Learning open-system dynamics

Characterizing an unknown open-system evolution is essential for calibration, verification and control. Full process tomography scales exponentially and treats each time independently, whereas a physical model may be specified compactly by a Hamiltonian, a Lindblad generator, or a finite-memory process tensor. The learning problem is to exploit that structure without assuming it in a way that hides important noise.

What is known: Efficient algorithms exist for local or sparse Hamiltonians, Pauli channels and several structured Lindbladians, while process-tensor tomography can reconstruct non-Markovian multi-time statistics at a cost governed by memory and temporal complexity. General learnability depends on access assumptions — short-time evolution, ancillas, coherent control, adaptivity and the available state preparations and measurements — and robustness to state-preparation and measurement errors is often decisive.

Preprint progress (July 2026): Chen–Yu give nearly optimal experiment-count and evolution-time guarantees for learning bounded-dynamical-strength Pauli-expanded Lindbladians. Their error is coefficient-wise, with a thresholded support guarantee; it is not automatically a diamond-norm guarantee for an arbitrary evolved channel. The nonadaptive, ancilla-free protocol requires no control during evolution, but its coefficient-learning stage uses global stabilizer/Clifford preparation and measurement resources. These access assumptions are part of the theorem.

Further progress (August–September 2026): Ramos Ramos et al. combined stochastic tensor-network simulation with optimization to learn local Lindblad dissipation rates up to 16 sites and a seven-parameter homogeneous model up to 160 sites, with exact variance identities and finite-covariance error guarantees. Pancotti, Saravanan and Svore instead learned fault-event probabilities directly from error-correction syndrome and logical-observable data: an exact maximum-likelihood tensor-network decoder supplies differentiable gradients, recovers Sycamore noise parameters, and tracks synthetic drift by warm starts. These advances address scalable and experimentally realistic structured models, not the optimal-resource theory for arbitrary generators or multi-time non-Markovian processes.

These newest tensor-network results are preprints with structured-model and numerical evidence, not a universal optimal-resource theorem. The remaining targets include restricted local preparation/measurement, translating coefficient error into prediction error, SPAM-robust identification, time-dependent generators and finite-memory non-Markovian processes, each with explicit upper and lower bounds. Related: O1, O2, O5.

Source disclosures

The previous update recorded an author statement about interactive ChatGPT use for checking, references and polishing, with responsibility attributed to the human authors. That declaration was not independently rechecked in this audit and is not evidence of theorem correctness. Source

Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.

preprint: Near-optimal bounded-strength coefficient learning with thresholded support, using specified product/stabilizer access; not a universal diamond-norm process-learning guarantee. Evidence

numerical: Structured Lindblad-rate learning with stochastic tensor networks; simulation scaling does not certify arbitrary-process learnability. Evidence

numerical: Tensor-network likelihood learning of fault-event probabilities from error-correction data, a restricted noise model. Evidence