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:2610.01669

Dissipation-Enabled Operator-Norm Locality Bounds for Bose-Hubbard Hamiltonians

Marius Lemm, Tim Möbus

quant-phmath-phSubmitted Oct 1, 2026• Announced Oct 2, 2026• 0 citations• Revised Oct 27, 2026 (v2)
v1 · Oct 1, 2026v2 · Oct 27, 2026
arXivHTMLPDF

Abstract

Closed bosonic lattice systems do not generally admit operator norm Lieb-Robinson bounds uniformly in the initial state. The reason is that the information propagation velocity can grow with the local boson occupancy, which can be macroscopically large. Here, we show that local dissipation restores an operator-norm Lieb-Robinson bound. We consider the dissipative Bose-Hubbard model described by a Lindbladian operator with on-site $\ell$-photon loss, $\ell>2$. For our main result, we establish an almost-ballistic Lieb-Robinson bound. Dissipation rapidly depletes highly occupied sites, thus regularizing the state on the Sobolev-type scale of local particle moments. The resulting moment bounds diverge as time approaches zero but remain integrable near zero at sufficiently low orders, which is crucial for our argument. We extend these ideas to treat cat-code dissipation and, for initial states in the code space, we prove a local adiabatic approximation uniform in the total volume. Further consequences include local channel approximation, a thermodynamic limit, and efficient hybrid bosonic-qubit simulation. The point is that these applications are now available uniformly in the input state, as for quantum spin systems, but in contrast to closed Bose-Hubbard systems.

Related papers

Symmetry-Enhanced Lieb–Robinson Bounds for a Class of Bose–Hubbard Type Hamiltonians

Tomotaka Kuwahara, Marius Lemm

Abstract Several recent works have derived Lieb–Robinson bounds (LRBs) for Bose–Hubbard-type Hamiltonians. For certain structured initial states, e.g., vacuum perturbations or near-stationary states, information propagates with velocity $$v \le C$$ v ≤ C . However, for general bounded-density initial states, it was shown by the first author, Vu, and Saito that the velocity can grow in time as $$v \sim t^{D-1}$$ v ∼ t D - 1 , where D is the spatial dimension—demonstrating the possibility of accelerated information spreading in bosonic systems. In this work, we introduce a new perspective on this phenomenon: we show that translation invariance combined with local p -body repulsion ( $$n^p$$ n p with $$p > D+1$$ p > D + 1 ) qualitatively alters the propagation behavior, leading to a bound of the form $$v \sim t^{\frac{D}{p - D - 1}}$$ v ∼ t D p - D - 1 for general bounded-energy-density initial states. In particular, this establishes an almost-linear light cone at large p , in stark contrast to the previously found accelerated regimes. Our result identifies symmetry-driven constraints as a new mechanism for suppressing propagation speed in bosonic systems and thereby reframes the scope of what types of LRBs can hold. We further provide matching examples showing that, under the given assumptions, this bound is sharp—no further improvement in the power of t is possible without invoking additional dynamical constraints.

arXiv:2405.04672•Annales Henri Poincaré•Jul 28, 2026•0 citations

Maximal Speed for Macroscopic Particle Transport in the Bose-Hubbard Model

Jérémy Faupin, Marius Lemm, Israel Michael Sigal

The Lieb-Robinson bound asserts the existence of a maximal propagation speed for the quantum dynamics of lattice spin systems. Such general bounds are not available for most bosonic lattice gases due to their unbounded local interactions. Here we establish for the first time a general ballistic upper bound on macroscopic particle transport in the paradigmatic Bose-Hubbard model. The bound is the first to cover a broad class of initial states with positive density including Mott states, which resolves a longstanding open problem. It applies to Bose-Hubbard-type models on any lattice with not too long-ranged hopping. The proof is rigorous and rests on controlling the time evolution of a new kind of adiabatic spacetime localization observable via iterative differential inequalities.

arXiv:2110.04313•Physical Review Letters•Apr 12, 2022•31 citations

Lieb-Robinson Bound and Almost-Linear Light Cone in Interacting Boson Systems

Tomotaka Kuwahara, Keiji Saito

In this work, we investigate how quickly local perturbations propagate in interacting boson systems with Bose-Hubbard-type Hamiltonians. In general, these systems have unbounded local energies, and arbitrarily fast information propagation may occur. We focus on a specific but experimentally natural situation in which the number of bosons at any one site in the unperturbed initial state is approximately limited. We rigorously prove the existence of an almost-linear information-propagation light cone, thus establishing a Lieb-Robinson bound: the wave front grows at most as t log^{2}(t). We prove the clustering theorem for gapped ground states and study the time complexity of classically simulating one-dimensional quench dynamics, a topic of great practical interest.

arXiv:2103.11592•Physical Review Letters•Aug 13, 2021•38 citations

A ballistic upper bound on the accumulation of bosonic on-site energies

Tomotaka Kuwahara, Marius Lemm, Carla Rubiliani

In this note, we study transport properties of the dynamics generated by translation-invariant and possibly long-ranged Hamiltonians of Bose-Hubbard type. For translation-invariant initial states with controlled boson density, we improve the known bound on the local repulsive energy at time $t$ from $\langle n^2_x\rangle_t\lesssim t^{2d}$ to $\langle n^2_x\rangle_t\lesssim t^d$. This shows that bosonic on-site energies accumulate at most ballistically. Extending the result to higher moments would have powerful implications for bosonic Lieb-Robinson bounds. While previous approaches focused on controlling particle transport, our proof develops novel ASTLOs (adiabatic space-time localization observables) that are able to track the growth of local boson-boson correlations.

math-phCross-listedarXiv:2511.07558•Nov 12, 2025•0 citations

Instantaneous Sobolev Regularization for Dissipative Bosonic Dynamics

Pablo Costa Rico, Paul Gondolf, Tim Möbus

We investigate quantum Markov semigroups on bosonic Fock space and identify a broad class of infinite-dimensional dissipative evolutions that exhibit instantaneous Sobolev regularization. Motivated by stability problems in quantum computation, we show that for certain Lindblad operators that are polynomials of creation and annihilation operators, the resulting dynamics immediately transform any initial state into one with finite expectation in all powers of the number operator. A key application is in the bosonic cat code, where we obtain explicit estimates in the trace norm for the speed of convergence. These estimates sharpen existing perturbative bounds at both short and long times, offering new analytic tools for assessing stability and error suppression in bosonic quantum information processing. For example, we improve the strong exponential convergence of the (shifted) $2$-photon dissipation to its asymptotic channel to the uniform topology. For multi-mode systems, a generation theorem in concentrated single-sandwich norms supplies the domain properties required for the regularization argument.

math-phCross-listedarXiv:2512.04066•Dec 4, 2025•0 citations

On the quantum dynamics of long-ranged Bose-Hubbard Hamiltonians

Marius Lemm, Carla Rubiliani, Jingxuan Zhang

We study the quantum dynamics generated by Bose-Hubbard Hamiltonians with long-ranged (power law) terms. We prove two ballistic propagation bounds for suitable initial states: (i) A bound on all moments of the local particle number for all power law exponents $α>d+1$ in $d$ dimensions, the sharp condition. (ii) The first thermodynamically stable Lieb-Robinson bound (LRB) for these Hamiltonians. To handle the long-ranged and unbounded terms, we further develop the multiscale ASTLO (adiabatic space time localization observables) method introduced in our recent work [arXiv:2310.14896].

arXiv:2505.01786•May 3, 2025•0 citations
Closed bosonic lattice systems do not generally admit operator norm Lieb-Robinson bounds uniformly in the initial state. The reason is that the information propagation velocity can grow with the local boson occupancy, which can be macroscopically large. Here, we show that local dissipation restores an operator-norm Lieb-Robinson bound. We consider the dissipative Bose-Hubbard model described by a Lindbladian operator with on-site ℓ\ellℓ-photon loss, ℓ>2\ell>2ℓ>2. For our main result, we establish an almost-ballistic Lieb-Robinson bound. Dissipation rapidly depletes highly occupied sites, thus regularizing the state on the Sobolev-type scale of local particle moments. The resulting moment bounds diverge as time approaches zero but remain integrable near zero at sufficiently low orders, which is crucial for our argument. We extend these ideas to treat cat-code dissipation and, for initial states in the code space, we prove a local adiabatic approximation uniform in the total volume. Further consequences include local channel approximation, a thermodynamic limit, and efficient hybrid bosonic-qubit simulation. The point is that these applications are now available uniformly in the input state, as for quantum spin systems, but in contrast to closed Bose-Hubbard systems.
Abstract Several recent works have derived Lieb–Robinson bounds (LRBs) for Bose–Hubbard-type Hamiltonians. For certain structured initial states, e.g., vacuum perturbations or near-stationary states, information propagates with velocity v≤Cv \le Cv≤C v ≤ C . However, for general bounded-density initial states, it was shown by the first author, Vu, and Saito that the velocity can grow in time as v∼tD−1v \sim t^{D-1}v∼tD−1 v ∼ t D - 1 , where D is the spatial dimension—demonstrating the possibility of accelerated information spreading in bosonic systems. In this work, we introduce a new perspective on this phenomenon: we show that translation invariance combined with local p -body repulsion ( npn^pnp n p with p>D+1p > D+1p>D+1 p > D + 1 ) qualitatively alters the propagation behavior, leading to a bound of the form v∼tDp−D−1v \sim t^{\frac{D}{p - D - 1}}v∼tp−D−1D​ v ∼ t D p - D - 1 for general bounded-energy-density initial states. In particular, this establishes an almost-linear light cone at large p , in stark contrast to the previously found accelerated regimes. Our result identifies symmetry-driven constraints as a new mechanism for suppressing propagation speed in bosonic systems and thereby reframes the scope of what types of LRBs can hold. We further provide matching examples showing that, under the given assumptions, this bound is sharp—no further improvement in the power of t is possible without invoking additional dynamical constraints.
The Lieb-Robinson bound asserts the existence of a maximal propagation speed for the quantum dynamics of lattice spin systems. Such general bounds are not available for most bosonic lattice gases due to their unbounded local interactions. Here we establish for the first time a general ballistic upper bound on macroscopic particle transport in the paradigmatic Bose-Hubbard model. The bound is the first to cover a broad class of initial states with positive density including Mott states, which resolves a longstanding open problem. It applies to Bose-Hubbard-type models on any lattice with not too long-ranged hopping. The proof is rigorous and rests on controlling the time evolution of a new kind of adiabatic spacetime localization observable via iterative differential inequalities.
In this work, we investigate how quickly local perturbations propagate in interacting boson systems with Bose-Hubbard-type Hamiltonians. In general, these systems have unbounded local energies, and arbitrarily fast information propagation may occur. We focus on a specific but experimentally natural situation in which the number of bosons at any one site in the unperturbed initial state is approximately limited. We rigorously prove the existence of an almost-linear information-propagation light cone, thus establishing a Lieb-Robinson bound: the wave front grows at most as t log^{2}(t). We prove the clustering theorem for gapped ground states and study the time complexity of classically simulating one-dimensional quench dynamics, a topic of great practical interest.
In this note, we study transport properties of the dynamics generated by translation-invariant and possibly long-ranged Hamiltonians of Bose-Hubbard type. For translation-invariant initial states with controlled boson density, we improve the known bound on the local repulsive energy at time ttt from ⟨nx2⟩t≲t2d\langle n^2_x\rangle_t\lesssim t^{2d}⟨nx2​⟩t​≲t2d to ⟨nx2⟩t≲td\langle n^2_x\rangle_t\lesssim t^d⟨nx2​⟩t​≲td. This shows that bosonic on-site energies accumulate at most ballistically. Extending the result to higher moments would have powerful implications for bosonic Lieb-Robinson bounds. While previous approaches focused on controlling particle transport, our proof develops novel ASTLOs (adiabatic space-time localization observables) that are able to track the growth of local boson-boson correlations.
We investigate quantum Markov semigroups on bosonic Fock space and identify a broad class of infinite-dimensional dissipative evolutions that exhibit instantaneous Sobolev regularization. Motivated by stability problems in quantum computation, we show that for certain Lindblad operators that are polynomials of creation and annihilation operators, the resulting dynamics immediately transform any initial state into one with finite expectation in all powers of the number operator. A key application is in the bosonic cat code, where we obtain explicit estimates in the trace norm for the speed of convergence. These estimates sharpen existing perturbative bounds at both short and long times, offering new analytic tools for assessing stability and error suppression in bosonic quantum information processing. For example, we improve the strong exponential convergence of the (shifted) 222-photon dissipation to its asymptotic channel to the uniform topology. For multi-mode systems, a generation theorem in concentrated single-sandwich norms supplies the domain properties required for the regularization argument.
We study the quantum dynamics generated by Bose-Hubbard Hamiltonians with long-ranged (power law) terms. We prove two ballistic propagation bounds for suitable initial states: (i) A bound on all moments of the local particle number for all power law exponents α>d+1α>d+1α>d+1 in ddd dimensions, the sharp condition. (ii) The first thermodynamically stable Lieb-Robinson bound (LRB) for these Hamiltonians. To handle the long-ranged and unbounded terms, we further develop the multiscale ASTLO (adiabatic space time localization observables) method introduced in our recent work [arXiv:2310.14896].