Open-Loop Control Design via Parametrization Applied in a Two-Level Quantum System Model

TL;DR

This paper presents a novel open-loop control method for two-level quantum systems, using parametrization and flatness-based control to achieve population transfer, supported by a differential equation model and preliminary simulations.

Contribution

It introduces a parametrization approach with flatness-based control for quantum state transfer, applying Lie algebraic methods to a two-level quantum system model.

Findings

Feasible input-output pairs constructed for state transfer

Population transfer achieved through parameter function selection

Preliminary simulation validates the control approach

Abstract

In the design of quantum computing devices of the future the basic element is the qubit. It is a two-level quantum system which may describe population transfer from one steady-state to another controlled by a coherent laser field. A four-dimensional real-variable differential equation model is constructed from the complex-valued two-level model describing the wave function of the system. The state transition matrix of the model is constructed via the Wei-Norman technique and Lie algebraic methodology. The idea of parametrization using flatness-based control, is applied to construct feasible input--output pairs of the model. This input drives the state of the system from the given initial state to the given final state in a finite time producing the corresponding output of the pair. The population transfer is obtained by nullifying part of the state vector via careful selection of the parameter functions. A preliminary simulation study completes the paper.