "Quantum metrology in the presence of correlated noise via Markovian embedding", Physical Review A 113 2, 022418 (2026).

[3] Stanisław Kurdziałek, Francesco Albarelli, and Rafał Demkowicz-Dobrzański, "Universal Bounds for Quantum Metrology in the Presence of Correlated Noise", Physical Review Letters 135 13, 130801 (2025).

[4] Piotr Dulian, Stanisław Kurdziałek, and Rafał Demkowicz-Dobrzański, "QMetro++ – Python optimization package for large scale quantum metrology with customized strategy structures", Quantum 10, 1991 (2026).

[5] Srijon Ghosh, Arkadiusz Kobus, Stanisław Kurdziałek, and Rafał Demkowicz-Dobrzański, "Optimal phase estimation in the presence of correlated dephasing", arXiv:2511.07211, (2025).

[6] Sisi Zhou, "Limits of Noisy Quantum Metrology with Restricted Quantum Controls", Physical Review Letters 133 17, 170801 (2024).

[7] Qiushi Liu, Zihao Hu, Haidong Yuan, and Yuxiang Yang, "Fully-Optimized Quantum Metrology: Framework, Tools, and Applications", arXiv:2409.07068, (2024).

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