We consider the problem of quantum 1-PCA: given copies of an unknown $n$-qubit mixed state, recover a classical description of its leading eigenvector. Our goal is to do so using non-adaptive and single-qubit measurements. For an $n$-qubit state with top eigenvalue $λ$ and spectral gap at least $Δ> 0$, we give an algor …
The Fréchet Inception Distance (FID) is widely used to evaluate generative models, but its empirical plug-in estimator suffers from finite-sample bias [BSAG18, CF20]. We study the sample complexity $n$ of estimating FID to error $ε$ between $d$-dimensional Gaussians with bounded mean distance and covariances, when one …
We study agnostic tomography of pure bosonic Gaussian states: given copies of an arbitrary $n$-mode bosonic state $ρ$, the goal is to output a pure Gaussian state whose infidelity with $ρ$ is at most $\mathrm{opt} + ε$, where $\mathrm{opt}$ is the minimum infidelity achievable by any pure Gaussian state. We give effici …
We introduce Gacha Decoding, an inference-time method for eliciting diverse language model generations that scales with model capability. Across open-ended domains (in-the-wild chat, creative writing, planning for image generation, and protein design), Gacha Decoding significantly outperforms existing generation divers …