Learning Arbitrary Lindbladians with Quantum Error Correction

Abstract

We study ansatz-free Lindbladian learning, the problem of reconstructing the generator of an open quantum system without prior knowledge of its Hamiltonian or dissipator structures. This problem exhibits two fundamental precision limits. Hamiltonian components not obscured by dissipation are Heisenberg-limited, while full Lindbladian reconstruction is subject to the quadratically worse standard quantum limit. This creates an apparent algorithmic impasse: achieving the Heisenberg-limited Hamiltonian learning requires suppressing unknown dissipation, which seemingly demands prior reconstruction of the noise and thereby incurs the standard-quantum-limit cost. In this work, we resolve this obstruction by giving an algorithm that learns the Hamiltonian disjoint from dissipator (HDD) at the Heisenberg limit without prior knowledge of either the Hamiltonian or dissipator supports. Our main technical ingredient is a randomized recursive stabilizer-code construction that progressively identifies and suppresses the dominant dissipative terms without reconstructing the full dissipator. Building on this framework, we also introduce an efficient end-to-end algorithm that learns the entire sparse Lindbladian at the standard quantum limit. Finally, we prove that in the ansatz-free setting, the HDD terms constitute the maximal set of Hamiltonian coefficients uniformly learnable at the Heisenberg limit. We show that every term outside HDD is fundamentally standard-quantum limited, extending prior no-go results to the ansatz-free setting. Together, our protocols provide a scalable framework for characterizing open quantum systems, with quantum error correction serving as a key learning primitive.

Learning Logical Operations for Arbitrary Quantum Error Correction Codes
Nico Meyer, Christopher Mutschler, Dominik Seuß +2
arXiv9 Sep 2026PreprintarXiv licenceFull textQuantum physics & quantum informationarXiv
Learning Arbitrary Lindbladians from Time Evolution
Zhili Chen, Zhan Yu
arXiv3 Nov 2026PreprintCC BY 4.0Full textQuantum physics & quantum informationarXiv
Bosonic quantum error correction with microwave cavities for quantum repeaters
S. Siddardha Chelluri, Sanchar Sharma, Frank Schmidt +2
Physical Review A21 Jul 2026Peer-reviewedLicence not statedFull textQuantum physics & quantum informationHAL
Error-Correction Transitions in Finite-Depth Quantum Channels
Arman Sauliere, Guglielmo Lami, Pedro Ribeiro +2
Physical Review Letters16 Sep 2026Peer-reviewedLicence not statedGeneral physicsHAL
Quantum Error Correction and the Limits of Quantum Metrology
Zhuoran Bao, Daniel F. V. James
arXiv28 Sep 2026PreprintCC0Full textOptics & photonics Quantum physics & quantum informationarXiv

Cite

BibTeX RIS

BibTeX

@misc{romanov2026learning,
  title = {{Learning Arbitrary Lindbladians with Quantum Error Correction}},
  author = {Nikita Romanov and Petr Ivashkov and Weiyuan Gong and Ishaan Kannan and Andi Gu and Hong-Ye Hu and Susanne F. Yelin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.18188},
  eprint = {2606.18188},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.18188},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Learning Arbitrary Lindbladians with Quantum Error Correction
AU  - Nikita Romanov
AU  - Petr Ivashkov
AU  - Weiyuan Gong
AU  - Ishaan Kannan
AU  - Andi Gu
AU  - Hong-Ye Hu
AU  - Susanne F. Yelin
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2606.18188
UR  - https://arxiv.org/abs/2606.18188
AB  - We study ansatz-free Lindbladian learning, the problem of reconstructing the generator of an open quantum system without prior knowledge of its Hamiltonian or dissipator structures. This problem exhibits two fundamental precision limits. Hamiltonian components not obscured by dissipation are Heisenberg-limited, while full Lindbladian reconstruction is subject to the quadratically worse standard quantum limit. This creates an apparent algorithmic impasse: achieving the Heisenberg-limited Hamiltonian learning requires suppressing unknown dissipation, which seemingly demands prior reconstruction of the noise and thereby incurs the standard-quantum-limit cost. In this work, we resolve this obstruction by giving an algorithm that learns the Hamiltonian disjoint from dissipator (HDD) at the Heisenberg limit without prior knowledge of either the Hamiltonian or dissipator supports. Our main technical ingredient is a randomized recursive stabilizer-code construction that progressively identifies and suppresses the dominant dissipative terms without reconstructing the full dissipator. Building on this framework, we also introduce an efficient end-to-end algorithm that learns the entire sparse Lindbladian at the standard quantum limit. Finally, we prove that in the ansatz-free setting, the HDD terms constitute the maximal set of Hamiltonian coefficients uniformly learnable at the Heisenberg limit. We show that every term outside HDD is fundamentally standard-quantum limited, extending prior no-go results to the ansatz-free setting. Together, our protocols provide a scalable framework for characterizing open quantum systems, with quantum error correction serving as a key learning primitive.
ER  -

Abstract

Related

Cite