Generalizable control for multiparameter quantum metrology

Han Xu, Lingna Wang, Haidong Yuan, and Xin Wang
Phys. Rev. A 103, 042615 – Published 29 April 2021

Abstract

Quantum control can be employed in quantum metrology to improve the precision limit for the estimation of unknown parameters. The optimal control, however, typically depends on the actual values of the parameters and thus needs to be designed adaptively with the updated estimations of those parameters. Traditional methods, such as gradient ascent pulse engineering (GRAPE), need to be rerun for each new set of parameters encountered, making the optimization costly, especially when many parameters are involved. Here we study the generalizability of optimal control, namely, optimal controls that can be systematically updated across a range of parameters with minimal cost. In cases where control channels can completely reverse the shift in the Hamiltonian due to a change in parameters, we provide an analytical method which efficiently generates optimal controls for any parameter starting from an initial optimal control found by either GRAPE or reinforcement learning. When the control channels are restricted, the analytical scheme is invalid, but reinforcement learning still retains a level of generalizability, albeit in a narrower range. In cases where the shift in the Hamiltonian is impossible to decompose to available control channels, no generalizability is found for either the reinforcement learning or the analytical scheme. We argue that the generalization of reinforcement learning is through a mechanism similar to the analytical scheme. Our results provide insights into when and how the optimal control in multiparameter quantum metrology can be generalized, thereby facilitating efficient implementation of optimal quantum estimation of multiple parameters, particularly for an ensemble of systems with ranges of parameters.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
5 More
  • Received 24 December 2020
  • Revised 22 February 2021
  • Accepted 13 April 2021

DOI:https://doi.org/10.1103/PhysRevA.103.042615

©2021 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Han Xu1,2, Lingna Wang3, Haidong Yuan3,*, and Xin Wang1,†

  • 1Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen, Guangdong 518057, China
  • 2School of Physics and Technology, Wuhan University, Wuhan 430072, China
  • 3Department of Mechanical and Automation Engineering, Chinese University of Hong Kong, Shatin, Hong Kong SAR, China

  • *hdyuan@mae.cuhk.edu.hk
  • x.wang@cityu.edu.hk

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 103, Iss. 4 — April 2021

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×