Inverse Engineering Control in Open Quantum Systems

TL;DR

This paper introduces a method for inverse engineering control in open quantum systems, enabling the design of Hamiltonians to achieve target states, and analyzes its robustness under noise and decoherence effects.

Contribution

It presents a novel scheme for inverse control in open quantum systems, deriving Hamiltonians from desired evolutions and analyzing noise effects on control fidelity.

Findings

Control fidelity is affected by noise, with dephasing and depolarization as dominant decoherence processes.

The control protocol is robust under certain noise conditions, maintaining high fidelity.

The formalism applies to both Markovian and non-Markovian environments.

Abstract

We propose a scheme for inverse engineering control in open quantum systems. Starting from an undetermined time evolution operator, a time-dependent Hamiltonian is derived in order to guide the system to attain an arbitrary target state at a predefined time. We analyze the fidelity of our control protocol under noise with respect to the stochastic fluctuation of the linear parameters of the Hamiltonian during the time evolution. For a special family of Hamiltonians for two-level systems, we show that the control evolution of the system under noise can be categorized into two standard decohering processes: dephasing and depolarization, for both Markovian and non- Markovian conditions. In particular, we illustrate our formalism by analysing the robustness of the engineered target state.