Agnostic Tomography of Stabilizer Product States
This addresses the challenge of robust quantum state learning for quantum computing applications, representing an incremental advance by extending tomography to an agnostic setting for a specific class of states.
The paper tackles the problem of agnostic tomography for quantum states, where the goal is to approximate an arbitrary state as well as any state in a given class, and presents an efficient algorithm for n-qubit stabilizer product states with a runtime of n^{O(1 + log(1/τ))} / ε^2, which is quasipolynomial and polynomial if τ is constant.
We define a quantum learning task called agnostic tomography, where given copies of an arbitrary state $ρ$ and a class of quantum states $\mathcal{C}$, the goal is to output a succinct description of a state that approximates $ρ$ 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 $ρ$. We give an efficient agnostic tomography algorithm for the class $\mathcal{C}$ of $n$-qubit stabilizer product states. Assuming $ρ$ has fidelity at least $τ$ with a stabilizer product state, the algorithm runs in time $n^{O(1 + \log(1/τ))} / \varepsilon^2$. This runtime is quasipolynomial in all parameters, and polynomial if $τ$ is a constant.