aiqbench analysis
This paper gives a theoretical protocol for learning time-dependent Hamiltonians and dephasing rates in locally interacting qubit systems, with provable error and sample-complexity bounds. Its value is in verification: it offers a route to characterizing how quantum hardware and simulators evolve over time, not just at fixed parameters. Readers should note that the results rest on stated assumptions, including a weak-dissipation condition and a known function class, and that the numerical experiments are the main evidence for practical behavior.
Learning and certification of local time-dependent quantum dynamics and noise
arXiv:2510.08500v2 Announce Type: replace Abstract: Hamiltonian learning protocols are becoming valuable tools for benchmarking and verifying quantum computers and simulators, yet few rigorous protocols address explicitly time-dependent dynamics. We give a scalable protocol for learning the time-dependent coefficients of a locally interacting $n$-qubit system on a graph $\mathsf{G}$ of effective dimension $D$. The unknown generator contains geometrically local Hamiltonian terms and weak onsite Pauli-dephasing terms with time-dependent, nonnegative rates. Its coefficient functions and their derivatives admit a certified simultaneous $C^1$ approximation in a known finite-dimensional function class that supports stable interpolation. The only experimental primitives are preparation of product Pauli eigenstates, evolution for chosen times, and product-Pauli measurements. Under an explicit weak-dissipation condition, the Lieb--Robinson estimates proved here, and a certified effective approximation/interpolation degree $m_{\rm eff}$, the protocol reconstructs every coefficient uniformly on a constant interval with error $\epsilon$ and success probability $1-\delta$ using $\widetilde{\mathcal{O}}\!\left(\epsilon^{-2}\operatorname{poly}(m_{\rm eff})\log(n\delta^{-1})\right)$ samples and polynomial classical processing. The method estimates derivatives of finite-time channel overlaps by stable interpolation, uses process shadows to learn the required local transfer matrices, and constructs sparse diagonally dominant systems through localized semidefinite programs.
Abstract:Hamiltonian learning protocols are becoming valuable tools for benchmarking and verifying quantum computers and simulators, yet few rigorous protocols address explicitly time-dependent dynamics. We give a scalable protocol for learning the time-dependent coefficients of a locally interacting $n$-qubit system on a graph $\mathsf{G}$ of effective dimension $D$. The unknown generator contains geometrically local Hamiltonian terms and weak onsite Pauli-dephasing terms with time-dependent, nonnegative rates. Its coefficient functions and their derivatives admit a certified simultaneous $C^1$ approximation in a known finite-dimensional function class that supports stable interpolation. The only experimental primitives are preparation of product Pauli eigenstates, evolution for chosen times, and product-Pauli measurements. Under an explicit weak-dissipation condition, the Lieb--Robinson estimates proved here, and a certified effective approximation/interpolation degree $m_{\rm eff}$, the protocol reconstructs every coefficient uniformly on a constant interval with error $\epsilon$ and success probability $1-\delta$ using $\widetilde{\mathcal{O}}\!\left(\epsilon^{-2}\operatorname{poly}(m_{\rm eff})\log(n\delta^{-1})\right)$ samples and polynomial classical processing. The method estimates derivatives of finite-time channel overlaps by stable interpolation, uses process shadows to learn the required local transfer matrices, and constructs sparse diagonally dominant systems through localized semidefinite programs.
47 pages, 5 figures. Corrected mistakes in previous versions and added numerical experiments
arXiv:2510.08500 [quant-ph]
(or arXiv:2510.08500v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2510.08500 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 279 words
