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As the title suggests, I'm searching for published examples of quantum algorithms being applied to problems in computational biology. Clearly the odds are high that practical examples don't exist (yet) – what I'm interested in is any proof of concepts. Some examples of computational biology problems in this context would be:

  • Protein Structure Prediction (Secondary, Tertiary)
  • Drug-Ligand Binding
  • Multiple Sequence Alignment
  • De-novo Assembly
  • Machine Learning Applications

I've found only one such reference that I think is illustrative of what I'm looking for. In this research, a D-Wave was used for transcription factor binding, however, it would be interesting to have examples outside the realm of adiabatic quantum computing.

There are several in terms of quantum simulation. While they clearly aren't simulations at a scale often considered to be biologically relevant, one could imagine that this line of research is a precursor to modeling larger molecules of biological significance (among many other things).

So, aside from transcription factor binding and quantum simulation, are there any other proof of concepts that exist and are relevant to biology?

Update I: I’ve accepted the best answer so far but I’ll be checking in to see if any more examples come up. Here's another I found, somewhat old (2010), that aimed at demonstrating identification of low energy protein conformations in lattice protein models – also a D-Wave publication.

Update II: A table in this paper covers some existing applications, most using quantum annealing hardware.

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  • $\begingroup$ Why did you classify "Machine Learning Applications" under "computational biology problems" ? $\endgroup$
    – JanVdA
    Commented Sep 6, 2018 at 15:56
  • $\begingroup$ I guess there is also an overlap between your question and my recent question : quantumcomputing.stackexchange.com/questions/4150/… E.g. I guess the ability to use a quantum computer to measure the drug-ligand binding could revolutionize the identification of new drugs. $\endgroup$
    – JanVdA
    Commented Sep 6, 2018 at 16:06
  • $\begingroup$ I used machine learning applications because they are ubiquitous in computational biology and bioinformatics. The other examples could be considered modeling biological processes using first principles, however, machine learning is generally an empirical rather than first principles based approach. I did not want to limit responses to first-principles based modeling because this is as much about the application of a novel model of computation as it is the modeling of the biological process itself. $\endgroup$
    – Greenstick
    Commented Sep 6, 2018 at 17:19
  • $\begingroup$ @JanVdA Thanks for the link to your question, it's definitely interesting. $\endgroup$
    – Greenstick
    Commented Sep 6, 2018 at 17:23

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I was not able to find references specifically in quantum biology. I found however a review called Quantum Assisted biomolecular modeling.

You may find it interesting but this is from 2010. The field has evolved since but I guess the ideas remain similar. The authors focus more on the idea of the ability of a quantum computer to try every classical paths simultaneously.

I do not know much about the field and common practice. However if computational biology is more focused on Optimization, then applying quantum search algorithms or hybrid classical-quantum setups should be suited (even if not that practical at the moment).

Now about Machine Learning, it is a bit unclear with quantum computing. Especially with the name Quantum Machine Learning. Different approaches/goals are taken. Some algorithms are designed for getting a speedup on classical algorithms (based on a hypothetical device called qRAM) like K-Means, SVM... Or use QC for helping the learning process in classical algorithms like restricted boltzmann machines. Some focus on doing ML with quantum data like compressing quantum data for instance.

Conclusion: we do not have a clear idea yet but this makes it exciting. In the process, we may just create new algorithms or improve current classical ones.

Edit: Recently a press release announced a partnership between Rigetti Computing and Entropica Labs to develop real world applications of quantum computing to bioinformatics and genomics.

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    $\begingroup$ This is a great reference. Yes, optimization is fairly common in certain areas, especially modeling of molecular structures and binding. I’ve heard about the ambiguities with QML; thanks for your clarification and conclusion. It’s helpful! $\endgroup$
    – Greenstick
    Commented Sep 6, 2018 at 21:00
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    $\begingroup$ Nice — I missed that but somehow still saw that they announced a 128 qubit hybrid system was on their roadmap for 2019. Thanks for sharing this! $\endgroup$
    – Greenstick
    Commented Sep 8, 2018 at 15:48
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    $\begingroup$ Is the first paper really answering the question (= examples of quantum algorithms being applied to problems in computational biology) ? When I read it very quickly the paper is mainly stating that quantum computing "may in the future" assist in biomolecules modeling which is still far from stating that there are already known quantum algorithms that we can execute today (or even maybe in the future when the quantum computers are powerful enough) to solve problems in biomolecules modelling. $\endgroup$
    – JanVdA
    Commented Sep 9, 2018 at 20:36
  • $\begingroup$ I am bit wondering what the relevance of the Rigetti link is with respect to the question. $\endgroup$
    – JanVdA
    Commented Sep 9, 2018 at 20:58
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    $\begingroup$ @JanVdA It seems to me that the assumption is that certain existing algorithms may be augmented with quantum computational steps (e.g. QFT, quantum walks), but yes, the authors don't spell out what exactly those algorithms are. One which may be relevant is quantum annealing, given it's relationship to simulated annealing, which is widely used in molecular dynamics simulation. $\endgroup$
    – Greenstick
    Commented Sep 10, 2018 at 18:37
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Quantum simulation can be used to test models that could describe certain biological process. For example, a 2018 paper by Potočnik et al. examined light harvesting models using superconducting quantum circuits (see figure below).

Currently, it's an open question whether quantum mechanics plays an important functional role in biological processes. Some candidate biological processes where quantum mechanics may have such a role include magnetoreception in birds, olfaction, and light harvesting.

Figure from the paper by Potočnik et al. 2018

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  • $\begingroup$ Thanks for your response. While interesting, unfortunately modeling how photosynthesis could be quantum isn’t quite in the scope of the question. I’m very much interested in the applications of quantum algorithms on a quantum device (a QC of some kind) for canonical problems in computational biology. Some examples could be modeling drug-target binding with the adiabatic quantum algorithm or some kind of machine learning for, say, calling gene variants using an HHL inspired algorithm. These of course would be toy examples — but it’s these existing proof of concepts I’m after. $\endgroup$
    – Greenstick
    Commented Sep 6, 2018 at 15:55
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    $\begingroup$ It is a bit unclear what is the link between your first paragraph and the actual question. Maybe it should be clarified a bit. $\endgroup$
    – JanVdA
    Commented Sep 6, 2018 at 16:00
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This happens to be the topic I did my master's thesis on and am still invested in as part of my doctoral research. Very few works existed prior to 2016. The one I found most relevant back then was https://journals.aps.org/pre/abstract/10.1103/PhysRevE.62.7532

My research was on both types of quantum accelerated genome sequence reconstruction: ab-initio (reference alignment) and de-novo (read assembly).

Here are the quantum primitives we developed:

While it is a fascinating and promising application, realistically (as you mentioned) it is still too early in the days of QC for an MVP in this domain. We mostly work with artificially constructed sequences which is closer to the field of Meta-biology. A quantum computing formulation for understanding algorithmic properties of DNA sequences is explored in this:

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An IBM group has been working on protein folding with gate-model quantum computers. Here is a paper: https://arxiv.org/abs/1908.02163

It is ostensibly a tertiary structure calculation, but confines residues to a tetrahedral lattice, so it's a bit of a simplification. Still, it's a compelling idea for how to approach large molecules even on the small quantum computers we have today.

I think the following website is connected to the same research group: https://protein-folding-demo.mybluemix.net/

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