Classical Hardness of Learning Functions of Hamiltonians
Morohoshi, Nakayama, Manabe, and Mitarai proposed a physically motivated quantum machine learning problem in which the goal is to predict quantities of the form $\operatorname{Tr}[f(H)ρ]$ from classical descriptions of a Hamiltonian $H$ and a quantum state $ρ$, where $f$ is an unknown function. We call this problem Hamiltonian function learning in this paper. They constructed an efficient quantum learning algorithm under suitable conditions, while leaving a rigorous proof of average-case classical hardness open. In this paper, we rigorously prove the average-case classical hardness for two distribution-specific Hamiltonian function learning problems for $f_{\cos,π}(λ)=\cos(πλ)$ and $f_{\e...
| Authors | Sota Hashimoto, Akinori Kawachi |
|---|---|
| Primary category | quant-ph |
| Published | 1 October 2026 |
| Last updated at source | 1 October 2026 |
Popularity, last 2 days
0 now. Counts as reported by the source, snapshotted daily by Silytics.
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.