analiza aiqbench
This research introduces an efficient protocol for learning unknown $k$-local Lindblad generators on quantum systems using only product-state preparations and single-qubit measurements. The method achieves logarithmic sample dependence on system size for exactly sparse models while providing rigorous guarantees without relying on degree or sparsity promises. It represents a significant advancement in the theoretical foundations of quantum process tomography and Hamiltonian learning.
Robust Structure Learning of $k$-local Lindbladians
arXiv:2606.23652v2 Announce Type: replace Abstract: We present an efficient protocol for learning an unknown $k$-local Lindblad generator on $n$ qubits using only product-state preparations, short-time evolution, and single-qubit Pauli measurements, without prior knowledge of the interaction structure. For fixed $k$ and a supplied weighted interaction-strength bound $\bar\alpha$, the protocol estimates all Hamiltonian and dissipative Pauli--GKSL coefficients with total coefficient error at each site at most $\varepsilon$ with probability at least $1-\delta$ using $\widetilde{\mathcal O}_k(\bar\alpha^2n^{2k-2}\varepsilon^{-2}\log(n/\delta))$ samples and polylogarithmically many distinct evolution times. This guarantee requires no degree, sparsity, or tail promise. A convex optimization converts these estimates into a valid $k$-local Lindblad generator with diamond-norm error at most $\varepsilon$ using $\widetilde{\mathcal O}_k(\bar\alpha^2n^{2k}\varepsilon^{-2}\log(n/\delta))$ samples and polynomial-time classical postprocessing. With a supplied local effective-sparsity bound $r$ and a sufficiently small sitewise subthreshold tail $\mathcal O_k(\varepsilon)$, coefficient recovery requires only $\widetilde{\mathcal O}_k(\bar\alpha^2r^2\varepsilon^{-2}\log(n/\delta))$ samples, without a supplied threshold or coefficient locations and without a coefficient-gap assumption. In particular, exactly sparse bounded-degree models have logarithmic sample dependence on $n$. We also provide guard-band support recovery and complementary supplied-candidate guarantees, extend the guarantees to model misspecification, and prove complementary sample-complexity lower bounds.
Abstract:We present an efficient protocol for learning an unknown $k$-local Lindblad generator on $n$ qubits using only product-state preparations, short-time evolution, and single-qubit Pauli measurements, without prior knowledge of the interaction structure. For fixed $k$ and a supplied weighted interaction-strength bound $\bar\alpha$, the protocol estimates all Hamiltonian and dissipative Pauli--GKSL coefficients with total coefficient error at each site at most $\varepsilon$ with probability at least $1-\delta$ using $\widetilde{\mathcal O}_k(\bar\alpha^2n^{2k-2}\varepsilon^{-2}\log(n/\delta))$ samples and polylogarithmically many distinct evolution times. This guarantee requires no degree, sparsity, or tail promise. A convex optimization converts these estimates into a valid $k$-local Lindblad generator with diamond-norm error at most $\varepsilon$ using $\widetilde{\mathcal O}_k(\bar\alpha^2n^{2k}\varepsilon^{-2}\log(n/\delta))$ samples and polynomial-time classical postprocessing. With a supplied local effective-sparsity bound $r$ and a sufficiently small sitewise subthreshold tail $\mathcal O_k(\varepsilon)$, coefficient recovery requires only $\widetilde{\mathcal O}_k(\bar\alpha^2r^2\varepsilon^{-2}\log(n/\delta))$ samples, without a supplied threshold or coefficient locations and without a coefficient-gap assumption. In particular, exactly sparse bounded-degree models have logarithmic sample dependence on $n$. We also provide guard-band support recovery and complementary supplied-candidate guarantees, extend the guarantees to model misspecification, and prove complementary sample-complexity lower bounds.
Quantum Physics (quant-ph); Information Theory (cs.IT); Numerical Analysis (math.NA); Statistics Theory (math.ST)
arXiv:2606.23652 [quant-ph]
(or arXiv:2606.23652v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.23652 Focus to learn more arXiv-issued DOI via DataCite
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 281 cuvinte
Subiecte conexe
Characterizing Arbitrary Lindbladian Dynamics with a Few Pauli Measurements
arXiv · 28 iul. 2026
SIGMA: Structured Noise-Effect-Aware Grouped Multi-Agent Aggregation
arXiv · 28 aug. 2026
Learning the structure of open quantum systems
arXiv · 5 oct. 2026
PIRAMID: Progress and Plans
LessWrong · 27 iul. 2026