Learning Local Fermionic Lindbladians under Parity Superselection
Abstract
Parity superselection forbids direct measurement of odd Majorana observables. We learn time-independent, parity-covariant, k-mode-local Lindbladians on m modes using even preparations and measurements with uninterrupted short-time evolution. Internal markers turn odd probes into even observables, and pair measurements among three separated markers calibrate their dynamical contributions. Signed Fierz inversion recovers canonical coefficients, while semidefinite fitting yields a valid generator. For finite-range models on known bounded-degree graphs with suitable marker access and a supplied weighted-strength bound α̅, entrywise error ε is achieved using 𝒪̃(α̅2ε−2log(m/δ)) samples, without external modes or known nonzero coefficient locations. Recovery to diamond-norm error ε costs an additional factor m2, matching lower bounds for short-time experiments on fresh systems up to logarithmic and fixed geometric factors. Without a supplied graph, one idle ancillary mode per system mode and potentially nonlocal pair operations give total absolute coefficient error at most ε per mode using 𝒪̃k(α̅2d2m⌊ k/2⌋ε−2log(m/δ)) samples, under a supplied approximate coefficient-degree bound d and controlled weak-coefficient tails. All guarantees hold with probability at least 1−δ. For geometric models, fixed-support even observables can be predicted with logarithmic system-size sample complexity at fixed time and accuracy. We also give finite-volume and exponential-tail extensions.
Related
- Robust Structure Learning of k-local Lindbladians
- Parity-dependent sublattice structure of local 2×2 correlations in domino tilings of the Aztec diamond
- Superselection theory for 2D braided quantum spin systems via Connes fusion
- Optimal relaxation for Witten Lindbladians
- Superselection Rigidity of Topological Calderbank--Shor--Steane Codes: From Koszul-Complex Models to Nonsplit Extensions
BibTeX
@misc{mobus2026learning,
title = {{Learning Local Fermionic Lindbladians under Parity Superselection}},
author = {Tim Möbus and Daniel Stilck França and Cambyse Rouzé},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00448},
eprint = {2610.00448},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00448},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Learning Local Fermionic Lindbladians under Parity Superselection
AU - Tim Möbus
AU - Daniel Stilck França
AU - Cambyse Rouzé
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00448
UR - https://arxiv.org/abs/2610.00448
AB - Parity superselection forbids direct measurement of odd Majorana observables. We learn time-independent, parity-covariant, k-mode-local Lindbladians on m modes using even preparations and measurements with uninterrupted short-time evolution. Internal markers turn odd probes into even observables, and pair measurements among three separated markers calibrate their dynamical contributions. Signed Fierz inversion recovers canonical coefficients, while semidefinite fitting yields a valid generator. For finite-range models on known bounded-degree graphs with suitable marker access and a supplied weighted-strength bound α̅, entrywise error ε is achieved using 𝒪̃(α̅^2ε^−2log(m/δ)) samples, without external modes or known nonzero coefficient locations. Recovery to diamond-norm error ε costs an additional factor m^2, matching lower bounds for short-time experiments on fresh systems up to logarithmic and fixed geometric factors. Without a supplied graph, one idle ancillary mode per system mode and potentially nonlocal pair operations give total absolute coefficient error at most ε per mode using 𝒪̃_k(α̅^2d^2m^⌊ k/2⌋ε^−2log(m/δ)) samples, under a supplied approximate coefficient-degree bound d and controlled weak-coefficient tails. All guarantees hold with probability at least 1−δ. For geometric models, fixed-support even observables can be predicted with logarithmic system-size sample complexity at fixed time and accuracy. We also give finite-volume and exponential-tail extensions.
ER -