Agnostic Tomography of Stabilizer Product States
<|reference_start|>Agnostic Tomography of Stabilizer Product States: 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 $n^{O(1 + \log(1/\tau))} / \varepsilon^2$. This runtime is quasipolynomial in all parameters, and polynomial if $\tau$ is a constant.<|reference_end|>
@article{grewal2024agnostic,
    title={Agnostic Tomography of Stabilizer Product States},
    author={Sabee Grewal, Vishnu Iyer, William Kretschmer, Daniel Liang},
    journal={arXiv preprint arXiv:2404.03813},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.03813},
    primaryClass={quant-ph cs.LG}
}