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

European Control Conference (ECC)

Flatness-based control of a single qubit gate

Paulo Sérgio Pereira da Silva, Pierre Rouchon

Published Jul 1, 2007• 3 citations
Publisher

Abstract

This work considers the open-loop control problem of steering a two level quantum system, from an initial to a final condition. The model of this system evolves on the state space X = SU(2), having two inputs that corresponds to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric setting. Using a particular parametrization, some simulation results of the flatness based control are presented for the Hadamard gate.

DOI
10.23919/ecc.2007.7068575

Related papers

1 Flatness-based control of a single qubit gate

Paulo Sergio, Pereira Silva, Pierre Rouchon

This work considers the open-loop control problem of steering a two level quantum system from an initial to a final condition. The model of this system evolves on the state space X = SU(2), having two inputs that correspond to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations. Simulation results of this flatness-based open-loop control are provided.

•Jan 1, 2007•23 citations

Flatness-Based Control of a Single Qubit Gate

Paulo Sergio Pereira da Silva, Pierre Rouchon

This work considers the open-loop control problem of steering a two-level quantum system from any initial to any final condition. The model of this system evolves on the state space , having two inputs that correspond to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations. Simulation results of this flatness-based open-loop control are provided.

arXiv:math/0701056•IEEE Transactions on Automatic Control•Apr 1, 2008•18 citations

Technical Notes and Correspondence Flatness-Based Control of a Single Qubit Gate

Paulo Sérgio, Pereira da Silva, Pierre Rouchon

Abstract—This work considers the open-loop control problem of steering a two-level quantum system from any initial to any final condition. The model of this system evolves on the state space X = SU(2), havingtwo inputs that correspond to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations. Simulation results of this flatness-based open-loop control are provided. Index Terms—Flatness, geometric control, nonlinear systems, quantum control, qubit gate. I.

•Mar 20, 2010•0 citations

Open-loop control design via parametrization applied in a two-level quantum system model

M.T. Nihtilä

In the design of quantum computing devices of the future the basic element is the qubit. It is a two-level quantum system which may describe population transfer from one steady-state to another controlled by a coherent laser field. A four-dimensional real-variable differential equation model is constructed from the complex-valued two-level model describing the wave function of the system. The state transition matrix of the model is constructed via the Wei-Norman technique and Lie algebraic methodology. The idea of parametrization using flatness-based control, is applied to construct feasible input-output pairs of the model. This input drives the state of the system from the given initial state to the given final state in a finite time producing the corresponding output of the pair. The population transfer is obtained by nullifying part of the state vector via careful selection of the parameter functions.

arXiv:1002.4260•International Symposium on Communications, Control and Signal Processing•Mar 1, 2010•0 citations

Realization of quantum Hadamard gate by applying optimal control fields to a spin qubit

S. Mohammad Nejad, Mohammad Mehmandoost

We study the manipulation of a two level quantum mechanical system which is the basic unit of representing data in quantum information science, a qubit. This research is motivated by the design of the quantum Hadamard gate for solid state spin qubits. We consider the problem of driving the initial state of a qubit into a desired final state in a specified time, while minimizing the energies of the control fields. Optimal control theory is employed to define optimum control fields which satisfy both dynamical constraints and optimality conditions. Time evolution of the system is calculated within the Schrödinger equation and a gradient method is used for tailoring optimal control fields.

International Conference on Mechanical and Electronics Engineering•Aug 1, 2010•5 citations

Preparation of Hadamard Gate for Open Quantum Systems by the Lyapunov Control Method

Nourallah Ghaeminezhad, Shuang Cong

In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation. Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.

IEEE/CAA Journal of Automatica Sinica•Apr 5, 2018•25 citations
This work considers the open-loop control problem of steering a two level quantum system, from an initial to a final condition. The model of this system evolves on the state space X = SU(2), having two inputs that corresponds to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric setting. Using a particular parametrization, some simulation results of the flatness based control are presented for the Hadamard gate.
Abstract—This work considers the open-loop control problem of steering a two-level quantum system from any initial to any final condition. The model of this system evolves on the state space X = SU(2), havingtwo inputs that correspond to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations. Simulation results of this flatness-based open-loop control are provided. Index Terms—Flatness, geometric control, nonlinear systems, quantum control, qubit gate. I.
In the design of quantum computing devices of the future the basic element is the qubit. It is a two-level quantum system which may describe population transfer from one steady-state to another controlled by a coherent laser field. A four-dimensional real-variable differential equation model is constructed from the complex-valued two-level model describing the wave function of the system. The state transition matrix of the model is constructed via the Wei-Norman technique and Lie algebraic methodology. The idea of parametrization using flatness-based control, is applied to construct feasible input-output pairs of the model. This input drives the state of the system from the given initial state to the given final state in a finite time producing the corresponding output of the pair. The population transfer is obtained by nullifying part of the state vector via careful selection of the parameter functions.
We study the manipulation of a two level quantum mechanical system which is the basic unit of representing data in quantum information science, a qubit. This research is motivated by the design of the quantum Hadamard gate for solid state spin qubits. We consider the problem of driving the initial state of a qubit into a desired final state in a specified time, while minimizing the energies of the control fields. Optimal control theory is employed to define optimum control fields which satisfy both dynamical constraints and optimality conditions. Time evolution of the system is calculated within the Schrödinger equation and a gradient method is used for tailoring optimal control fields.
In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation. Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.