Equation of motion for process matrix: Hamiltonian identification and dynamical control of open quantum systems

TL;DR

This paper introduces a new dynamical equation for the process matrix in open quantum systems, enabling Hamiltonian identification and optimal control, even in non-Markovian or strong coupling regimes.

Contribution

It formulates a process matrix evolution equation applicable to complex regimes and demonstrates its use in Hamiltonian estimation and decoherence control.

Findings

Efficient Hamiltonian estimation via partial process tomography.

Applicable to non-Markovian and strong coupling regimes.

Provides a framework for decoherence suppression through optimal control.

Abstract

We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of the process matrix acting on a system. This equation is applicable to non-Markovian and/or strong coupling regimes. We propose two distinct applications for this dynamical equation. We first demonstrate identification of quantum Hamiltonians generating dynamics of closed or open systems via performing process tomography. In particular, we argue how one can efficiently estimate certain classes of sparse Hamiltonians by performing partial tomography schemes. In addition, we introduce a novel optimal control theoretic setting for manipulating quantum dynamics of Hamiltonian systems, specifically for the task of decoherence suppression.