# Characterizing Arbitrary Lindbladian Dynamics with a Few Pauli Measurements

arXiv: https://arxiv.org/abs/2607.23044 · HTML: https://mlsanity.com/paper/2607.23044/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 91 references that are in the map.
- First posted on arXiv 25 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Efficient quantum tomography II](https://mlsanity.com/paper/1612.00034/) (2016)
- [Sample-efficient learning of quantum many-body systems](https://mlsanity.com/paper/2004.07266/) (2020)
- [Learning many-body Hamiltonians with Heisenberg-limited scaling](https://mlsanity.com/paper/2210.03030/) (2022)
- [Learning quantum Hamiltonians at any temperature in polynomial time](https://mlsanity.com/paper/2310.02243/) (2023)
- [Practical Black Box Hamiltonian Learning](https://mlsanity.com/paper/2206.15464/) (2022)
- [Structure learning of Hamiltonians from real-time evolution](https://mlsanity.com/paper/2405.00082/) (2024)
- [Learning k-body Hamiltonians via compressed sensing](https://mlsanity.com/paper/2410.18928/) (2024)
- [Learning the structure of any Hamiltonian from minimal assumptions](https://mlsanity.com/paper/2410.21635/) (2024)
- [Ansatz-free Hamiltonian learning with Heisenberg-limited scaling](https://mlsanity.com/paper/2502.11900/) (2025)
- [Optimal detection of dissipation in Lindbladian dynamics](https://mlsanity.com/paper/2603.17736/) (2026)
- [Heisenberg-limited Hamiltonian learning without short-time control](https://mlsanity.com/paper/2604.27838/) (2026)
- [Optimal Ansatz-free Hamiltonian Learning In Situ](https://mlsanity.com/paper/2606.19486/) (2026)
- [SPAM Tolerance for Pauli Error Estimation](https://mlsanity.com/paper/2510.00230/) (2025)

## Built on by (most cited first, 1 of 1)

- [Hamiltonian locality testing and certification do not achieve the Heisenberg limit](https://mlsanity.com/paper/2610.03205/) (2026)

## Abstract (arXiv)

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 M0 and a strength bound Gamma of the Lindbladian, every coefficient is learned to precision ε from widetildeO(Gamma2M02/ε4) experiments and widetildeO(Gamma M02/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.