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I recently read this report from BCG, which stated:

For scientists trying to design a compound that will attach itself to, and modify, a target disease pathway, the critical first step is to determine the electronic structure of the molecule. But modeling the structure of a molecule of an everyday drug such as penicillin, which has 41 atoms at ground state, requires a classical computer with some $10^{86}$ bits—more transistors than there are atoms in the observable universe. Such a machine is a physical impossibility. But for quantum computers, this type of simulation is well within the realm of possibility, requiring a processor with 286 quantum bits, or qubits.

Along with this resource estimate for penicillin, I've also seen similar mentions of the number of qubits required to model the ground state of caffeine (160 qubits). Given that the above report offers no reference(s) (probably in the name of business intelligence) and much Internet searching and looking into the quantum chemistry literature has come up short, my question is: Where are these resource estimates coming from – is there a journal article that published these numbers? I would really like to identify the methodology and assumptions used in making these estimates.

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    $\begingroup$ $\log_210^{86}=285.6$, so I guess the question is where did the statement that penicillin "requires a classical computer with some $10^{86}$ bits" come from. $\endgroup$ – Mark S Aug 11 at 3:03
  • $\begingroup$ @MarkS I was really hoping it would be more nuanced than that, but I fear you’re right. I’ll pull this thread and see if I can find more details. $\endgroup$ – Greenstick Aug 11 at 3:19
  • $\begingroup$ No need to pull the question! It’s a good one. $\endgroup$ – Mark S Aug 11 at 12:18
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They are just estimates. But they are not arbitrary estimates, but are based on a reference algorithm.

For example, a simple algorithm for a particle: Grover's algorithm is constructed with two qbits and can be used to find the correct answer to four quantum states of a particle, in a single step.

Eventually, a scientific publication would be more accurate in saying: "We have simulated a caffeine molecule using 90 qbits, thanks to the Yerkobits topological algorithm."

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  • $\begingroup$ Right, but estimates should have a basis nonetheless. For example, are they imagining a simulation with a VQE? What type of hardware is being assumed? I would guess they’re referencing an implementation on a NISQ device, but whether they mean EC/logical qubits is nonetheless not clear. Further, while we may be able to put much of the articles that pop up when you search the Internet down marketing hype, the BCG report is different in that it’s intended to guide corporate decision making and the authors specifically note that they reviewed around 130 journal articles for their synthesis. $\endgroup$ – Greenstick Aug 11 at 2:49
  • $\begingroup$ There is no standard. Reviewing many publications is an old scientific technique: objectivity is a shared subjectivity; that is, 'axiom', and the axioms are simply "a tacit agreement". I like to use the pre-standard: "configuration (hardware) A versus configuration B; what is the ratio between the two of the time spent looking for the prime factors for the same number X (where X is a number greater than 10^100000 ...) " $\endgroup$ – Yerko Bits Aug 12 at 3:17

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