Quantum Internal Model Principle: Decoherence Control

TL;DR

This paper introduces a novel quantum internal model principle for decoherence control, demonstrating how quantum controllers can completely decouple open quantum systems from environmental disturbances using geometric control theory.

Contribution

It formulates decoherence control as a disturbance rejection problem and establishes the first quantum internal model principle linking environmental models to control design.

Findings

Decoupling of a 2-qubit system from decoherence achieved

Conditions for perfect decoherence suppression derived

Introduces a new quantum internal model principle

Abstract

In this article, we study the problem of designing a Decoherence Control for quantum systems with the help of a scalable ancillary quantum control and techniques from geometric control theory, in order to successfully and completely decouple an open quantum system from its environment. We re-formulate the problem of decoherence control as a disturbance rejection scheme which also leads us to the idea of Internal Model Principle for quantum control systems which is first of its kind in the literature. It is shown that decoupling a quantum disturbance from an open quantum system, is possible only with the help of a quantum controller which takes into account the model of the environmental interaction. This is demonstrated for a simple 2-qubit system wherein the effects of decoherence are completely eliminated. The theory provides conditions to be imposed on the controller to ensure perfect decoupling. Hence the problem of decoherence control naturally gives rise to the quantum internal model principle which relates the disturbance rejecting control to the model of the environmental interaction. Classical internal model principle and disturbance decoupling focus on different aspects viz. perfect output tracking and complete decoupling of output from external disturbances respectively. However for quantum systems, the two problems come together and merge in order to produce an effective platform for decoherence control. In this article we introduce a seminal connection between disturbance decoupling and the corresponding analog for internal model principle for quantum systems.