Conjecture: *All naturally occuring quantum states allow for a compact **classical** description.* ... Where by compact I mean polynomial in system size. *NB: Mest sanns. ekvivalent til [[Extended Church-Turing-Deutsch thesis]]; se under.* ### Tanker Restrict to ground-states of naturally-occuring hamiltonians, or for *any* naturally-occuring state? Would imply that, apart from *finding* said description, it is mainly quantum *dynamics* that require a quantum computer (rather than the exponential size of the hilbert space to store the state itself). Assuming it is possible to make this notion precise, this conjecture implies the [[Extended Church-Turing-Deutsch thesis]]. Re finding said state: sounds [[NP]]-like, but doesn't have a clear notion of verification—unless it really is derived from first principles with a compact proof attached. Nature-states $\in$ NP? (Would be an even stronger conjecture – something like "Classically verifiable compact-state conjecture"; sounds unlikely to be true.) Relevant kompleksitetsklasse?: [[QCMA]], dvs [[QMA]] med en klassisk beskrivelse? Relatert til [[Algebraiske tall]]? Waitaminute ... Er ikke dette opplagt? Følger det ikke simpelthen av at [[BQP]] $\subseteq$ [[PSPACE]], i kombinasjon med [[Extended Church-Turing-Deutsch thesis]]: Nature-states $\in$ [[BQP]]? (Så klart, det han sier nedenfor er at de klassiske beskrivelsene er *veldig* kompakte, så kanskje nært lineære—om ikke logaritmiske—i systemstørrelse.) ### Inspirasjon Inspirert av [[Kvantekjemi]]-tutorial ved [[QIP'24]] (se del 2, 1:08:00). ![[image.jpg]] ![[image 2.jpg]] Se også ranten hans om [[Variational quantum eigensolver]].