Hamiltonian identifiability assisted by single-probe measurement

TL;DR

This paper investigates how to determine the parameters of a many-body spin-1/2 Hamiltonian using measurements from a single quantum probe, employing algebraic methods and control protocols to enhance identifiability.

Contribution

It introduces a Gr"obner basis approach for Hamiltonian identifiability testing and provides resource bounds and control strategies for spin chain models.

Findings

Identifiability conditions for spin chain Hamiltonians are established.

Resource bounds for measurements and evolution time are derived.

Control protocols can convert nonidentifiable Hamiltonians into identifiable ones.

Abstract

We study the Hamiltonian identifiability of a many-body spin-1/2 system assisted by the measure- ment on a single quantum probe based on the eigensystem realization algorithm (ERA) approach employed in Phys. Rev. Lett. 113, 080401 (2014). We demonstrate a potential application of Gr\"obner basis to the identifiability test of the Hamiltonian, and provide the necessary experimental resources, such as the lower bound in the number of the required measurement points, the upper bound in total required evolution time, and thus the total measurement time. Focusing on the examples of the identifiability in the spin chain model with nearest-neighboring interaction, we classify the spin-chain Hamiltonian based on its identifiability, and provide the control protocols to engineer the nonidentifiable Hamiltonian to be an identifiable Hamiltonian.