We study the problem of learning the dense Sachdev--Ye--Kitaev (SYK) Hamiltonian from copies of its Gibbs state. Existing algorithms for Hamiltonian learning typically rely on geometric locality or bounded interaction degree and therefore do not apply to SYK, where each quartic interaction overlaps with $\Theta(n^3)$ o...
Anurag Anshu, Srinivasan Arunachalam, Si-Tan Chen et al.· 0 citations
We study exact learning with membership queries for concept classes $\mathcal C\subseteq\{0,1\}^N$, focusing on the relationships among their deterministic, randomized, and quantum query complexities, denoted $\mathsf{D}(\mathcal C)$, $\mathsf{R}(\mathcal C)$, and $\mathsf{Q}(\mathcal C)$, respectively. The two canonic...
S. Arunachalam, Amin Shiraz Gilani, Nikhil S. Mande· 1 citation
Smoothed analysis is a central framework in classical algorithms for explaining the performance of algorithms beyond the worst case, often explaining why algorithms perform well in practice. We initiate a systematic study of its quantum counterpart and show the following results. $(1)$ We show that there is a total fun...
