Basically alt som omhandler molekyler for store til at Schrödingerlikningen lar seg løse numerisk, men små nok til at kvanteeffekter likevel er avgjørende for dynamikken. Antas å være en av de tidligeste anvendelsene av [[Kvantedatamaskiner]], kanskje allerede nå i [[NISQ]]-eraen (dog det virker mindre og mindre sannsynlig at [[NISQ]]-maskiner vil lykkes i å simulere noe som ikke også lar seg simulere klassisk). #### Anvendelser - [[Quantum Drug Design]] - [[Nitrogenase]] - [[Romtemperatur-superledere]] - [[Battericellesimulering]] #### Algoritmer/teknikker - Høsten 2023 kom et paper av [[John Preskill]], Robert Huang, etc., som ga en kvantealgoritme for noe vi forventer er klassisk vanskelig generelt, nemlig [[Finding local minima in quantum systems]]—men dette vil kreve fullskala [[Kvantedatamaskiner]] med [[Kvantefeilkorrigering]]. (Problemet er [[BQP]]-komplett.) - [[Variational quantum eigensolver]] - [[Phase estimation]] - [[Fermion encoding]] Basically studerer hele feltet bare [The Born-Oppenheimer Hamiltonian](https://en.wikipedia.org/wiki/Born–Oppenheimer_approximation). #### Take-home messages fra [kvantekjemitutorial](https://youtu.be/Eo_iiDJmp4w?si=uNY9IZOZgOeJfKcP) ved [[QIP'24]]: > Quantum effects in chemistry are often subtle, and it's important to know that you can get by without quantum mechanics in a lot of chemistry. It's not the most quantum discipline. It's not in fact, in my view, the first place you'd think about looking for quantum effects, because so much of chemistry is understood from classical intuition. > > Nonetheless, there are many open chemical problems which challenge classical heuristics. Most involve constant prefactors or polynomial scaling but the polynomial is too high. > > And the final point I want to say, is that when we say that chemicals problems are unsolved, or material problems are unsolved, it's not like saying we don't know the prime factors of a number, where you essentially know nothing about the solution. But in these problems of chemistry and of physics problems, when they are unsolved, we still usually know a lot about the phenomenon, whether it's from experiment or from earlier theoretical work. So the role of improving simulation, whether it's via improved classical or quantum algorithms, has to fit within the *remaining uncertainty*, rather than providing the entire answer. A good and clarifying audience question: > Q: (Could it be that) one of the reasons why methods today are polynomial in essense is because this is what classical computers are able to work with, and if we had one day in the future a truly powerful quantum computer, the set of problems we would even consider would be much wider? So are there problems that no one is tackling today just because they are fundamentally impossible, but we could imagine would one day to be relevant with a quantum computer? > > A: I don't think that's the case, right, because experimental probes, they don't care about the power of classical computation—you just study whatever phenomenon is *there*, and then you probe it. This is just an opinion, but this is kind of a good time to give it: The reason why chemistry as defined as a discipline is not that quantum mechanical, is because the conditions under which we do chemistry are extremely decohering, and so things are always very close to the classical description. We don't do chemical reactions with perfect quantum state control of the molecules, there just is some giant ensemble, and we don't even specify exactly what the environment is doing. So, if we had perfect quantum control of large ensembles, $10^{23}$ molecules, like the scale of chemistry is, you could imagine engineering quantum dynamical processes which would be very hard to describe. But that is very far outside of what we understand chemistry as a discipline to be today. Spørsmålet oppsummert senere: > Does anything look easy because we refuse to study hard problems? Og svaret er på en måte *obviously* nei, fordi naturen har fasiten, og den *er* en kvantedatamaskin (ihht [[Extended Church-Turing-Deutsch thesis]]): > One is not *actively* avoiding things in the field. (Slik jeg kjenner forskere ville det vel heller vært omvendt—jo vanskeligere problem, jo flere som flokker til det!) > (Chemistry) is done in a very dissipating environment, which I think promotes classical behaviour. De har en artikkel: [Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry](https://www.nature.com/articles/s41467-023-37587-6). Kort oppsummert: Gitt et godt startpunkt ("reference"), så ser det ut til (fra begrensede empiriske undersøkelser) at over alle de vanlige heuristiske metodene for kvantekjemi, så synker feilraten ("refinement") polynomt med økende beregningskraft. Hvis å finne et godt startpunkt er polynomt (og dette er ofte enkelt, da man i kjemi ofte jobber med tilstander som er nært å være produkttilstander (altså separable (altså med lav-til-ingen [[Sammenfiltring]]))), ville dette implisert at problemet å simulere systemet (eller en valgvariant derav) er i [[BPP]]. På den annen side så *er* det noen problemer hvor å finne dette gode startpunktet involverer søk over eksponentielt store spaces (slik at problemet blir "[[NP]]-aktig", hvor *verifiseringen* stammer fra eksperimenter heller enn klassiske beregninger I guess). ![[image 3.jpg]]