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:2209.14675

Optimizing for an arbitrary Schrödinger cat state

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

Published Sep 29, 2022• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.17169/refubium-41454

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. II. Application in the presence of dissipation

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

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.

arXiv:2209.14678•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

Optimal thermodynamic control in open quantum systems

Vasco Cavina, Andrea Mari, A. Carlini +1 more

We apply advanced methods of control theory to open quantum systems and we determine finite-time processes which are optimal with respect to thermodynamic performances. General properties and necessary conditions characterizing optimal drivings are derived, obtaining bang-bang-type solutions corresponding to control strategies switching between adiabatic and isothermal transformations. A direct application of these results is the maximization of the work produced by a generic quantum heat engine, where we show that the maximum power is directly linked to a particular conserved quantity naturally emerging from the control problem. Finally we apply our general approach to the specific case of a two-level system, which can be put in contact with two different baths at fixed temperatures, identifying the processes that minimize heat dissipation. Moreover, we explicitly solve the optimization problem for a cyclic two-level heat engine driven beyond the linear-response regime, determining the corresponding optimal cycle, the maximum power, and the efficiency at maximum power.

arXiv:1709.07400•Physical Review A•Jul 27, 2018•47 citations

Generalized Kerr-Cat Qubit Codes

Alonso Viladomat, Shahram Dehdashti, Amin Kargarian +2 more

We present a systematic study of Schrödinger cat codes constructed from Kerr-type coherent states, including displaced Kerr coherent states and Barut--Girardello Kerr coherent states, each admitting two distinct families determined by the sign of the Kerr nonlinearity. By tuning the Kerr parameter and coherent-state amplitude, these states interpolate between $\mathfrak{su}(2)$, $\mathfrak{su}(1,1)$ coherent states, providing a unified and versatile foundation for this type of bosonic quantum error correction. Unlike standard two-component Schrödinger cat codes, where a single photon-loss event induces an uncorrectable bit-flip, the nonlinear phase-space structure of Kerr cat states enables simultaneous detection and correction of both photon-loss and dephasing errors within a unified recovery framework, with optimal recovery operations determined via convex optimization. We demonstrate that Kerr cat encodings significantly outperform conventional cat codes under combined loss and dephasing noise, and that judicious parameter optimization can suppress both error channels to a level that reduces the overhead of additional error correction layers. We further show that Kerr-deformed coherent-state manifolds under engineered two-photon driving emerge as effective steady states of driven-dissipative dynamics, with single-photon decoherence strongly suppressed and leakage outside the protected manifold appearing only as higher-order corrections in the deformation strength. Our extended formalism identifies generalized Kerr Schrödinger cat codes as promising candidates for fault-tolerant bosonic quantum computation in experimental platforms such as nonlinear photonics.

quant-pharXiv:2606.14901•Jun 16, 2026•0 citations

Optimizing for an arbitrary perfect entangler. I. Functionals

Paul Watts, Jiří Vala, Matthias M. Müller +5 more

Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capable of creating a maximally entangled state out of some initial product state. The functional depends on easily computable local invariants and unequivocally determines whether a gate is a perfect entangler. Optimization with our functional is most useful if the two-qubit dynamics allows for the implementation of more than one perfect entangler. We discuss the reachable set of perfect entanglers for a generic Hamiltonian that corresponds to several quantum information platforms of current interest.

arXiv:1412.7347•Physical Review A•Jun 8, 2015•60 citations
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.
We apply advanced methods of control theory to open quantum systems and we determine finite-time processes which are optimal with respect to thermodynamic performances. General properties and necessary conditions characterizing optimal drivings are derived, obtaining bang-bang-type solutions corresponding to control strategies switching between adiabatic and isothermal transformations. A direct application of these results is the maximization of the work produced by a generic quantum heat engine, where we show that the maximum power is directly linked to a particular conserved quantity naturally emerging from the control problem. Finally we apply our general approach to the specific case of a two-level system, which can be put in contact with two different baths at fixed temperatures, identifying the processes that minimize heat dissipation. Moreover, we explicitly solve the optimization problem for a cyclic two-level heat engine driven beyond the linear-response regime, determining the corresponding optimal cycle, the maximum power, and the efficiency at maximum power.
We present a systematic study of Schrödinger cat codes constructed from Kerr-type coherent states, including displaced Kerr coherent states and Barut--Girardello Kerr coherent states, each admitting two distinct families determined by the sign of the Kerr nonlinearity. By tuning the Kerr parameter and coherent-state amplitude, these states interpolate between su(2)\mathfrak{su}(2)su(2), su(1,1)\mathfrak{su}(1,1)su(1,1) coherent states, providing a unified and versatile foundation for this type of bosonic quantum error correction. Unlike standard two-component Schrödinger cat codes, where a single photon-loss event induces an uncorrectable bit-flip, the nonlinear phase-space structure of Kerr cat states enables simultaneous detection and correction of both photon-loss and dephasing errors within a unified recovery framework, with optimal recovery operations determined via convex optimization. We demonstrate that Kerr cat encodings significantly outperform conventional cat codes under combined loss and dephasing noise, and that judicious parameter optimization can suppress both error channels to a level that reduces the overhead of additional error correction layers. We further show that Kerr-deformed coherent-state manifolds under engineered two-photon driving emerge as effective steady states of driven-dissipative dynamics, with single-photon decoherence strongly suppressed and leakage outside the protected manifold appearing only as higher-order corrections in the deformation strength. Our extended formalism identifies generalized Kerr Schrödinger cat codes as promising candidates for fault-tolerant bosonic quantum computation in experimental platforms such as nonlinear photonics.
Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization functional. Here, we derive a functional that targets the full set of two-qubit perfect entanglers, gates capable of creating a maximally entangled state out of some initial product state. The functional depends on easily computable local invariants and unequivocally determines whether a gate is a perfect entangler. Optimization with our functional is most useful if the two-qubit dynamics allows for the implementation of more than one perfect entangler. We discuss the reachable set of perfect entanglers for a generic Hamiltonian that corresponds to several quantum information platforms of current interest.