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:2603.07778

Lindbladian Learning with Neural Differential Equations

Timothy Heightman, Roman Aseguinolaza Gallo, Edward Jiang, JRM Saavedra, Antonio Acín, Marcin Płodzień

quant-phcond-mat.dis-nncs.LGSubmitted Mar 8, 2026• Announced Mar 10, 2026• 0 citations
arXivHTMLPDF

Abstract

Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in the purely unitary case, because coherent and dissipative mechanisms can produce similar measurement statistics and long-time data can be insensitive to coherent couplings. Here we tackle this so-called Lindbladian learning problem of open-system characterisation with maximum-likelihood on Pauli measurements at multiple experimentally friendly \emph{transient} times, exploiting the richer information content of transient dynamics. To navigate the resulting non-convex likelihood loss-landscape, we augment the physical model neural differential-equation term, which is progressively removed during training to distil an interpretable Lindbladian solution. Our method reliably learns open-system dynamics across neutral-atom (with 2D connectivity) and superconducting Hamiltonians, as well as the Heisenberg XYZ, and PXP models on a spin-1/2 chain. For the dissipative part, we show robustness over phase noise, thermal noise, and their combination. Our algorithm can robustly infer these dissipative systems over noise-to-signal ratios spanning four orders of magnitude, and system sizes up to $N=6$ qubits with fewer than $5 \times 10^5$ shots.

Comments
22 pages, 15 figures

Related papers

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

Solving the quantum many-body Hamiltonian learning problem with neural differential equations

Timothy Heightman, Edward Jiang, Antonio Acín

Abstract Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under the action of such Hamiltonians. This inherent complexity limits our ability to characterise quantum many-body systems, highlighting the need for innovative approaches to unlock their full potential. To address this challenge, we propose a novel method to solve the Hamiltonian learning (HL) problem -inferring quantum dynamics from many-body state trajectories. Our approach has the unprecedented advantage of distilling and filtering an estimator Hamiltonian from a Neural ODE representation of state trajectories. By distilling Hamiltonian information from Neural ODE onto an ansatz Hamiltonian, our method is reliably convergent, experimentally friendly, and interpretable. In addition to this, we propose a new quantitative benchmark based on power laws, which can objectively compare the reliability and generalisation capabilities of any two HL algorithms. Finally, we benchmark our method against state-of-the-art HL algorithms with a 1D spin- 1 / 2 chain proof of concept, giving a stable solution for HL on a set of Hamiltonians previously unlearnable in the literature. Code for our method is available and open source.

arXiv:2408.08639•Quantum Science and Technology•Sep 30, 2025•6 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

Large-scale Lindblad learning from time-series data

Ewout van den Berg, Brad Mitchell, Ken Xuan Wei +1 more

Learned open-quantum-system models have broad applications in device characterization, device calibration, realistic noise model construction, and bounding observable estimates in quantum simulation. To this end, we develop a highly scalable Lindblad learning protocol assuming an effective time-independent Lindblad generator with local interactions. For a given operation that can be applied repeatedly on a quantum computer, the protocol learns the Lindbladian by forming a linear system of equations for the model parameters in terms of a set of observable values and their gradients. The required gradient information is obtained by fitting time-series data with sums of exponentially damped sinusoids and differentiating those curves. We develop a robust curve-fitting procedure that finds a parsimonious representation of the data up to shot noise. We demonstrate the approach by learning the Lindbladian for a full layer of gates on a 156-qubit superconducting quantum processor, providing the first learning experiment of this kind. We study the effects of state-preparation and measurement errors and limitations on the operations that can be learned. For improved performance under readout errors, we propose an optional fine-tuning strategy that improves the fit between the time-evolved model and the measured data.

quant-pharXiv:2512.08165•Dec 10, 2025•0 citations

Characterizing Arbitrary Lindbladian Dynamics with a Few Pauli Measurements

Taiqi Zhou, Weiyuan Gong

Quantum devices are open systems whose dynamics interleave coherent evolution with dissipation, and benchmarking, error mitigation, and error correction all rest on a faithful model of both. Existing characterization protocols either assume prior knowledge of the interaction and noise structure, or demand ancillas, entangled probes, or mid-circuit control, or capture only the Pauli-diagonal part of the noise. Here, we present a protocol that reconstructs an arbitrary sparse Markovian generator, including every Hamiltonian together with the jump operator coefficients, using only product Pauli state preparation, single uninterrupted forward evolutions, and product Pauli measurements. Given a sparsity budget $M_0$ and a strength bound $Γ$ of the Lindbladian, every coefficient is learned to precision $ε$ from $\widetilde{O}(Γ^2M_0^2/ε^4)$ experiments and $\widetilde{O}(ΓM_0^2/ε^2)$ total evolution time, with both supports identified from data without locality assumptions. The protocol runs at a logarithmic number of positive evolution times on a hardware clock lattice and is provably robust to calibrated state-preparation and measurement errors.

quant-pharXiv:2607.23044•Jul 28, 2026•0 citations

Transformer-Based Time-Series Inference of Lindblad Dynamics in Open Quantum Systems

Julian Guam, Jianqing Liu

The Lindblad master equation is the standard framework for describing the non-unitary evolution of open quantum systems, where environmental interactions induce dissipation and decoherence. When both the system Hamiltonian and the dissipation rates are partially unknown or explicitly time-dependent, traditional analytical inversion and system-identification techniques become intractable. Recent works have demonstrated that Transformer-based models can infer unknown dissipation rates from observable time series, yet these approaches typically rely on hand-crafted statistical features under idealized and highly restricted conditions. Here we advance the paradigm by introducing a raw time-series Transformer that directly ingests the full trajectories of Pauli expectation values $\langleσ_x(t)\rangle$, $\langleσ_y(t)\rangle$, and $\langleσ_z(t)\rangle$, thereby fully exploiting the self-attention mechanism for temporal modeling. The architecture is further extended to jointly learn unknown Hamiltonian parameters, handle multiple dissipation channels, and operate robustly under realistic measurement noise. Across all tested scenarios the model achieves consistently high reconstruction accuracy while eliminating manual feature engineering. This provides a scalable, robust, and versatile framework for quantum environment sensing in realistic open quantum systems.

quant-pharXiv:2610.05647•Oct 6, 2026•0 citations
Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in the purely unitary case, because coherent and dissipative mechanisms can produce similar measurement statistics and long-time data can be insensitive to coherent couplings. Here we tackle this so-called Lindbladian learning problem of open-system characterisation with maximum-likelihood on Pauli measurements at multiple experimentally friendly \emph{transient} times, exploiting the richer information content of transient dynamics. To navigate the resulting non-convex likelihood loss-landscape, we augment the physical model neural differential-equation term, which is progressively removed during training to distil an interpretable Lindbladian solution. Our method reliably learns open-system dynamics across neutral-atom (with 2D connectivity) and superconducting Hamiltonians, as well as the Heisenberg XYZ, and PXP models on a spin-1/2 chain. For the dissipative part, we show robustness over phase noise, thermal noise, and their combination. Our algorithm can robustly infer these dissipative systems over noise-to-signal ratios spanning four orders of magnitude, and system sizes up to N=6N=6N=6 qubits with fewer than 5×1055 \times 10^55×105 shots.
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.
Abstract Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under the action of such Hamiltonians. This inherent complexity limits our ability to characterise quantum many-body systems, highlighting the need for innovative approaches to unlock their full potential. To address this challenge, we propose a novel method to solve the Hamiltonian learning (HL) problem -inferring quantum dynamics from many-body state trajectories. Our approach has the unprecedented advantage of distilling and filtering an estimator Hamiltonian from a Neural ODE representation of state trajectories. By distilling Hamiltonian information from Neural ODE onto an ansatz Hamiltonian, our method is reliably convergent, experimentally friendly, and interpretable. In addition to this, we propose a new quantitative benchmark based on power laws, which can objectively compare the reliability and generalisation capabilities of any two HL algorithms. Finally, we benchmark our method against state-of-the-art HL algorithms with a 1D spin- 1 / 2 chain proof of concept, giving a stable solution for HL on a set of Hamiltonians previously unlearnable in the literature. Code for our method is available and open source.
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.
Learned open-quantum-system models have broad applications in device characterization, device calibration, realistic noise model construction, and bounding observable estimates in quantum simulation. To this end, we develop a highly scalable Lindblad learning protocol assuming an effective time-independent Lindblad generator with local interactions. For a given operation that can be applied repeatedly on a quantum computer, the protocol learns the Lindbladian by forming a linear system of equations for the model parameters in terms of a set of observable values and their gradients. The required gradient information is obtained by fitting time-series data with sums of exponentially damped sinusoids and differentiating those curves. We develop a robust curve-fitting procedure that finds a parsimonious representation of the data up to shot noise. We demonstrate the approach by learning the Lindbladian for a full layer of gates on a 156-qubit superconducting quantum processor, providing the first learning experiment of this kind. We study the effects of state-preparation and measurement errors and limitations on the operations that can be learned. For improved performance under readout errors, we propose an optional fine-tuning strategy that improves the fit between the time-evolved model and the measured data.
Quantum devices are open systems whose dynamics interleave coherent evolution with dissipation, and benchmarking, error mitigation, and error correction all rest on a faithful model of both. Existing characterization protocols either assume prior knowledge of the interaction and noise structure, or demand ancillas, entangled probes, or mid-circuit control, or capture only the Pauli-diagonal part of the noise. Here, we present a protocol that reconstructs an arbitrary sparse Markovian generator, including every Hamiltonian together with the jump operator coefficients, using only product Pauli state preparation, single uninterrupted forward evolutions, and product Pauli measurements. Given a sparsity budget M0M_0M0​ and a strength bound ΓΓΓ of the Lindbladian, every coefficient is learned to precision εεε from O~(Γ2M02/ε4)\widetilde{O}(Γ^2M_0^2/ε^4)O(Γ2M02​/ε4) experiments and O~(ΓM02/ε2)\widetilde{O}(ΓM_0^2/ε^2)O(ΓM02​/ε2) total evolution time, with both supports identified from data without locality assumptions. The protocol runs at a logarithmic number of positive evolution times on a hardware clock lattice and is provably robust to calibrated state-preparation and measurement errors.
The Lindblad master equation is the standard framework for describing the non-unitary evolution of open quantum systems, where environmental interactions induce dissipation and decoherence. When both the system Hamiltonian and the dissipation rates are partially unknown or explicitly time-dependent, traditional analytical inversion and system-identification techniques become intractable. Recent works have demonstrated that Transformer-based models can infer unknown dissipation rates from observable time series, yet these approaches typically rely on hand-crafted statistical features under idealized and highly restricted conditions. Here we advance the paradigm by introducing a raw time-series Transformer that directly ingests the full trajectories of Pauli expectation values ⟨σx(t)⟩\langleσ_x(t)\rangle⟨σx​(t)⟩, ⟨σy(t)⟩\langleσ_y(t)\rangle⟨σy​(t)⟩, and ⟨σz(t)⟩\langleσ_z(t)\rangle⟨σz​(t)⟩, thereby fully exploiting the self-attention mechanism for temporal modeling. The architecture is further extended to jointly learn unknown Hamiltonian parameters, handle multiple dissipation channels, and operate robustly under realistic measurement noise. Across all tested scenarios the model achieves consistently high reconstruction accuracy while eliminating manual feature engineering. This provides a scalable, robust, and versatile framework for quantum environment sensing in realistic open quantum systems.