aiqbench analysis
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
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