[2404.03813] Agnostic Tomography of Stabilizer Product States

Quantum Physics arXiv:2404.03813 (quant-ph) [Submitted on 4 Apr 2024 (v1), last revised 4 Mar 2026 (this version, v5)] Title:Agnostic Tomography of Stabilizer Product States Authors:Sabee Grewal, Vishnu Iyer, William Kretschmer, Daniel Liang View a PDF of the paper titled Agnostic Tomography of Stabilizer Product States, by Sabee Grewal and 3 other authors View PDF HTML (experimental) Abstract:We define a quantum learning task called agnostic tomography, where given copies of an arbitrary state $\rho$ and a class of quantum states $\mathcal{C}$, the goal is to output a succinct description of a state that approximates $\rho$ at least as well as any state in $\mathcal{C}$ (up to some small error $\varepsilon$). This task generalizes ordinary quantum tomography of states in $\mathcal{C}$ and is more challenging because the learning algorithm must be robust to perturbations of $\rho$. We give an efficient agnostic tomography algorithm for the class $\mathcal{C}$ of $n$-qubit stabilizer product states. Assuming $\rho$ has fidelity at least $\tau$ with a stabilizer product state, the algorithm runs in time $n^{O(\log(2/\tau))} / \varepsilon^2$, which is $\mathsf{poly}(n/\varepsilon)$ for any constant $\tau$. Comments: Subjects: Quantum Physics (quant-ph); Machine Learning (cs.LG) Cite as: arXiv:2404.03813 [quant-ph]   (or arXiv:2404.03813v5 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2404.03813 Focus to learn more arXiv-issued DOI via DataCite Submission histo...