Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2403.04854 · New Journal of Physics

Quantum metrology using quantum combs and tensor network formalism

Stanisław Kurdziałek, Piotr Dulian, Joanna Majsak, Sagnik Chakraborty, Rafał Demkowicz-Dobrzański

Published Jan 1, 2025• 16 citations
arXivHTMLPDF

Abstract

Abstract 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.

DOI
10.1088/1367-2630/ada8d1

Related papers

Efficient tensor networks for control-enhanced quantum metrology

Qiushi Liu, Yuxiang Yang

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.

arXiv:2403.09519•Quantum•Dec 18, 2024•2 citations

Optimal phase estimation in the presence of correlated dephasing

Srijon Ghosh, Arkadiusz Kobus, Stanisław Kurdziałek +1 more

We investigate optimal metrological protocols for phase estimation in the presence of correlated dephasing noise, including spin-squeezed state sensing strategies as well as parallel and adaptive protocols optimized using tensor-network-based numerical methods. The results are benchmarked against fundamental bounds obtained either via the latest quantum comb extension method or an optimized classical simulation method. We find that the spin-squeezed states offer practically optimal performance in the regime where phase fluctuations are positively correlated but can be outperformed by tensor-network-optimized strategies for negatively correlated fluctuations.

quant-pharXiv:2511.07211•Quantum•Nov 11, 2025•0 citations

Adaptive quantum channel discrimination using methods of quantum metrology

Stanisław Sieniawski, Rafał Demkowicz-Dobrzański

Abstract We present an efficient tensor-network based algorithm for finding the optimal adaptive quantum channel discrimination strategies inspired by recently developed numerical methods in quantum metrology to find the optimal adaptive channel estimation protocols. We examine the connection between channel discrimination and estimation problems, highlighting in particular an appealing structural similarity between models that admit Heisenberg scaling estimation performance, and models that admit perfect channel discrimination in finite–number of channel uses.

arXiv:2510.15506•New Journal of Physics•Jan 28, 2026•1 citation

Tensor-network approach for quantum metrology in many-body quantum systems

Krzysztof Chabuda, Jacek Dziarmaga, Tobias J. Osborne +1 more

Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide a comprehensive framework exploiting matrix product operators (MPO) type tensor networks for quantum metrological problems. The maximal achievable estimation precision as well as the optimal probe states in previously inaccessible regimes can be identified including models with short-range noise correlations. Moreover, the application of infinite MPO (iMPO) techniques allows for a direct and efficient determination of the asymptotic precision in the limit of infinite particle numbers. We illustrate the potential of our framework in terms of an atomic clock stabilization (temporal noise correlation) example as well as magnetic field sensing (spatial noise correlations). As a byproduct, the developed methods may be used to calculate the fidelity susceptibility—a parameter widely used to study phase transitions. © 2020, The Author(s).

•Jan 1, 2020•27 citations

Tensor-network approach for quantum metrology in many-body quantum systems

Krzysztof Chabuda, Jacek Dziarmaga, Tobias J. Osborne +1 more

Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide a comprehensive framework exploiting matrix product operators (MPO) type tensor networks for quantum metrological problems. The maximal achievable estimation precision as well as the optimal probe states in previously inaccessible regimes can be identified including models with short-range noise correlations. Moreover, the application of infinite MPO (iMPO) techniques allows for a direct and efficient determination of the asymptotic precision in the limit of infinite particle numbers. We illustrate the potential of our framework in terms of an atomic clock stabilization (temporal noise correlation) example as well as magnetic field sensing (spatial noise correlations). As a byproduct, the developed methods may be used to calculate the fidelity susceptibility-a parameter widely used to study phase transitions.

arXiv:1906.02761•Nature Communications•Jan 14, 2020•44 citations

Optimal Strategies for Multi-parameter Quantum Metrology

Linxuan Li, Zihao Hu, Longyun Chen +2 more

Estimating multiple unknown parameters simultaneously is essential for practical quantum sensing. However, it faces a fundamental challenge: the optimal strategy for estimating one parameter is often incompatible with that for another, making it impossible to simultaneously achieve the ultimate precision limits for all parameters. Here we develop a general and efficient computational framework that jointly optimizes probe states, control operations, and measurements across different strategy families, including parallel, sequential, and those with indefinite causal order. Our approach provides exact semidefinite-program formulations for several precision bounds, including the Holevo, Nagaoka-Hayashi, and quantum Cramér-Rao bounds. We demonstrate the capabilities of the framework in multiparameter magnetometry and frequency estimation, identifying optimal protocols within each class and revealing a strict hierarchy among the achievable performances of different classes in the multiparameter regime. The framework also directly incorporates resource constraints, such as energy budgets, enabling systematic investigation of experimentally realistic sensing scenarios. Furthermore, we develop a finite-memory optimization method for sequential strategies with restricted ancillary-memory dimension. By decomposing the protocol into initial probe preparation and intermediate control operations, this method provides a practical route to designing resource-constrained sequential sensing schemes. Our work establishes a versatile computational tool for determining fundamental precision limits and designing optimal quantum-sensing protocols in complex multiparameter settings.

quant-pharXiv:2608.01114•Aug 4, 2026•0 citations
Abstract 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.
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.
We investigate optimal metrological protocols for phase estimation in the presence of correlated dephasing noise, including spin-squeezed state sensing strategies as well as parallel and adaptive protocols optimized using tensor-network-based numerical methods. The results are benchmarked against fundamental bounds obtained either via the latest quantum comb extension method or an optimized classical simulation method. We find that the spin-squeezed states offer practically optimal performance in the regime where phase fluctuations are positively correlated but can be outperformed by tensor-network-optimized strategies for negatively correlated fluctuations.
Abstract We present an efficient tensor-network based algorithm for finding the optimal adaptive quantum channel discrimination strategies inspired by recently developed numerical methods in quantum metrology to find the optimal adaptive channel estimation protocols. We examine the connection between channel discrimination and estimation problems, highlighting in particular an appealing structural similarity between models that admit Heisenberg scaling estimation performance, and models that admit perfect channel discrimination in finite–number of channel uses.
Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide a comprehensive framework exploiting matrix product operators (MPO) type tensor networks for quantum metrological problems. The maximal achievable estimation precision as well as the optimal probe states in previously inaccessible regimes can be identified including models with short-range noise correlations. Moreover, the application of infinite MPO (iMPO) techniques allows for a direct and efficient determination of the asymptotic precision in the limit of infinite particle numbers. We illustrate the potential of our framework in terms of an atomic clock stabilization (temporal noise correlation) example as well as magnetic field sensing (spatial noise correlations). As a byproduct, the developed methods may be used to calculate the fidelity susceptibility—a parameter widely used to study phase transitions. © 2020, The Author(s).
Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide a comprehensive framework exploiting matrix product operators (MPO) type tensor networks for quantum metrological problems. The maximal achievable estimation precision as well as the optimal probe states in previously inaccessible regimes can be identified including models with short-range noise correlations. Moreover, the application of infinite MPO (iMPO) techniques allows for a direct and efficient determination of the asymptotic precision in the limit of infinite particle numbers. We illustrate the potential of our framework in terms of an atomic clock stabilization (temporal noise correlation) example as well as magnetic field sensing (spatial noise correlations). As a byproduct, the developed methods may be used to calculate the fidelity susceptibility-a parameter widely used to study phase transitions.
Estimating multiple unknown parameters simultaneously is essential for practical quantum sensing. However, it faces a fundamental challenge: the optimal strategy for estimating one parameter is often incompatible with that for another, making it impossible to simultaneously achieve the ultimate precision limits for all parameters. Here we develop a general and efficient computational framework that jointly optimizes probe states, control operations, and measurements across different strategy families, including parallel, sequential, and those with indefinite causal order. Our approach provides exact semidefinite-program formulations for several precision bounds, including the Holevo, Nagaoka-Hayashi, and quantum Cramér-Rao bounds. We demonstrate the capabilities of the framework in multiparameter magnetometry and frequency estimation, identifying optimal protocols within each class and revealing a strict hierarchy among the achievable performances of different classes in the multiparameter regime. The framework also directly incorporates resource constraints, such as energy budgets, enabling systematic investigation of experimentally realistic sensing scenarios. Furthermore, we develop a finite-memory optimization method for sequential strategies with restricted ancillary-memory dimension. By decomposing the protocol into initial probe preparation and intermediate control operations, this method provides a practical route to designing resource-constrained sequential sensing schemes. Our work establishes a versatile computational tool for determining fundamental precision limits and designing optimal quantum-sensing protocols in complex multiparameter settings.