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Related Experiment Video

Updated: Jun 24, 2026

A Protocol for Real-time 3D Single Particle Tracking

A Protocol for Real-time 3D Single Particle Tracking

Published on: January 3, 2018

Multiple solutions in the tracking control of quantum systems.

Abhinav Jha¹, Vincent Beltrani, Carey Rosenthal

¹Frick Laboratory, Princeton University, Princeton, New Jersey 08540, USA.

The Journal of Physical Chemistry. A

|April 9, 2009

Summary

Quantum systems exhibit multiple control solutions due to nonlinear dynamics. This leads to an exponentially growing number of distinct quantum control fields for tracking desired system evolutions.

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Area of Science:

Quantum mechanics
Quantum control theory
Nonlinear dynamics

Background:

Quantum control aims to steer quantum systems to desired states.
Understanding the landscape of possible control strategies is crucial for practical applications.
Previous work has explored the complexity of quantum control landscapes.

Purpose of the Study:

To demonstrate the existence of multiple solutions in tracking control of quantum systems.
To investigate the origin of these multiple solutions.
To analyze the implications for the space of achievable quantum control fields.

Main Methods:

Analysis of short-time propagators in quantum systems.
Investigating the nonlinear dependence of propagators on control fields.
Application to a small model quantum system to illustrate the findings.

Main Results:

Multiple distinct solutions for tracking control exist at each time point.
These solutions arise from the nonlinear dependence of short-time propagators on the control field.
The number of solutions expands exponentially with time, creating a vast control landscape.

Conclusions:

The multiplicity of tracking control solutions is a fundamental aspect of quantum control.
This phenomenon necessitates choices at each time step, leading to a complex control landscape.
Findings are consistent with predictions from quantum control landscape theory.