Dissipation is usually viewed as an obstacle to predicting quantum dynamics, yet it can also contract trajectories toward steady states and thereby suppress accumulated prediction errors, leaving it unclear whether dissipation ultimately helps or hinders the learnability of open quantum dynamics. We investigate this question using Neural Ordinary Differential Equation (NODE) surrogates for open Heisenberg XYZ spin chains. Closed-system learnability deteriorates rapidly with system size, culminating in a static-prediction collapse at four qubits; dissipation reverses this trend, creating a broad high-fidelity regime at intermediate system sizes, while at four qubits a fidelity-aware objective recovers learnable rollout structure that is absent under closed-system training. Comparison against static and steady-state baselines reveals that dissipation improves performance through two fundamentally different mechanisms: at weak-to-moderate dissipation the surrogate captures nontrivial transient dynamics and substantially outperforms trivial predictors, whereas at stronger damping high fidelity increasingly reflects trajectory simplification toward the steady state rather than improved learned dynamics. These results show that dissipation can enhance the learnability of open quantum dynamics, but that fidelity alone is insufficient to distinguish genuine dynamical learning from steady-state trivialization: dissipative contraction and trajectory simplification are distinct effects that peak in different regimes and should be disentangled when evaluating learned quantum-dynamical surrogates.
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13 pages, 6 figures. Supplementary material included as ancillary file
Dissipation is usually viewed as an obstacle to predicting quantum dynamics, yet it can also contract trajectories toward steady states and thereby suppress accumulated prediction errors, leaving it unclear whether dissipation ultimately helps or hinders the learnability of open quantum dynamics. We investigate this question using Neural Ordinary Differential Equation (NODE) surrogates for open Heisenberg XYZ spin chains. Closed-system learnability deteriorates rapidly with system size, culminating in a static-prediction collapse at four qubits; dissipation reverses this trend, creating a broad high-fidelity regime at intermediate system sizes, while at four qubits a fidelity-aware objective recovers learnable rollout structure that is absent under closed-system training. Comparison against static and steady-state baselines reveals that dissipation improves performance through two fundamentally different mechanisms: at weak-to-moderate dissipation the surrogate captures nontrivial transient dynamics and substantially outperforms trivial predictors, whereas at stronger damping high fidelity increasingly reflects trajectory simplification toward the steady state rather than improved learned dynamics. These results show that dissipation can enhance the learnability of open quantum dynamics, but that fidelity alone is insufficient to distinguish genuine dynamical learning from steady-state trivialization: dissipative contraction and trajectory simplification are distinct effects that peak in different regimes and should be disentangled when evaluating learned quantum-dynamical surrogates.
Quantum dissipation arises from the unavoidable coupling between a quantum system and its surrounding environment, which is known as a major obstacle in the quantum processing of information. Apart from its existence, examining how to trace dissipation from observational data is important and may stimulate ways to suppress the dissipation. In this paper, we propose to learn about quantum dissipation from dynamical observations using the neural ordinary differential equation, and then demonstrate this method concretely on two open quantum-spin systems: A large spin system and a spin-1/2 chain. We also investigate the learning efficiency of the dataset, which provides useful guidance for data acquisition in experiments. Our work helps to facilitate effective modeling and decoherence suppression in open quantum systems.
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 5×105 shots.
Modeling open quantum dynamics without full knowledge of the system Hamiltonian or noise model is a key challenge in quantum control and quantum state estimation. We introduce an Augmented Quantum Neural Ordinary Differential Equation (AQNODE) framework that learns quantum trajectories and dissipation parameters directly from partial continuous measurement data. By embedding the system into a latent space evolved via neural ODEs, AQNODE captures both observable and hidden non-Markovian dynamics with temporal smoothness and physical consistency. Our approach integrates weak measurement data to reconstruct qubit states and time-dependent decoherence rates, enabling accurate state prediction and parameter inference without explicit physical equations. Furthermore, we incorporate AQNODE-based feedback control techniques, including proportional-derivative and time-varying linear-quadratic regulator (LQR) strategies, to steer the quantum system toward target states in real time. Extensive numerical simulations demonstrate AQNODE's ability to generalize across system configurations, achieve low prediction errors, and perform robust quantum filtering and control. These results establish AQNODE as a scalable, differentiable, and experimentally compatible framework for real-time modeling and control of dissipative quantum systems.
A quantum many-body system coupled to an environment relaxes to a nonequilibrium steady state that can sustain order with no equilibrium counterpart. Computing such steady states is harder than closed-system dynamics as the density matrix problem squares the Hilbert-space dimension, and no free energy selects the steady state. The dissipative spin-1/2 Heisenberg chain is a benchmark example for nonequilibrium steady state physics; various methods have each calculated its phase diagram but do not agree, and a controlled determination at large system size has remained out of reach. Here we simulate the Lindblad dynamics of chains of up to 50 sites on the superconducting processor ibm_kingston -- 100 simultaneously active qubits at up to 1700 entangling-gate depths -- realizing the dissipation via Stinespring dilation. The system's dissipative evolution is a self-correcting mechanism that effectively erases errors, so hardware noise enters only as a weak competing dissipator. We measure static structure factors and resolve ferromagnetic, antiferromagnetic, spin-density-wave, and paramagnetic steady states, mapping the phase diagram with 117 quantum hardware data points across the Jx--Jy plane. We uncover a rich non-equilibrium phase diagram of ordered phases with only remnants of the mean-field order, and where sharp transitions give way to the crossovers expected in one dimension. We also find the existence of an incipient (Trotter-induced) spin density wave phase, highlighting the potential of controlled Trotterization as a tool to engineer various magnetic phases in dissipative spin systems. Our quantum simulations largely settle the lingering uncertainty regarding the correct phase diagram of this benchmark system. Moreover, they show that quantum computers are now a feasible tool for addressing scientific questions involving dissipative quantum systems.
Accurately modeling quantum dissipative dynamics remains challenging due to environmental complexity and non-Markovian memory effects. Although machine learning provides a promising alternative to conventional simulation techniques, most existing models employ real-valued neural networks (RVNNs) that inherently mismatch the complex-valued nature of quantum mechanics. By decoupling the real and imaginary parts of the density matrix, RVNNs can obscure essential amplitude-phase correlations, compromising physical consistency. Here, we introduce complex-valued neural networks (CVNNs) as a physics-consistent framework for learning quantum dissipative dynamics. CVNNs operate directly on complex-valued inputs, preserve the algebraic structure of quantum states, and naturally encode quantum coherences. Through numerical benchmarks on the spin-boson model and few variants of the Fenna-Matthews-Olson complex, we demonstrate that CVNNs outperform RVNNs in convergence speed, training stability, and physical fidelity-including significantly improved trace conservation and Hermiticity. These advantages increase with system size and coherence complexity, establishing CVNNs as a robust, scalable, quantum-aware classical approach for simulating open quantum systems in the pre-fault-tolerant quantum era.
Simulating open quantum multi-body systems governed by the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation is essential for quantum optimal control, superconducting qubit characterization, and quantum error mitigation. However, when deploying Physics-Informed Neural Networks (PINNs) or Neural Ordinary Differential Equations (Neural ODEs) as accelerated surrogates for open quantum dynamics, long-horizon autoregressive rollouts suffer from secular drift: (1) trace conservation breakdown (|Tr(ρ) − 1| > 0), violating total probability conservation; (2) loss of positive semi-definiteness (λmin(ρ) < 0), producing unphysical negative quantum measurement probabilities; and (3) distortion of purity and decoherence envelopes. While static metric projection of noisy density matrices onto the state spectrahedron is established in quantum tomography (Smolin et al., PRL 2012; Michelot 1986), its rigorous dynamical integration into autoregressive scientific machine learning (SciML) time-stepping loops remains unexplored. In this paper, we formulate an exact, non-dissipative dynamical framework: Idempotent Quantum State Manifold Projections (ΠS2 = ΠS) integrated via operator splitting into neural surrogate rollouts. We prove that ΠS is firmly non-expansive, preserving the high-order convergence rate of the underlying differential integrator while unconditionally eradicating secular trace runaway and negative probabilities without damping physical coherences. On a canonical benchmark of a driven-dissipative superconducting qubit under spontaneous relaxation and dephasing (4,000 integration steps, t = 20.0, replicated over 10 independent random seeds): Unconstrained neural rollouts suffer severe trace drift (|Tr(ρ) − 1| = (3.91 ± 1.25) × 10−3) and negative eigenvalues (λmin = (−1.21 ± 0.82) × 10−4); A standard Cholesky regularization baseline (ρ = L L† / Tr(L L†) with adaptive diagonal jitter εI) requires artificial diagonal entropy injection that dilutes low-entropy states; IdemSolver ΠS maintains exact unit trace ((8.44 ± 0.89) × 10−16), strictly non-negative eigenvalues (λmin ≥ 0), pristine Rabi coherence, exact steady-state purity (0.5244 ± 0.0005 matching the exact physical Lindblad baseline 0.5244), and machine-zero idempotency residual ((1.10 ± 0.08) × 10−15); and Achieves a step latency of 122.70 ± 4.70 μs (>8.1 kHz update rate), establishing a verified algebraic safeguard for real-time quantum control and SciML digital twins.