Heisenberg-limited metrology with perturbing interactions

Chao Yin and Andrew Lucas

Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder CO 80309, USA

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We show that it is possible to perform Heisenberg-limited metrology on GHZ-like states, in the presence of generic spatially local, possibly strong interactions during the measurement process. An explicit protocol, which relies on single-qubit measurements and feedback based on polynomial-time classical computation, achieves the Heisenberg limit. In one dimension, matrix product state methods can be used to perform this classical calculation, while in higher dimensions the cluster expansion underlies the efficient calculations. The latter approach is based on an efficient classical sampling algorithm for short-time quantum dynamics, which may be of independent interest.

Presentation “Heisenberg limited metrology with perturbing interactions and efficient sampling” by Chao Yin and Andrew Lucas at QIP 2024

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[1] Luis Pedro García-Pintos, Kishor Bharti, Jacob Bringewatt, Hossein Dehghani, Adam Ehrenberg, Nicole Yunger Halpern, and Alexey V. Gorshkov, "Estimation of Hamiltonian parameters from thermal states", arXiv:2401.10343, (2024).

[2] Jia-Xuan Liu, Jing Yang, Hai-Long Shi, and Sixia Yu, "Optimal Local Measurements in Many-body Quantum Metrology", arXiv:2310.00285, (2023).

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