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

Journal of Physics A Mathematical and General

Quantum control by decomposition ofSU(1, 1)

Jianwu Wu, Chunwen Li, Re-Bing Wu, Tzyh‐Jong Tarn, Jing Zhang

Published Oct 10, 2006• 13 citations
Publisher

Abstract

Constructive algorithms are presented for controlling quantum systems evolving on the SU (1, 1) Lie group. These procedures are performed via structured decomposition of SU (1, 1), which achieve precise controls without any approximations or iterative computations, under the sufficient condition that examines the existence of such decomposition. The technique is applied to controlling transitions between SU (1, 1) coherent states. These results open up new perspectives on the control design of infinite-dimensional quantum systems involving discrete or continuous spectra.

DOI
10.1088/0305-4470/39/43/010

Related papers

Quantum control by decompositions of SU(2)

Viswanath Ramakrishna, Kathryn L. Flores, HERSCHEL A. RABITZ +1 more

Constructive procedures that make no use of optimization or iterative calculations for the control of many quantum and classical systems, via controls that are required to satisfy constraints on their power or pulse area, are presented. These procedures are based on structured decompositions of SU(2). A general technique for obtaining such structured decompositions is given. Illustrative examples are provided.

Physical Review A•Oct 13, 2000•60 citations

Controllability of quantum mechanical systems with continuous spectra

TZYH JONG TARN, J. W. Clark, Dennis G. Lucarelli

The property of controllability of quantum systems is revisited. In the case of a system having this property, couplings to external agents are available whose adjustment can guide the state to any chosen target on a suitably defined manifold (or arbitrarily close to any such target) at any chosen time. With due consideration to unbounded operators corresponding to physical observables possessing continuous spectra, sufficient conditions for controllability based on Lie-algebraic arguments are obtained. The results are not limited to finite-dimensional systems, nor to infinite-dimensional systems with discrete spectra. The applicability of the results to systems with both bound and scattering states is demonstrated for the case of the one-dimensional Poschl-Teller potential. Attention is also directed to transitivity of the pertinent Lie algebra of a system without drift as a necessary and sufficient condition for controllability.

IEEE Conference on Decision and Control (CDC)•Nov 11, 2002•11 citations

Decompositions of unitary evolutions and dynamics of quantum systems

Domenico D’Alessandro, Raffaele Romano

Decompositions of the Lie group of unitary matrices are very useful tools in the control and analysis of quantum dynamics. In this paper, we survey recent results on decompositions, concerning their significance in terms of symmetries, entanglement, and their applications to control and dynamics. Several decompositions can be obtained by recursively applying the Cartan classification of the symmetric spaces of the classical Lie groups. The emphasis is on a novel recursive procedure to decompose the unitary evolution of bipartite quantum systems of arbitrary dimensions, in simpler factors. This procedure makes transparent the contributions of the entangling and non entangling transformations

IEEE Conference on Decision and Control (CDC)•Dec 1, 2006•0 citations

Constructive controllability for systems with drift motivated by and applied to quantum control

Viswanath Ramakrishna, Kathryn L. Flores, HERSCHEL A. RABITZ +1 more

The purpose of this paper is four fold: 1) a brief description of how finite dimensional models arise in quantum control is given; 2) many notions in quantum engineering such as universality of logic gates, hard pulse approximation in NMR spectroscopy, etc., are related to controllability of systems on the unitary groups; 3) recent results of the authors, on constructive controllability, in the class of piecewise constant controls with constraints placed on them, for systems with drift on the unitary groups are sketched; and 4) a new decomposition of SU(2) matrices is provided and used to illustrate how problems caused by periodicity arguments, to address the presence of drift, may be circumvented.

IEEE Conference on Decision and Control (CDC)•Nov 11, 2002•1 citation

Analytic Approach to Quantum Control Using Quantum Signal Processing

Aishwarya Majumdar, John M. Martyn, Yuan Liu +1 more

Realizing coherent quantum computation requires precise and robust manipulation of quantum systems through quantum control protocols. Most quantum control techniques rely on heuristic methods for designing the driving pulses that steer the system towards a target state. Such methods are often based on brute-force optimization and offer limited understanding of the solution landscape. In contrast, quantum algorithms offer a rich body of analytical methods with rigorous error guarantees for implementing unitary and non-unitary transformations, which suggests a promising direction for developing new approaches to quantum control. Among various such algorithms, quantum signal processing (QSP) has emerged as a powerful framework for quantum algorithm design, implementation, and optimization. However, its potential for quantum control remains largely unexplored. In this work, we establish QSP-Control, an analytical framework for quantum control of qubit-oscillator dynamics. We focus on dispersively coupled qubit-oscillator systems and employ the QSP formalism to mitigate unwanted nonlinear effects arising from cross-Kerr interactions. In addition, we develop constructions for precise manipulation of Fock states by designing Fock-state-selective operators, based on structural parallels between the Jaynes-Cummings interaction and QSP. These findings demonstrate how several practically relevant problems in quantum control can be mapped to forms amenable to QSP, offering both a systematic design framework and an interpretable perspective on quantum control.

quant-pharXiv:2606.26085•Jun 25, 2026•0 citations

Algorithms for quantum control based on decompositions of Lie groups

Domenico D’Alessandro

Algorithms for the control of quantum mechanical systems are presented which are based on decompositions of Lie groups. The derived control laws drive the state of two and four level systems to any desired final configuration. The algorithms for the two-level case allow the use of an arbitrarily bounded control.

IEEE Conference on Decision and Control (CDC)•Nov 11, 2002•20 citations
Constructive algorithms are presented for controlling quantum systems evolving on the SU (1, 1) Lie group. These procedures are performed via structured decomposition of SU (1, 1), which achieve precise controls without any approximations or iterative computations, under the sufficient condition that examines the existence of such decomposition. The technique is applied to controlling transitions between SU (1, 1) coherent states. These results open up new perspectives on the control design of infinite-dimensional quantum systems involving discrete or continuous spectra.
The property of controllability of quantum systems is revisited. In the case of a system having this property, couplings to external agents are available whose adjustment can guide the state to any chosen target on a suitably defined manifold (or arbitrarily close to any such target) at any chosen time. With due consideration to unbounded operators corresponding to physical observables possessing continuous spectra, sufficient conditions for controllability based on Lie-algebraic arguments are obtained. The results are not limited to finite-dimensional systems, nor to infinite-dimensional systems with discrete spectra. The applicability of the results to systems with both bound and scattering states is demonstrated for the case of the one-dimensional Poschl-Teller potential. Attention is also directed to transitivity of the pertinent Lie algebra of a system without drift as a necessary and sufficient condition for controllability.
Decompositions of the Lie group of unitary matrices are very useful tools in the control and analysis of quantum dynamics. In this paper, we survey recent results on decompositions, concerning their significance in terms of symmetries, entanglement, and their applications to control and dynamics. Several decompositions can be obtained by recursively applying the Cartan classification of the symmetric spaces of the classical Lie groups. The emphasis is on a novel recursive procedure to decompose the unitary evolution of bipartite quantum systems of arbitrary dimensions, in simpler factors. This procedure makes transparent the contributions of the entangling and non entangling transformations
The purpose of this paper is four fold: 1) a brief description of how finite dimensional models arise in quantum control is given; 2) many notions in quantum engineering such as universality of logic gates, hard pulse approximation in NMR spectroscopy, etc., are related to controllability of systems on the unitary groups; 3) recent results of the authors, on constructive controllability, in the class of piecewise constant controls with constraints placed on them, for systems with drift on the unitary groups are sketched; and 4) a new decomposition of SU(2) matrices is provided and used to illustrate how problems caused by periodicity arguments, to address the presence of drift, may be circumvented.
Realizing coherent quantum computation requires precise and robust manipulation of quantum systems through quantum control protocols. Most quantum control techniques rely on heuristic methods for designing the driving pulses that steer the system towards a target state. Such methods are often based on brute-force optimization and offer limited understanding of the solution landscape. In contrast, quantum algorithms offer a rich body of analytical methods with rigorous error guarantees for implementing unitary and non-unitary transformations, which suggests a promising direction for developing new approaches to quantum control. Among various such algorithms, quantum signal processing (QSP) has emerged as a powerful framework for quantum algorithm design, implementation, and optimization. However, its potential for quantum control remains largely unexplored. In this work, we establish QSP-Control, an analytical framework for quantum control of qubit-oscillator dynamics. We focus on dispersively coupled qubit-oscillator systems and employ the QSP formalism to mitigate unwanted nonlinear effects arising from cross-Kerr interactions. In addition, we develop constructions for precise manipulation of Fock states by designing Fock-state-selective operators, based on structural parallels between the Jaynes-Cummings interaction and QSP. These findings demonstrate how several practically relevant problems in quantum control can be mapped to forms amenable to QSP, offering both a systematic design framework and an interpretable perspective on quantum control.