Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2209.14678

Optimizing for an arbitrary Schrödinger cat state. II. Application in the presence of dissipation

Matthias G. Krauss, Daniel M. Reich, Christiane P. Koch

Published Sep 29, 2022• 0 citations
arXivHTMLPDF

Abstract

We extend here the optimization functional targeting arbitrary cat states, derived in the companion paper, to open quantum system dynamics. Applying it to a Jaynes-Cummings model with decay on the oscillator, we find, for strong dissipation and large cat radii, a change in the control strategy for preparing an entangled cat state. Our results illustrate the versatility of the quantum optimal control toolbox for practical applications in the quantum technologies.

DOI
10.48550/arxiv.2209.14678

Related papers

Optimizing for an arbitrary Schrödinger cat state

Matthias G. Krauss, Christiane P. Koch, Daniel M. Reich

We derive a set of functionals for optimization towards an arbitrary cat state and demonstrate their application by optimizing the dynamics of a Kerr-nonlinear Hamiltonian with two-photon driving. The versatility of our framework allows us to adapt our functional towards optimization of maximally entangled cat states, applying it to a Jaynes-Cummings model. We identify the strategy of the obtained control fields and determine the quantum speed limit as a function of the cat state's excitation. Finally, we extend our optimization functionals to open quantum system dynamics and apply it to the Jaynes-Cummings model with decay on the oscillator. For strong dissipation and large cat radii, we find a change in the control strategy compared to the case without dissipation. Our results highlight the power of optimal control with functionals specifically crafted for complex physical tasks and the versatility of the quantum optimal control toolbox for practical applications in the quantum technologies.

Physical Review Research•Oct 17, 2023•3 citations

Optimizing for an arbitrary Schrödinger cat state

Matthias G. Krauss, Christiane P. Koch, Daniel M. Reich

We derive a set of functionals for optimization towards an arbitrary cat state and demonstrate their application by optimizing the dynamics of a Kerr-nonlinear Hamiltonian with two-photon driving. The versatility of our framework allows us to adapt our functional towards optimization of maximally entangled cat states, applying it to a Jaynes-Cummings model. We identify the strategy of the obtained control fields and determine the quantum speed limit as a function of the cat state's excitation. Finally, we extend our optimization functionals to open quantum system dynamics and apply it to the Jaynes-Cummings model with decay on the oscillator. For strong dissipation and large cat radii, we find a change in the control strategy compared to the case without dissipation. Our results highlight the power of optimal control with functionals specifically crafted for complex physical tasks and the versatility of the quantum optimal control toolbox for practical applications in the quantum technologies.

arXiv:2209.14675•Sep 29, 2022•0 citations

Development and Application of Optimal Control Methods for Quantum Technologies

Matthias G. Krauss

The precise control of quantum systems enables the development of a wide range of promising quantum technologies. These technologies allow for beating the limits of their classical pendants and outperform them in various tasks. This thesis employs and expands a variety of methods and concepts of optimal control theory in order to address different problems in quantum technologies and work towards their realization. Schrödinger cat states present a particularly versatile set of states, that have a broad range of applications for all types of quantum technologies. We employ optimal control theory to investigate how cat states can be prepared in different physical systems. This allows us to investigate the role of higher order nonlinearities in anharmonic resonators. Further, this enables the identification of strategies for cat state preparation in the presence of higher order anharmonicities and an analysis if they can be exploited as resource. Additionally, we develop a set of functionals, which allow for optimizing towards arbitrary cat states. This facilitates the preparation of cat states even in systems, where the reachable set of states is not immediately apparent. Quantum computing is a particularly prominent quantum technology and promises a completely new paradigm for computing. Crosstalk, the undesired interaction between different parts of a quantum processor, poses a major challenge across various architectures. Therefore, we utilize concepts from optimal control to introduce the perfect entangler spectrum as a tool to detect operational crosstalk, caused by spectator qubits. This allows us to identify parameter regimes of superconducting qubits, which exhibit crosstalk and determine the underlying mechanisms. In addition, we utilize optimal control and parameter optimizations to explore mitigation strategies for the different crosstalk mechanisms. Our work paves the way for systematically eliminating crosstalk, when scaling up quantum computing architectures.

•Jan 1, 2025•0 citations

Training Schrödinger’s cat: quantum optimal control

Steffen J. Glaser, Ugo Boscain, Tommaso Calarco +9 more

It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a dynamical system from a given initial state into a desired target state with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. In this communication, state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium of experts in optimal control theory and applications to spectroscopy, imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap for future developments.

arXiv:1508.00442•The European Physical Journal D•Dec 1, 2015•773 citations

Introduction to quantum control: From basic concepts to applications in quantum technologies

Christiane P. Koch

Quantum control refers to our ability to manipulate quantum systems. This tutorial-style chapter focuses on the use of classical electromagnetic fields to steer the system dynamics. In this approach, the quantum nature of the control stems solely from the underlying dynamics, through the exploitation of destructive and constructive interference to reach the control target. We first discuss two basic control principles -- coherent control which uses manipulation in frequency or time to design these interferences, and adiabatic following where access to the control target is enabled by tracking the time-dependent ground state. For complex control targets and system dynamics that exceed the scope of these basic principles, optimal control theory provides a powerful suite of tools to design the necessary protocols. A key consideration for the successful application of optimal control theory is a proper choice of the optimization functional. All concepts are illustrated using recent work from my research group, with a focus on controlling atoms and superconducting qubits. The chapter concludes with an outlook on integrating coherent control with engineered dissipation and a discussion of open questions in the field.

quant-pharXiv:2512.04990•Dec 5, 2025•0 citations

Optimal Control of Open Quantum Systems in Lindblad Equation

Shuang Cong

In order to solve the state of an open quantum system with relaxation and dissipation,the dynamical equation of the system in matrix was transformed into vector form in Liouville space. Taking the expectation value for the state under control reaching the target state as performance indicators,an optimal control function was derived for the system transformed. The control a 2-level open quantum system was simulated on in MATLAB. The influence to population transfer probability and control time caused by changing of parameters were analysed contrastively.

Jisuanji fangzhen•Jan 1, 2010•0 citations
We extend here the optimization functional targeting arbitrary cat states, derived in the companion paper, to open quantum system dynamics. Applying it to a Jaynes-Cummings model with decay on the oscillator, we find, for strong dissipation and large cat radii, a change in the control strategy for preparing an entangled cat state. Our results illustrate the versatility of the quantum optimal control toolbox for practical applications in the quantum technologies.
We derive a set of functionals for optimization towards an arbitrary cat state and demonstrate their application by optimizing the dynamics of a Kerr-nonlinear Hamiltonian with two-photon driving. The versatility of our framework allows us to adapt our functional towards optimization of maximally entangled cat states, applying it to a Jaynes-Cummings model. We identify the strategy of the obtained control fields and determine the quantum speed limit as a function of the cat state's excitation. Finally, we extend our optimization functionals to open quantum system dynamics and apply it to the Jaynes-Cummings model with decay on the oscillator. For strong dissipation and large cat radii, we find a change in the control strategy compared to the case without dissipation. Our results highlight the power of optimal control with functionals specifically crafted for complex physical tasks and the versatility of the quantum optimal control toolbox for practical applications in the quantum technologies.
We derive a set of functionals for optimization towards an arbitrary cat state and demonstrate their application by optimizing the dynamics of a Kerr-nonlinear Hamiltonian with two-photon driving. The versatility of our framework allows us to adapt our functional towards optimization of maximally entangled cat states, applying it to a Jaynes-Cummings model. We identify the strategy of the obtained control fields and determine the quantum speed limit as a function of the cat state's excitation. Finally, we extend our optimization functionals to open quantum system dynamics and apply it to the Jaynes-Cummings model with decay on the oscillator. For strong dissipation and large cat radii, we find a change in the control strategy compared to the case without dissipation. Our results highlight the power of optimal control with functionals specifically crafted for complex physical tasks and the versatility of the quantum optimal control toolbox for practical applications in the quantum technologies.
The precise control of quantum systems enables the development of a wide range of promising quantum technologies. These technologies allow for beating the limits of their classical pendants and outperform them in various tasks. This thesis employs and expands a variety of methods and concepts of optimal control theory in order to address different problems in quantum technologies and work towards their realization. Schrödinger cat states present a particularly versatile set of states, that have a broad range of applications for all types of quantum technologies. We employ optimal control theory to investigate how cat states can be prepared in different physical systems. This allows us to investigate the role of higher order nonlinearities in anharmonic resonators. Further, this enables the identification of strategies for cat state preparation in the presence of higher order anharmonicities and an analysis if they can be exploited as resource. Additionally, we develop a set of functionals, which allow for optimizing towards arbitrary cat states. This facilitates the preparation of cat states even in systems, where the reachable set of states is not immediately apparent. Quantum computing is a particularly prominent quantum technology and promises a completely new paradigm for computing. Crosstalk, the undesired interaction between different parts of a quantum processor, poses a major challenge across various architectures. Therefore, we utilize concepts from optimal control to introduce the perfect entangler spectrum as a tool to detect operational crosstalk, caused by spectator qubits. This allows us to identify parameter regimes of superconducting qubits, which exhibit crosstalk and determine the underlying mechanisms. In addition, we utilize optimal control and parameter optimizations to explore mitigation strategies for the different crosstalk mechanisms. Our work paves the way for systematically eliminating crosstalk, when scaling up quantum computing architectures.
It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a dynamical system from a given initial state into a desired target state with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. In this communication, state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium of experts in optimal control theory and applications to spectroscopy, imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap for future developments.
Quantum control refers to our ability to manipulate quantum systems. This tutorial-style chapter focuses on the use of classical electromagnetic fields to steer the system dynamics. In this approach, the quantum nature of the control stems solely from the underlying dynamics, through the exploitation of destructive and constructive interference to reach the control target. We first discuss two basic control principles -- coherent control which uses manipulation in frequency or time to design these interferences, and adiabatic following where access to the control target is enabled by tracking the time-dependent ground state. For complex control targets and system dynamics that exceed the scope of these basic principles, optimal control theory provides a powerful suite of tools to design the necessary protocols. A key consideration for the successful application of optimal control theory is a proper choice of the optimization functional. All concepts are illustrated using recent work from my research group, with a focus on controlling atoms and superconducting qubits. The chapter concludes with an outlook on integrating coherent control with engineered dissipation and a discussion of open questions in the field.
In order to solve the state of an open quantum system with relaxation and dissipation,the dynamical equation of the system in matrix was transformed into vector form in Liouville space. Taking the expectation value for the state under control reaching the target state as performance indicators,an optimal control function was derived for the system transformed. The control a 2-level open quantum system was simulated on in MATLAB. The influence to population transfer probability and control time caused by changing of parameters were analysed contrastively.