Quantum Multiobservable Control

TL;DR

This paper introduces deterministic algorithms for the simultaneous control of multiple quantum observables, enabling precise tracking of target expectation values through quantum multiobservable tracking control (MOTC).

Contribution

It presents a novel MOTC framework that leverages the topology of quantum control landscapes and introduces the multiobservable controllability Gramian for efficient multiobjective quantum control.

Findings

Algorithms successfully track homotopic trajectories to target observables.

Quantum control landscapes facilitate convergence and efficiency.

Techniques are adaptable to general quantum multiobjective problems.

Abstract

We present deterministic algorithms for the simultaneous control of an arbitrary number of quantum observables. Unlike optimal control approaches based on cost function optimization, quantum multiobservable tracking control (MOTC) is capable of tracking predetermined homotopic trajectories to target expectation values in the space of multiobservables. The convergence of these algorithms is facilitated by the favorable critical topology of quantum control landscapes. Fundamental properties of quantum multiobservable control landscapes that underlie the efficiency of MOTC, including the multiobservable controllability Gramian, are introduced. The effects of multiple control objectives on the structure and complexity of optimal fields are examined. With minor modifications, the techniques described herein can be applied to general quantum multiobjective control problems.