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:1912.06775 · Physical Review Research

Protecting operations on qudits from noise by continuous dynamical decoupling

Reginaldo de Jesus Napolitano, Felipe Fernandes Fanchini, Adonai Hilário da Silva, Bruno Bellomo

Published Mar 12, 2021• 14 citations
arXivHTMLPDF

Abstract

We develop a procedure of generalized continuous dynamical decoupling (GCDD) for an ensemble of d-level systems (qudits), allowing one to protect the action of an arbitrary multiqudit gate from general noise.We first present our GCDD procedure for the case of an arbitrary qudit and apply it to the case of a Hadamard gate acting on a qutrit.This is done using a model that, in principle, could be implemented using the three magnetic hyperfine states of the ground energy level of 87 Rb and laser beams whose intensities and phases are modulated according to our prescription.We show that this model allows one to generate continuously all the possible SU(3) group operations which are, in general, needed to apply the GCDD procedure.We finally show that our method can be extended to the case of an ensemble of qudits, identical or not.

DOI
10.1103/physrevresearch.3.013235

Related papers

Time-dependent Rabi frequencies to protect quantum operations on an atomic qutrit by continuous dynamical decoupling

Adonai Hilário da Silva, Reginaldo de Jesus Napolitano, F. F. Fanchini +1 more

We investigate the form required for the time-dependent Rabi frequencies involved in a procedure capable to protect the action of quantum gates on an atomic qutrit by means of external fields continuously decoupling the system from the environmental noise. Several simulations are considered to protect the action of quantum-gate models, including randomly chosen ones. We argue that the requirements for the Rabi frequencies could be nowadays experimentally met. We also investigate the transition from one gate operation to another, including protecting a qutrit memory state. We finally apply our methodology to protect from noise the application of an algorithm capable of distinguishing the parity of permutations of three elements.

arXiv:2212.07545•Physical Review A•Mar 13, 2024•3 citations

Dynamical decoupling and quantum error correction with SU(d) symmetries

Colin Read, Eduardo Serrano-Ensástiga, John Martin

Dynamical decoupling is a long-established and effective way to suppress unwanted interactions in qubit systems, enabling advances in fields ranging from quantum metrology to quantum computing. For general qudit systems, however, comparable protocols remain rare, mainly because Hamiltonian engineering in higher dimensions lacks the geometric intuition available for qubits. Here we present a general framework for dynamical decoupling in qudit systems, based on Lie group representation theory. By extending the group theory approach to dynamical decoupling, we show how decoupling groups can be systematically identified among the finite subgroups of SU(d) by analyzing their access to the irreducible components of the operator space. As an application, we construct new pulse sequences for interacting qutrit systems based on finite subgroups of SU(3), and show how subgroup factorizations and group orientations can be exploited to obtain shorter and more experimentally practical protocols for spin-1 systems with large zero-field splitting. We further show that the same symmetry-based framework yields quantum error-correcting codes: whenever a finite subgroup of SU(d) acts as a decoupling group for the relevant set of operators, the associated one-dimensional symmetry sectors define codespaces satisfying the Knill-Laflamme conditions, thereby unifying dynamical decoupling and quantum error correction in multi-level quantum systems.

quant-pharXiv:2604.05871•Apr 8, 2026•0 citations

Dynamical decoupling protection for three-level systems

P. Z. Zhao, Lei Qiao

In addition to the traditional two-level system, the three-level system serves as another important elemental building block for the manipulation of qubits. However, the quantum information processing in the three-level system is also subject to the decoherence induced by the interaction between the quantum system and its environment or by the crosstalk between different qutrits. In this work, we construct a sequence of physically feasible dynamical decoupling operators for the three-level system to mitigate not only the transverse dephasing between the excited state and ground states but also the longitudinal relaxation among them. Combining the Hamiltonian engineering and our constructed dynamical decoupling sequence, we further realize the dynamical decoupling protection of qutrit-based quantum gates. Our scheme can effectively enhance the fidelity of three-level-based quantum gates through filtering out the environmental noises, which may provide a new horizon to improve the accuracy of three-level-based quantum manipulation.

arXiv:2509.15063•Physical Review A•Sep 3, 2025•0 citations

Continuously decoupling a Hadamard quantum gate from independent classes of errors

F. F. Fanchini, José Eduardo Martinho Hornos, Reginaldo de Jesus Napolitano

We consider protecting a Hadamard operation from independent dephasing, bit flipping, and dissipation. These environment-induced errors are represented by three uncorrelated reservoirs of thermalized bosons and we show that the protection is achievable through continuous dynamical decoupling. We find that, to decouple the Hadamard evolution from the environmental influence, we need a control field of higher frequency if the boson spectral density is superohmic rather than if it is ohmic. We also study the relevance of bit flipping and dissipation to the gate fidelity when it is protected from dephasing, showing how robust this partial protection is against these other perturbations. Finally, we calculate an efficient field arrangement capable of protecting simultaneously the gate operation from these three error classes.

arXiv:0707.1033•Physical Review A•Sep 19, 2007•11 citations

Universal dynamical decoupling from slow noise with minimal control

Guy Bensky, E. Brion, F. Carlier +2 more

We propose a technique that allows to simultaneously perform universal control of the evolution operator of a system and compensate for the first-order contribution of any Hermitian constant noise and the action of the environment. We show that, at least, a three-valued Hamiltonian is needed in order to protect the system against any such noise and propose an explicit algorithm for finding an appropriate control sequence. This algorithm is applied to numerically design a safe gate in an atomic qutrit.

Europhysics Letters (EPL)•Jan 1, 2010•9 citations

Preserving multilevel quantum coherence by dynamical decoupling

Xinxing Yuan, Yue Li, Mengxiang Zhang +6 more

Quantum information processing with multilevel systems (qudits) provides additional features and applications than the two-level systems. However, qudits are more prone to dephasing and dynamical decoupling for qudits has never been experimentally demonstrated. Here, as a proof-of-principle demonstration, we experimentally apply dynamical decoupling to protect superpositions with three levels of a trapped $^{9}\mathrm{Be}^{+}$ ion from ambient noisy magnetic field, prolonging coherence by up to approximately an order of magnitude. Our demonstration, straightforwardly scalable to more levels, may open up a path toward long coherence quantum memory, metrology, and information processing with qudits.

arXiv:2203.00852•Physical Review A•Aug 15, 2022•14 citations
We develop a procedure of generalized continuous dynamical decoupling (GCDD) for an ensemble of d-level systems (qudits), allowing one to protect the action of an arbitrary multiqudit gate from general noise.We first present our GCDD procedure for the case of an arbitrary qudit and apply it to the case of a Hadamard gate acting on a qutrit.This is done using a model that, in principle, could be implemented using the three magnetic hyperfine states of the ground energy level of 87 Rb and laser beams whose intensities and phases are modulated according to our prescription.We show that this model allows one to generate continuously all the possible SU(3) group operations which are, in general, needed to apply the GCDD procedure.We finally show that our method can be extended to the case of an ensemble of qudits, identical or not.
We investigate the form required for the time-dependent Rabi frequencies involved in a procedure capable to protect the action of quantum gates on an atomic qutrit by means of external fields continuously decoupling the system from the environmental noise. Several simulations are considered to protect the action of quantum-gate models, including randomly chosen ones. We argue that the requirements for the Rabi frequencies could be nowadays experimentally met. We also investigate the transition from one gate operation to another, including protecting a qutrit memory state. We finally apply our methodology to protect from noise the application of an algorithm capable of distinguishing the parity of permutations of three elements.
Dynamical decoupling is a long-established and effective way to suppress unwanted interactions in qubit systems, enabling advances in fields ranging from quantum metrology to quantum computing. For general qudit systems, however, comparable protocols remain rare, mainly because Hamiltonian engineering in higher dimensions lacks the geometric intuition available for qubits. Here we present a general framework for dynamical decoupling in qudit systems, based on Lie group representation theory. By extending the group theory approach to dynamical decoupling, we show how decoupling groups can be systematically identified among the finite subgroups of SU(d) by analyzing their access to the irreducible components of the operator space. As an application, we construct new pulse sequences for interacting qutrit systems based on finite subgroups of SU(3), and show how subgroup factorizations and group orientations can be exploited to obtain shorter and more experimentally practical protocols for spin-1 systems with large zero-field splitting. We further show that the same symmetry-based framework yields quantum error-correcting codes: whenever a finite subgroup of SU(d) acts as a decoupling group for the relevant set of operators, the associated one-dimensional symmetry sectors define codespaces satisfying the Knill-Laflamme conditions, thereby unifying dynamical decoupling and quantum error correction in multi-level quantum systems.
In addition to the traditional two-level system, the three-level system serves as another important elemental building block for the manipulation of qubits. However, the quantum information processing in the three-level system is also subject to the decoherence induced by the interaction between the quantum system and its environment or by the crosstalk between different qutrits. In this work, we construct a sequence of physically feasible dynamical decoupling operators for the three-level system to mitigate not only the transverse dephasing between the excited state and ground states but also the longitudinal relaxation among them. Combining the Hamiltonian engineering and our constructed dynamical decoupling sequence, we further realize the dynamical decoupling protection of qutrit-based quantum gates. Our scheme can effectively enhance the fidelity of three-level-based quantum gates through filtering out the environmental noises, which may provide a new horizon to improve the accuracy of three-level-based quantum manipulation.
We consider protecting a Hadamard operation from independent dephasing, bit flipping, and dissipation. These environment-induced errors are represented by three uncorrelated reservoirs of thermalized bosons and we show that the protection is achievable through continuous dynamical decoupling. We find that, to decouple the Hadamard evolution from the environmental influence, we need a control field of higher frequency if the boson spectral density is superohmic rather than if it is ohmic. We also study the relevance of bit flipping and dissipation to the gate fidelity when it is protected from dephasing, showing how robust this partial protection is against these other perturbations. Finally, we calculate an efficient field arrangement capable of protecting simultaneously the gate operation from these three error classes.
We propose a technique that allows to simultaneously perform universal control of the evolution operator of a system and compensate for the first-order contribution of any Hermitian constant noise and the action of the environment. We show that, at least, a three-valued Hamiltonian is needed in order to protect the system against any such noise and propose an explicit algorithm for finding an appropriate control sequence. This algorithm is applied to numerically design a safe gate in an atomic qutrit.
Quantum information processing with multilevel systems (qudits) provides additional features and applications than the two-level systems. However, qudits are more prone to dephasing and dynamical decoupling for qudits has never been experimentally demonstrated. Here, as a proof-of-principle demonstration, we experimentally apply dynamical decoupling to protect superpositions with three levels of a trapped 9Be+^{9}\mathrm{Be}^{+}9Be+ ion from ambient noisy magnetic field, prolonging coherence by up to approximately an order of magnitude. Our demonstration, straightforwardly scalable to more levels, may open up a path toward long coherence quantum memory, metrology, and information processing with qudits.