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:2603.20091

Symmetric Resourceful Steady States via Non-Markovian Dissipation

Baptiste Debecker, Eduardo Serrano-Ensástiga, Thierry Bastin, François Damanet, John Martin

quant-phSubmitted Mar 20, 2026• Announced Mar 23, 2026• 0 citations
arXivHTMLPDF

Abstract

We prove a no-go theorem for symmetry-based dissipative engineering of collective-spin steady states: in spin-only Lindblad dynamics with jump operators linear in the collective-spin operators, any unique steady state exhibiting at least $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry is necessarily the maximally mixed state. We then show that bath memory lifts this obstruction, enabling unique entangled steady states with a prescribed symmetry and a metrological gain, and providing a steady-state witness of non-Markovianity. Notably, this framework is largely insensitive to the microscopic details of the bath.

Comments
5 pages and 4 figures (main); 6 pages and 1 figure (supplemental)

Related papers

Dissipative State Engineering of Complex Entanglement with Markovian Dynamics

Manish Chaudhary

Highly multipartite entangled states play an important role in various quantum computing tasks. We investigate the dissipative generation of a complex entanglement structure as in a cluster state through engineered Markovian dynamics in the spin systems coupled via Ising interactions. Using the Lindblad master equation, we design a projection based dissipative channel that drives the system toward a unique pure steady state corresponding to the desired cluster state. This is done by removing the contribution of the orthogonal states. By explicitly constructing the Liouvillian superoperator in the full $2^N$-dimensional Hilbert space, we compute the steady-state density matrix, the Liouvillian spectral gap, entanglement witness and the fidelity with respect to the ideal cluster state. The results demonstrate that the cluster state emerges as the steady state when the engineered Liouvillian dissipation dominates over the local Ising interaction between spins. Moreover, we find that the fidelity and Liouvillian spectral gap is relatively insensitive to the system size once the saturation dissipation has been achieved that scales linearly with the qubit number. This analysis illustrates a physically realizable path towards steady-state entanglement generation in the spin systems using engineered dissipation.

quant-pharXiv:2601.09597•Jan 15, 2026•0 citations

Emergent quantum algebras in dissipative time crystals

Joseph Tindall

Strong dynamical symmetries provide an algebraic description of persistent oscillations in open quantum systems governed by the Lindblad equation. For finite-dimensional systems with a full-rank stationary state, such symmetries are necessary and sufficient for non-decaying oscillatory modes to appear in the Liouvillian's spectrum. These modes can be directly constructed by acting on stationary states with the identified symmetry operators. Here we establish an asymptotic counterpart of this algebra for collective spins. Taking a single spin $S$ in a magnetic field, subject to dissipation through linear jump operators, we identify the exact conditions on the field and dissipative couplings under which non-decaying oscillatory modes emerge as $S \rightarrow \infty$. We then write down a simple, closed form for the corresponding `symmetry' operator which can be applied to the steady state to construct these modes, which are eigenvectors of the Liouvillian, with imaginary eigenvalues, up to $O(1/S)$ corrections. A second operator, an emergent conserved quantity, completes the algebra, and its slow relaxation determines how quantum noise selects the stationary state. The construction can be directly extended to a pair of interacting spins sharing a common reservoir, with the resulting quantum algebra making the entanglement during a quench analytically accessible.

quant-pharXiv:2610.16609•Oct 13, 2026•0 citations

Dissipation-induced topological insulators: A no-go theorem and a recipe

Moshe Goldstein

Nonequilibrium conditions are traditionally seen as detrimental to the appearance of quantum-coherent many-body phenomena, and much effort is often devoted to their elimination. Recently this approach has changed: It has been realized that driven-dissipative dynamics could be used as a resource. By proper engineering of the reservoirs and their couplings to a system, one may drive the system towards desired quantum-correlated steady states, even in the absence of internal Hamiltonian dynamics. An intriguing category of equilibrium many-particle phases are those which are distinguished by topology rather than by symmetry. A natural question thus arises: which of these topological states can be achieved as the result of dissipative Lindblad-type (Markovian) evolution? Beside its fundamental importance, it may offer novel routes to the realization of topologically-nontrivial states in quantum simulators, especially ultracold atomic gases. Here I give a general answer for Gaussian states and quadratic Lindblad evolution, mostly concentrating on the example of 2D Chern insulator states. I prove a no-go theorem stating that a finite-range Lindbladian cannot induce finite-rate exponential decay towards a unique topological pure state above 1D. I construct a recipe for creating such state by exponentially-local dynamics, or a mixed state arbitrarily close to the desired pure one via finite-range dynamics. I also address the cold-atom realization, classification, and detection of these states. Extensions to other types of topological insulators and superconductors are also discussed.

arXiv:1810.12050•SciPost Physics•Nov 27, 2019•49 citations

Steady States of a Single Trapped-Ion Spin Coupled to an Engineered Non-Markovian Bath

Anthony Vogliano, Lewis Hahn, Fabien Lefebvre +5 more

Quantum simulation of open quantum systems offers a pathway towards better understanding various non-equilibrium physics that would otherwise be challenging to study. While most open quantum systems studied are modeled as being memory-less (obeying the Markov approximation), real baths generally are influenced by the system-bath interaction, and some systems existing in structured non-Markovian environments can display novel behavior as a result. Here we utilize a trapped ion quantum simulator to simulate a single spin-$1/2$ driven-dissipative system with a non-Markovian dissipation channel, and experimentally compare steady-states to those from an analogous Markovian bath. We observe that a non-Markovian dissipative channel can shift the steady-state even for a single qubit, to a regime inaccessible for Markovian dissipation. The techniques used here are compatible with many-body extensions of the model, which can not be simulated efficiently on a classical computer in general. Our work also opens up new possibilities in quantum reservoir engineering beyond the Markovian regime.

quant-pharXiv:2607.19286•Jul 22, 2026•0 citations

Generating Multipartite Entanglement via Structured-Bath Engineering

Baptiste Debecker, Philipp Westhoff, Visal So +5 more

We present how to dissipatively prepare genuinely multipartite-entangled steady states with mutually independent local reservoirs by harnessing an Abelian strong symmetry and temporal bath correlations. In interacting Ising chains, we demonstrate that, for a broad class of system-environment couplings, flat baths exponentially erase Ising-axis correlations. Structured baths overcome this obstruction by converting temporal bath correlations into classical spatial correlations. Strong symmetry then promotes these correlations to the quantum domain, enabling global multipartite entanglement. Within weak-coupling theory, we obtain exact steady states despite the generator's nonquadratic nature: strong symmetry reduces their construction to a classical problem for arbitrary Ising couplings. This reduction reveals an exact connection between classical distinguishability and entanglement. We then show how to engineer the bath spectrum to increase the correlation length and enable the preparation of GHZ-like states from separable initial conditions. We test the mechanism beyond the analytical regime using exact Markovian embeddings and tensor-network simulations. Our approach is particularly suited to superconducting and trapped-ion platforms, and we propose a concrete implementation for the latter using sympathetically cooled motional modes.

quant-pharXiv:2610.38807•Oct 30, 2026•0 citations

Symmetric dynamics in dissipative quantum many-body models

Yi Zheng, Shuo Yang

We show symmetric dynamics in dissipative quantum many-body systems. Given some conditions on the Hamiltonian and the jump operators, the time evolution of certain observables can be identical for ferromagnetic and antiferromagnetic interactions in an Ising model with external fields or for repulsive and attractive interactions in a Hubbard model. We present two theorems to determine the existence of such a dynamical symmetry in dissipative quantum systems. The symmetry under the steady state is present independently on the initial state. Further constraint on the initial state leads to a stronger dynamical symmetry in real-time evolutions. We demonstrate the application of our theorems in dissipative Ising and Hubbard models. In addition, for the Fermi-Hubbard model, our results also reveal a connection between spin and charge densities in dissipative dynamics. We validate the discussions with numerical simulations performed using tensor network algorithms.

arXiv:1912.05495•Physical Review A•Aug 4, 2021•2 citations
We prove a no-go theorem for symmetry-based dissipative engineering of collective-spin steady states: in spin-only Lindblad dynamics with jump operators linear in the collective-spin operators, any unique steady state exhibiting at least Z2×Z2\mathbb{Z}_2 \times \mathbb{Z}_2Z2​×Z2​ symmetry is necessarily the maximally mixed state. We then show that bath memory lifts this obstruction, enabling unique entangled steady states with a prescribed symmetry and a metrological gain, and providing a steady-state witness of non-Markovianity. Notably, this framework is largely insensitive to the microscopic details of the bath.
Highly multipartite entangled states play an important role in various quantum computing tasks. We investigate the dissipative generation of a complex entanglement structure as in a cluster state through engineered Markovian dynamics in the spin systems coupled via Ising interactions. Using the Lindblad master equation, we design a projection based dissipative channel that drives the system toward a unique pure steady state corresponding to the desired cluster state. This is done by removing the contribution of the orthogonal states. By explicitly constructing the Liouvillian superoperator in the full 2N2^N2N-dimensional Hilbert space, we compute the steady-state density matrix, the Liouvillian spectral gap, entanglement witness and the fidelity with respect to the ideal cluster state. The results demonstrate that the cluster state emerges as the steady state when the engineered Liouvillian dissipation dominates over the local Ising interaction between spins. Moreover, we find that the fidelity and Liouvillian spectral gap is relatively insensitive to the system size once the saturation dissipation has been achieved that scales linearly with the qubit number. This analysis illustrates a physically realizable path towards steady-state entanglement generation in the spin systems using engineered dissipation.
Strong dynamical symmetries provide an algebraic description of persistent oscillations in open quantum systems governed by the Lindblad equation. For finite-dimensional systems with a full-rank stationary state, such symmetries are necessary and sufficient for non-decaying oscillatory modes to appear in the Liouvillian's spectrum. These modes can be directly constructed by acting on stationary states with the identified symmetry operators. Here we establish an asymptotic counterpart of this algebra for collective spins. Taking a single spin SSS in a magnetic field, subject to dissipation through linear jump operators, we identify the exact conditions on the field and dissipative couplings under which non-decaying oscillatory modes emerge as S→∞S \rightarrow \inftyS→∞. We then write down a simple, closed form for the corresponding `symmetry' operator which can be applied to the steady state to construct these modes, which are eigenvectors of the Liouvillian, with imaginary eigenvalues, up to O(1/S)O(1/S)O(1/S) corrections. A second operator, an emergent conserved quantity, completes the algebra, and its slow relaxation determines how quantum noise selects the stationary state. The construction can be directly extended to a pair of interacting spins sharing a common reservoir, with the resulting quantum algebra making the entanglement during a quench analytically accessible.
Nonequilibrium conditions are traditionally seen as detrimental to the appearance of quantum-coherent many-body phenomena, and much effort is often devoted to their elimination. Recently this approach has changed: It has been realized that driven-dissipative dynamics could be used as a resource. By proper engineering of the reservoirs and their couplings to a system, one may drive the system towards desired quantum-correlated steady states, even in the absence of internal Hamiltonian dynamics. An intriguing category of equilibrium many-particle phases are those which are distinguished by topology rather than by symmetry. A natural question thus arises: which of these topological states can be achieved as the result of dissipative Lindblad-type (Markovian) evolution? Beside its fundamental importance, it may offer novel routes to the realization of topologically-nontrivial states in quantum simulators, especially ultracold atomic gases. Here I give a general answer for Gaussian states and quadratic Lindblad evolution, mostly concentrating on the example of 2D Chern insulator states. I prove a no-go theorem stating that a finite-range Lindbladian cannot induce finite-rate exponential decay towards a unique topological pure state above 1D. I construct a recipe for creating such state by exponentially-local dynamics, or a mixed state arbitrarily close to the desired pure one via finite-range dynamics. I also address the cold-atom realization, classification, and detection of these states. Extensions to other types of topological insulators and superconductors are also discussed.
Quantum simulation of open quantum systems offers a pathway towards better understanding various non-equilibrium physics that would otherwise be challenging to study. While most open quantum systems studied are modeled as being memory-less (obeying the Markov approximation), real baths generally are influenced by the system-bath interaction, and some systems existing in structured non-Markovian environments can display novel behavior as a result. Here we utilize a trapped ion quantum simulator to simulate a single spin-1/21/21/2 driven-dissipative system with a non-Markovian dissipation channel, and experimentally compare steady-states to those from an analogous Markovian bath. We observe that a non-Markovian dissipative channel can shift the steady-state even for a single qubit, to a regime inaccessible for Markovian dissipation. The techniques used here are compatible with many-body extensions of the model, which can not be simulated efficiently on a classical computer in general. Our work also opens up new possibilities in quantum reservoir engineering beyond the Markovian regime.
We present how to dissipatively prepare genuinely multipartite-entangled steady states with mutually independent local reservoirs by harnessing an Abelian strong symmetry and temporal bath correlations. In interacting Ising chains, we demonstrate that, for a broad class of system-environment couplings, flat baths exponentially erase Ising-axis correlations. Structured baths overcome this obstruction by converting temporal bath correlations into classical spatial correlations. Strong symmetry then promotes these correlations to the quantum domain, enabling global multipartite entanglement. Within weak-coupling theory, we obtain exact steady states despite the generator's nonquadratic nature: strong symmetry reduces their construction to a classical problem for arbitrary Ising couplings. This reduction reveals an exact connection between classical distinguishability and entanglement. We then show how to engineer the bath spectrum to increase the correlation length and enable the preparation of GHZ-like states from separable initial conditions. We test the mechanism beyond the analytical regime using exact Markovian embeddings and tensor-network simulations. Our approach is particularly suited to superconducting and trapped-ion platforms, and we propose a concrete implementation for the latter using sympathetically cooled motional modes.
We show symmetric dynamics in dissipative quantum many-body systems. Given some conditions on the Hamiltonian and the jump operators, the time evolution of certain observables can be identical for ferromagnetic and antiferromagnetic interactions in an Ising model with external fields or for repulsive and attractive interactions in a Hubbard model. We present two theorems to determine the existence of such a dynamical symmetry in dissipative quantum systems. The symmetry under the steady state is present independently on the initial state. Further constraint on the initial state leads to a stronger dynamical symmetry in real-time evolutions. We demonstrate the application of our theorems in dissipative Ising and Hubbard models. In addition, for the Fermi-Hubbard model, our results also reveal a connection between spin and charge densities in dissipative dynamics. We validate the discussions with numerical simulations performed using tensor network algorithms.