Variational Principle for Optimal Quantum Controls in Quantum Metrology

Jing Yang, Shengshi Pang, Zekai Chen, Andrew N. Jordan, and Adolfo del Campo

Phys. Rev. Lett. 128, 160505 – Published 22 April 2022

Abstract

We develop a variational principle to determine the quantum controls and initial state that optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is limited, the exact optimal initial state and the optimal controls are, in general, dependent on the probe time, a feature missing in the unrestricted case. Yet, for time-independent Hamiltonians with restricted controls, the problem can be approximately reduced to the unconstrained case via Floquet engineering. In particular, we find for magnetometry with a time-independent spin chain containing three-body interactions, even when the controls are restricted to one- and two-body interaction, that the Heisenberg scaling can still be approximately achieved. Our results open the door to investigate quantum metrology under a limited set of available controls, of relevance to many-body quantum metrology in realistic scenarios.

Received 14 November 2021
Accepted 22 March 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.160505

Physics Subject Headings (PhySH)

Quantum control Quantum metrology Quantum sensing

Quantum Information, Science & Technology

Authors & Affiliations

Jing Yang ^1,*,§, Shengshi Pang ^2,†,§, Zekai Chen ³, Andrew N. Jordan ^4,3, and Adolfo del Campo ^1,5,‡

¹Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
²School of Physics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China
³Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
⁴Institute for Quantum Studies, Chapman University, 1 University Drive, Orange, California 92866, USA
⁵Donostia International Physics Center, E-20018 San Sebastián, Spain