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:2603.17736

Optimal detection of dissipation in Lindbladian dynamics

Yiyi Cai

quant-phcs.DSSubmitted Mar 18, 2026• Announced Mar 19, 2026• 0 citations
v1 · Mar 18, 2026v2 · May 8, 2026
arXivHTMLPDF

Abstract

Experimental implementations of Hamiltonian dynamics are often affected by dissipative noise arising from interactions with the environment. This raises the question of whether one can detect the presence or absence of such dissipation using only access to the observed time evolution of the system. We consider the following decision problem: given black-box access to the time-evolution channels $e^{t\mathcal{L}}$ generated by an unknown time-independent Lindbladian $\mathcal{L}$, determine whether the dynamics are purely Hamiltonian or contain dissipation of magnitude at least $ε$ in normalized Frobenius norm. We give a randomized procedure that solves this task using total evolution time $\mathcal{O}(ε^{-1})$, which is information-theoretically optimal. This guarantee holds under the assumptions that the Lindblad generator has bounded strength and its dissipative part is of constant locality with bounded degree. Our work provides a practical method for detecting dissipative noise in experimentally implemented quantum dynamics.

Comments
29 pages

Related papers

Optimal Tolerant Testing of Lindbladian Dissipation

Jinge Bao, Yiyi Cai, Zhong-Xia Shang

Quantifying dissipation is essential for controlling quantum noise and characterizing open-system dynamics. In practical experimental settings, residual noise may still persist despite efforts to suppress it, making it important to determine whether the dissipative strength remains within a prescribed tolerance threshold. We study this question for an unknown, time-independent Lindblad generator with bounded strength, where the jump operators are local but with unrestricted overlap, using only memoryless forward-evolution access. The task is to distinguish dissipative strength of at most $\varepsilon_1$ from strength of at least $\varepsilon_2$, for $0 \leq \varepsilon_1 < \varepsilon_2$, measured in the canonical dissipator's normalized Frobenius norm. We give an algorithm that solves this task in total evolution time $O(\varepsilon_2/(\varepsilon_2-\varepsilon_1)^2)$ for all nontrivial thresholds, with constant success probability, and provide a matching lower bound $Ω(\varepsilon_2/(\varepsilon_2-\varepsilon_1)^2)$ that establishes optimality even for adaptive protocols. This extends dissipation testing to the tolerant setting and eliminates the bounded-degree requirement, making the framework applicable to a broader range of experimentally relevant settings.

quant-pharXiv:2609.38160•Sep 30, 2026•0 citations

Near-Optimal Learning of Local Lindbladians

Itai Arad, Zhili Chen, Naixu Guo +2 more

We study the problem of learning local Lindbladians from black-box access to the physical evolution, where the goal is to estimate all Hamiltonian and dissipative coefficients. For local Lindbladians with low-intersection dissipators and local dynamical strength at most $Λ$, we design an algorithm that learns the coefficients to target accuracy $\varepsilon$, whose number of channel uses and total evolution time scale as $\widetilde{O}(Λ^2/\varepsilon^2)$ and $\widetilde{O}(Λ/\varepsilon^2)$, respectively, with only logarithmic dependence on the number of qubits. The algorithm is built directly from finite-time channel probes. It runs the unknown evolution for short times, estimates the corresponding Pauli transfer matrices from classical shadows, and converts these estimates into Lindbladian coefficients by stable local Fourier inversions. The algorithm is non-adaptive, uses no ancillas, and requires only random product states as inputs followed by random Pauli measurements. The method does not require knowing the structure of the Lindbladian in advance. We prove matching lower bounds that establish the near-optimality of the algorithm in both resources. By constructing a family of single-qubit dephasing Lindbladians, we show that any algorithm, even an adaptive one with arbitrary ancillas and measurements, requires $Ω(Λ^2/\varepsilon^2)$ channel uses and $Ω(Λ/\varepsilon^2)$ total evolution time. In particular, the lower bounds imply that the Heisenberg-limited scaling achievable for Hamiltonian learning is information-theoretically impossible once dissipative coefficients must be estimated.

quant-pharXiv:2606.20535•Jun 19, 2026•0 citations

Learning Arbitrary Lindbladians from Time Evolution

Zhili Chen, Zhan Yu

We study the problem of learning an unknown Markovian open-system generator from access to its physical time evolution. This generator, called a Lindbladian, contains Hamiltonian and dissipative coefficients indexed by an exponentially large family of possible Pauli terms. We propose an efficient algorithm that learns arbitrary Lindbladians from time evolution under minimal assumptions. For a Lindbladian of dynamical strength at most $Λ$, the algorithm estimates every coefficient to error $ε$ using $\widetilde O(Λ^2/ε^2)$ experiments and $\widetilde O(Λ/ε^2)$ total evolution time, together with polynomial classical running time. The algorithm consists of two nonadaptive, ancilla-free, and control-free stages: 1. The support-learning stage outputs a candidate support of size $\mathrm{poly}(Λ/η)$ that contains every Hamiltonian and dissipative coordinate of magnitude at least $η$, using $\widetilde O(Λ^2/η^2)$ experiments with preparations of product Pauli eigenstates and single-qubit Pauli measurements. 2.The coefficient-learning stage estimates all coefficients in any candidate support of size $M$ to error $ε$, using $\widetilde O(Λ^2\log M/ε^{2})$ experiments with preparations of random stabilizer states and measurements in random Clifford bases. Composing the two stages identifies and estimates every coefficient of an arbitrary Lindbladian in polynomial time. The experiment-count and total-evolution-time scalings match the lower bounds up to logarithmic factors, so the algorithm is nearly optimal for learning arbitrary Lindbladians.

quant-pharXiv:2607.28610•Jul 31, 2026•0 citations

Hamiltonian dynamics from pure dissipation

Zhong-Xia Shang, Daniel Stilck França

The fundamental difference between closed and open quantum dynamics lies in their environmental interaction: closed systems are perfectly isolated and evolve reversibly under unitary Hamiltonian dynamics, whereas open systems continuously couple to an external bath, resulting in irreversible dissipation and information loss. In this work, we show internal Hamiltonian dynamics can be "faked`` via external pure dissipation, i.e., Lindbladians without a coherent Hamiltonian part. More concretely, we show that, in a GKSL representation with zero explicit Hamiltonian term but nontraceless jump operators, bounded-norm dissipative generators can approximate Hamiltonian dynamics within $ε$ error in diamond norm using $\mathcal{O}(t^2/ε)$ evolution time. We further prove that for time-independent dynamics this $\mathcal{O}(t^2/ε)$ scaling is in the worst case, necessary and optimal from a geometric perspective, which captures the fundamental decoherence cost for catching up with the speed of Hamiltonian dynamics. Our construction leads to various implications, including the BQP-completeness of purely dissipative dynamics even before reaching approximate equilibrium, a Zeno-adjacent state-independent freezing effect, the no super-quadratic fast-forwarding theorem of a class of purely dissipative dynamics, and reducing Lindbladian simulation cost via gauge changing.

quant-pharXiv:2604.18533•Apr 21, 2026•0 citations

Ansatz-Free Learning of Lindbladian Dynamics In Situ

Petr Ivashkov, Nikita Romanov, Weiyuan Gong +3 more

Characterizing the dynamics of open quantum systems at the level of microscopic interactions and error mechanisms is essential for calibrating quantum hardware, designing robust simulation protocols, and developing tailored error-correction methods. Under Markovian noise/dissipation, a natural characterization approach is to identify the full Lindbladian generator that gives rise to both coherent (Hamiltonian) and dissipative dynamics. Prior protocols for learning Lindbladians from dynamical data assumed pre-specified interaction structure, which can be restrictive when the relevant noise channels or control imperfections are not known in advance. In this paper, we present a sample-efficient protocol for learning sparse Lindbladians without assuming any a priori structure. Our protocol is ancilla-free, uses only product-state preparations and Pauli-basis measurements, admits provably stable coefficient reconstruction, and achieves near-optimal time resolution, making it compatible with near-term experimental capabilities. Together, this provides a systematic route to scalable characterization of open-system quantum dynamics, especially in settings where the error mechanisms of interest are unknown.

quant-pharXiv:2603.05492•Mar 6, 2026•0 citations

Dissipation accelerates quantum and classical simulation of open-system dynamics

Armando Angrisani, Ricard Puig, Yanting Teng +1 more

Simulating open quantum systems reveals how environmental coupling shapes relaxation, excitation transport, and the dynamics of quantum correlations. On quantum hardware, dissipative channels add operations and might seem to increase cost. However, we show that a broad class of Pauli noise, including depolarization, can ease quantum and classical simulation by exponentially suppressing high-weight components of Heisenberg-evolved observables. For bounded-degree Lindblad dynamics, this permits system-size-independent Trotter steps when estimating local observables. Combining this compression with Richardson extrapolation, we provide classical and quantum error bounds with respect to the 2-norm of the propagated observable. These give high-probability expectation-value guarantees for random input states or random Hamiltonians acting on a fixed state and control (out-of-time-order) correlators. Concretely, we show that expectation values of local observables at time $t$ can be estimated to accuracy $\varepsilon$ using circuits of maximum depth $O\!\left(\left[1+\left(t/γ\right)^{3/2}\right]\log^2(1/\varepsilon)\right)$, independent of the system size $n$. Classically, we show that sparse Pauli propagation runs in time polynomial in $n$, $t$ and $1/\varepsilon$ for every fixed $γ>0$, with polynomial degree $O(1/γ)$ in the weak dissipation limit. The gap between our quantum and classical upper bounds leaves room for a substantial polynomial quantum advantage as dissipation weakens, an observation further supported by our numerical results.

quant-pharXiv:2609.40174•Oct 1, 2026•0 citations
Experimental implementations of Hamiltonian dynamics are often affected by dissipative noise arising from interactions with the environment. This raises the question of whether one can detect the presence or absence of such dissipation using only access to the observed time evolution of the system. We consider the following decision problem: given black-box access to the time-evolution channels etLe^{t\mathcal{L}}etL generated by an unknown time-independent Lindbladian L\mathcal{L}L, determine whether the dynamics are purely Hamiltonian or contain dissipation of magnitude at least εεε in normalized Frobenius norm. We give a randomized procedure that solves this task using total evolution time O(ε−1)\mathcal{O}(ε^{-1})O(ε−1), which is information-theoretically optimal. This guarantee holds under the assumptions that the Lindblad generator has bounded strength and its dissipative part is of constant locality with bounded degree. Our work provides a practical method for detecting dissipative noise in experimentally implemented quantum dynamics.
Quantifying dissipation is essential for controlling quantum noise and characterizing open-system dynamics. In practical experimental settings, residual noise may still persist despite efforts to suppress it, making it important to determine whether the dissipative strength remains within a prescribed tolerance threshold. We study this question for an unknown, time-independent Lindblad generator with bounded strength, where the jump operators are local but with unrestricted overlap, using only memoryless forward-evolution access. The task is to distinguish dissipative strength of at most ε1\varepsilon_1ε1​ from strength of at least ε2\varepsilon_2ε2​, for 0≤ε1<ε20 \leq \varepsilon_1 < \varepsilon_20≤ε1​<ε2​, measured in the canonical dissipator's normalized Frobenius norm. We give an algorithm that solves this task in total evolution time O(ε2/(ε2−ε1)2)O(\varepsilon_2/(\varepsilon_2-\varepsilon_1)^2)O(ε2​/(ε2​−ε1​)2) for all nontrivial thresholds, with constant success probability, and provide a matching lower bound Ω(ε2/(ε2−ε1)2)Ω(\varepsilon_2/(\varepsilon_2-\varepsilon_1)^2)Ω(ε2​/(ε2​−ε1​)2) that establishes optimality even for adaptive protocols. This extends dissipation testing to the tolerant setting and eliminates the bounded-degree requirement, making the framework applicable to a broader range of experimentally relevant settings.
We study the problem of learning local Lindbladians from black-box access to the physical evolution, where the goal is to estimate all Hamiltonian and dissipative coefficients. For local Lindbladians with low-intersection dissipators and local dynamical strength at most ΛΛΛ, we design an algorithm that learns the coefficients to target accuracy ε\varepsilonε, whose number of channel uses and total evolution time scale as O~(Λ2/ε2)\widetilde{O}(Λ^2/\varepsilon^2)O(Λ2/ε2) and O~(Λ/ε2)\widetilde{O}(Λ/\varepsilon^2)O(Λ/ε2), respectively, with only logarithmic dependence on the number of qubits. The algorithm is built directly from finite-time channel probes. It runs the unknown evolution for short times, estimates the corresponding Pauli transfer matrices from classical shadows, and converts these estimates into Lindbladian coefficients by stable local Fourier inversions. The algorithm is non-adaptive, uses no ancillas, and requires only random product states as inputs followed by random Pauli measurements. The method does not require knowing the structure of the Lindbladian in advance. We prove matching lower bounds that establish the near-optimality of the algorithm in both resources. By constructing a family of single-qubit dephasing Lindbladians, we show that any algorithm, even an adaptive one with arbitrary ancillas and measurements, requires Ω(Λ2/ε2)Ω(Λ^2/\varepsilon^2)Ω(Λ2/ε2) channel uses and Ω(Λ/ε2)Ω(Λ/\varepsilon^2)Ω(Λ/ε2) total evolution time. In particular, the lower bounds imply that the Heisenberg-limited scaling achievable for Hamiltonian learning is information-theoretically impossible once dissipative coefficients must be estimated.
We study the problem of learning an unknown Markovian open-system generator from access to its physical time evolution. This generator, called a Lindbladian, contains Hamiltonian and dissipative coefficients indexed by an exponentially large family of possible Pauli terms. We propose an efficient algorithm that learns arbitrary Lindbladians from time evolution under minimal assumptions. For a Lindbladian of dynamical strength at most ΛΛΛ, the algorithm estimates every coefficient to error εεε using O~(Λ2/ε2)\widetilde O(Λ^2/ε^2)O(Λ2/ε2) experiments and O~(Λ/ε2)\widetilde O(Λ/ε^2)O(Λ/ε2) total evolution time, together with polynomial classical running time. The algorithm consists of two nonadaptive, ancilla-free, and control-free stages: 1. The support-learning stage outputs a candidate support of size poly(Λ/η)\mathrm{poly}(Λ/η)poly(Λ/η) that contains every Hamiltonian and dissipative coordinate of magnitude at least ηηη, using O~(Λ2/η2)\widetilde O(Λ^2/η^2)O(Λ2/η2) experiments with preparations of product Pauli eigenstates and single-qubit Pauli measurements. 2.The coefficient-learning stage estimates all coefficients in any candidate support of size MMM to error εεε, using O~(Λ2log⁡M/ε2)\widetilde O(Λ^2\log M/ε^{2})O(Λ2logM/ε2) experiments with preparations of random stabilizer states and measurements in random Clifford bases. Composing the two stages identifies and estimates every coefficient of an arbitrary Lindbladian in polynomial time. The experiment-count and total-evolution-time scalings match the lower bounds up to logarithmic factors, so the algorithm is nearly optimal for learning arbitrary Lindbladians.
The fundamental difference between closed and open quantum dynamics lies in their environmental interaction: closed systems are perfectly isolated and evolve reversibly under unitary Hamiltonian dynamics, whereas open systems continuously couple to an external bath, resulting in irreversible dissipation and information loss. In this work, we show internal Hamiltonian dynamics can be "faked`` via external pure dissipation, i.e., Lindbladians without a coherent Hamiltonian part. More concretely, we show that, in a GKSL representation with zero explicit Hamiltonian term but nontraceless jump operators, bounded-norm dissipative generators can approximate Hamiltonian dynamics within εεε error in diamond norm using O(t2/ε)\mathcal{O}(t^2/ε)O(t2/ε) evolution time. We further prove that for time-independent dynamics this O(t2/ε)\mathcal{O}(t^2/ε)O(t2/ε) scaling is in the worst case, necessary and optimal from a geometric perspective, which captures the fundamental decoherence cost for catching up with the speed of Hamiltonian dynamics. Our construction leads to various implications, including the BQP-completeness of purely dissipative dynamics even before reaching approximate equilibrium, a Zeno-adjacent state-independent freezing effect, the no super-quadratic fast-forwarding theorem of a class of purely dissipative dynamics, and reducing Lindbladian simulation cost via gauge changing.
Characterizing the dynamics of open quantum systems at the level of microscopic interactions and error mechanisms is essential for calibrating quantum hardware, designing robust simulation protocols, and developing tailored error-correction methods. Under Markovian noise/dissipation, a natural characterization approach is to identify the full Lindbladian generator that gives rise to both coherent (Hamiltonian) and dissipative dynamics. Prior protocols for learning Lindbladians from dynamical data assumed pre-specified interaction structure, which can be restrictive when the relevant noise channels or control imperfections are not known in advance. In this paper, we present a sample-efficient protocol for learning sparse Lindbladians without assuming any a priori structure. Our protocol is ancilla-free, uses only product-state preparations and Pauli-basis measurements, admits provably stable coefficient reconstruction, and achieves near-optimal time resolution, making it compatible with near-term experimental capabilities. Together, this provides a systematic route to scalable characterization of open-system quantum dynamics, especially in settings where the error mechanisms of interest are unknown.
Simulating open quantum systems reveals how environmental coupling shapes relaxation, excitation transport, and the dynamics of quantum correlations. On quantum hardware, dissipative channels add operations and might seem to increase cost. However, we show that a broad class of Pauli noise, including depolarization, can ease quantum and classical simulation by exponentially suppressing high-weight components of Heisenberg-evolved observables. For bounded-degree Lindblad dynamics, this permits system-size-independent Trotter steps when estimating local observables. Combining this compression with Richardson extrapolation, we provide classical and quantum error bounds with respect to the 2-norm of the propagated observable. These give high-probability expectation-value guarantees for random input states or random Hamiltonians acting on a fixed state and control (out-of-time-order) correlators. Concretely, we show that expectation values of local observables at time ttt can be estimated to accuracy ε\varepsilonε using circuits of maximum depth O ⁣([1+(t/γ)3/2]log⁡2(1/ε))O\!\left(\left[1+\left(t/γ\right)^{3/2}\right]\log^2(1/\varepsilon)\right)O([1+(t/γ)3/2]log2(1/ε)), independent of the system size nnn. Classically, we show that sparse Pauli propagation runs in time polynomial in nnn, ttt and 1/ε1/\varepsilon1/ε for every fixed γ>0γ>0γ>0, with polynomial degree O(1/γ)O(1/γ)O(1/γ) in the weak dissipation limit. The gap between our quantum and classical upper bounds leaves room for a substantial polynomial quantum advantage as dissipation weakens, an observation further supported by our numerical results.