# Is VQE or one of its variations enough to help with medicine development?

One of the reasons quantum computing is often hyped in media is because of how it'll help with vaccine and medicine development. For example, this article in Financial Express and this other in Venture Beat.

However, these articles just say things like

Quantum computing can speed up vaccine development by solving complex equations with higher accuracy than classical computing.

and

The continued development of quantum computers, if successful, will allow for end-to-end in-silico drug discovery and the discovery of procedures to fabricate the drug.

The second article I linked also talks about how a quantum computer only takes about 286 qubits to simulate penicillin while classical computers would take over $$10^{86}$$ bits. It doesn't talk about the algorithm used to perform this simulation, but I guess it is VQE or some variation of it.

My question is: is VQE or one of its variations enough to actually help with vaccine/medicine development? If not, is there any algorithm that has been or is being developed with the purpose of helping vaccine/medicine development?

I found some references in this answer. But I would like to know more about the details of the specific algorithms they're developing, e.g. what properties of the molecules they try to simulate they are exploiting, what has resulted from these algorithms that may be useful outside of this niche purpose, and anything like this.

• I find the answer to "Is VQE or one of its variations enough..." is depending on who you talk to :) Jun 21 at 15:25
• @KAJ226 that’s true, but what would be your take on it? Jun 21 at 15:31
• the optimistic side of me want to say that it could potentially help with certain problems, like solving certain electronic problems. But if you sit down and calculate the quantum resource needed (time, qubits, the type of hardware you need) to do the problems that can't be done with classical computer right now, it is quite daunting. Giving the fact that VQE is heuristic, you might not getting global min energy consistently... Especially when the cost function landscape is difficult, you will end up stuck in local min in most of your VQE run. Jun 23 at 16:29
• There was a paper posted by the Schrodinger group late last year: "How will quantum computers provide an industrially relevant computation advantage in quantum chemistry?" arxiv.org/pdf/2009.12472.pdf You can look at some of the studies there. Also giving the flaw nature of VQE, using QPE is a better approach... but you do need QEC. There have been studies on resource estimate needed to solve the electronic structure problem for some complicated method using QPE with QEC. Jun 23 at 16:31
• @KAJ226 thanks for all the linked papers, I'll look into them and probably come back with some questions. I also read about an improvement to VQE called ADAPT-VQE (from this paper) that is supposed to work better with certain optimization methods. So I guess that would also contribute to this. Jun 23 at 17:17

Two big problems we're interested in for drug discovery where quantum computers may do well are high accuracy prediction of receptor-ligand binding affinities and electronic structure prediction. High accuracy quantum approaches addressing these problems that yield a quantum advantage can be expected to find a home in drug discovery pipelines. In terms of the computational problem being addressed, both of these are reducible to Hamiltonian simulation. Here's a paper (paywalled) that explains some particular drug discovery use cases.

Not necessarily variational approaches

There are quantum algorithms for Hamiltonian simulation, with one of the most interesting ones being quantum signal processing (QSP). This algorithm (and the practical implementations that may stem from it) may yield an advantage on NISQ devices in the next decade for chemical simulation problems (Note: that last that paper contains numerical estimates for a handful of quantum simulation algorithms applied to the time evolution of spin systems). But that does not necessarily mean they'll offer an advantage that's usable in drug discovery pipelines within the same time frame (though they could quickly follow).

Variational approaches

While VQE approaches may well help with these types of problems, there are quite a few challenges implementing them (for example, see this recent paper). That said, it is early days and, in general, variational approaches continue to improve rapidly. Variational quantum machine learning comprises a set of approaches similar to VQEs that are being explored. For example, here's one very recent approach using a quantum generative model (a GAN) with the aim of generating candidate ligands with (predicted) high binding affinities to a target receptor domain.

Update

I just wanted to add, seeing as the OP referenced the statement (common in popular articles) that a classical computer requiring $$>10^{86}$$ bits to simulate penicillin would only require $$286$$ qubits, that I previously asked a question about where these estimates were coming from. A starter hint: $$2^{286} \approx 10^{86}$$ (see answers to linked question for more details). The upshot is that these are just about the crudest estimates one might make.

• Thanks for the detailed answer! I’ll look over the algorithms you shared. Do you have any more references about Variational QML? Not specifically for drug development, but in general. I found this about deep VQE, is it related? Jun 21 at 22:12
• Sure do! In lieu of a string of links, here are some keywords that should surface some good literature on arXiv and Google Scholar: variational quantum classifier, quantum kernel estimation, quantum kernel methods, quantum neural network. The papers should by and large center on approaches where you have some optimizer (e.g. parameter-shift rule, quantum natural gradient, stochastic gradient descent) that learns parameters over a quantum circuit that processes data (typically a sensible ansatz that may have a layered structure). Jun 22 at 20:06
• Also, I highly recommend the QML lectures by Peter Wittek on YouTube. While they largely don’t focus on variational QML, they’re a great way to get oriented. Jun 22 at 20:11