Hamiltonian identification through enhanced observability utilizing quantum control

TL;DR

This paper demonstrates that quantum control techniques can enable the unique identification of a quantum system's Hamiltonian using limited measurements, by designing specific control inputs inspired by Ramsey interferometry.

Contribution

It proves local observability of the quantum dipole moment matrix with minimal measurements and constructs discriminating controls for Hamiltonian identification.

Findings

Quantum control allows for Hamiltonian identification with limited measurements.

Discriminating controls with three temporal components can distinguish close dipole matrices.

The approach enhances the potential for high-precision quantum system identification.

Abstract

This paper considers Hamiltonian identification for a controllable quantum system with non-degenerate transitions and a known initial state. We assume to have at our disposal a single scalar control input and the population measure of only one state at an (arbitrarily large) final time T. We prove that the quantum dipole moment matrix is locally observable in the following sense: for any two close but distinct dipole moment matrices, we construct discriminating controls giving two different measurements. Such discriminating controls are constructed to have three well defined temporal components, as inspired by Ramsey interferometry. This result suggests that what may appear at first to be very restrictive measurements are actually rich for identification, when combined with well designed discriminating controls, to uniquely identify the complete dipole moment of such systems. The assessment supports the employment of quantum control as a promising means to achieve high quality identification of a Hamiltonian.