Hamiltonian tomography of dissipative systems under limited access: A biomimetic case study

TL;DR

This paper explores Hamiltonian tomography in open quantum systems with limited access, using a gateway approach to estimate parameters in complex networks, including biomimetic topologies.

Contribution

It extends the gateway approach to Hamiltonian tomography for open systems with limited probes and classifies network properties for successful estimation.

Findings

Classified network properties enabling Hamiltonian estimation.

Demonstrated applicability to biomolecular-like network topologies.

Analyzed limitations due to signal decay in open quantum systems.

Abstract

The identification of parameters in the Hamiltonian that describes complex many-body quantum systems is generally a very hard task. Recent attention has focused on such problems of Hamiltonian tomography for networks constructed with two-level systems. For open quantum systems, the fact that injected signals are likely to decay before they accumulate sufficient information for parameter estimation poses additional challenges. In this paper, we consider use of the gateway approach to Hamiltonian tomography \cite{Burgarth2009,Burgarth2009a} to complex quantum systems with a limited set of state preparation and measurement probes. We classify graph properties of networks for which the Hamiltonian may be estimated under equivalent conditions on state preparation and measurement. We then examine the extent to which the gateway approach may be applied to estimation of Hamiltonian parameters for network graphs with non-trivial topologies mimicking biomolecular systems.