Quantum computing, the next big thing?

When we hear the term quantum computing most of us think of some sort of exotic machine somewhere in a laboratory that is cooled with liquid unobtanium and tended by a team of Ernst and dedicated white-coat-wearing care takers. As a description of the quantum computer itself, I’m really not that far off the mark. As it currently stands, there have been fewer than six quantum computers sold. So, I guess we could say that quantum computing is where classical computing was in roughly 1950 in terms of adoption and usage. People know it exists, they’ve heard about it, but they really aren’t sure how to apply it to their everyday tasks.

If we look at the academic literature around quantum computing and quantum information (a different, but related field), we see that the literature is casting about in the theoretical and algorithmic space, and if we distill it down to a bare essence, we find that quantum algorithms accelerate linear algebra operations in terms of time from exponential to polynomial. This is huge deal as it makes working with very large data sets now tractable. And this seems to be where, initially quantum computing will really demonstrate its utility. Others, will be quick to jump up and down about cryptography and some will get excited about Grover’s algorithm for search acceleration, but, in my opinion, it is data science and artificial intelligence where quantum computing will really shine.
Does this mean that we’ll be seeing quantum desktops as the new thing for all data-scientists. No. In my opinion, the quantum computer’s home will be with cloud providers for the foreseeable future. Now, the astute among you should be saying, “Now wait a minute, what about GPUs? They are hardware optimized for vector calculations and that encompasses linear algebra.” My answer to that is, yes, but an exponential algorithm accelerated is still an exponential algorithm, quantum allows you to convert these algorithms to polynomial time, your acceleration is not in terms of clock speed but in terms of algorithmic implementation.
So, the question is not so much, “What do we use quantum computing for?”, but rather, “How do we use it?” Subtle, but different, no? One area of particular interest to data scientists should be a paper entitled, “Geometrical and Topological Approaches to Big Data (Snasel, et al., 2017). In this paper, Snasel and colleages demonstrate topological approaches to examining data sets and using these computational approaches to demonstrate new methods for extracting sub-set of data for training automated classifiers, input into machine learning and deep learning methods. Bridging back to quantum computing is Loyd et al., 2016, which takes Betti number calculation into the quantum realm.
In short, a Betti number or numbers are a set of numbers that describe a topological space, see https://en.wikipedia.org/wiki/Betti_number, for a really good explanation. The Betti number(s) can be used to describe and compare the connectedness and overall “shape” of data. The concept of shape when talking about data may not be initially intuitive, but if we think of the data’s distribution along a set of axes, we can begin to think of that as a two-dimensional shape of the data.
“OK professor, get out of the theoretical weeds, what does this have to do with the price of tea in China or selecting data for me to train my classifier upon?”
Glad you asked, buckle up and put your trays in an upright position, this might get bumpy. As you know, when you train a classifier you are training it to recognize things that are like “self” — the training set. Where “like” is defined as some sort of function or discriminator that must be satisfied for inclusion into the set. This function is created from the training set and ideally should be representative of the distribution of all things true for that set. So far so good. Let’s use a biological example, the genus Canis, to those of you who are not biologists, the genus Canis encompasses Wolves (Canis lupus), Dogs (Canis familiaris), Coyotes (Canis latrans), and Jackals (Canis aureus). Now if you have a suitably large set of genus Canis, how are you going to adequately select a sub-set to train a classifier for Wolves, specifically grey wolves? Well, you’d have to identify those individuals that belong to the grey wolf clade and select a training set. To do this in an automated fashion, you’d need to look at topology of the set Canis and select from the area defined as Canis lupus. Seems like a trivial example, but, we know that members of the same genus can interbreed, what do you do with Canis lupus x Canis familiaris, the Wolf-Dog hybrid, https://en.wikipedia.org/wiki/Wolfdog? Do you classify based upon appearance, genetics, behavior, at this point, you are outside of the dimensions of the Linnean classification scheme, this is where you need data topology formed from descriptive metadata. In short, the topology allows classifiers to be created from sets of data that share similar structures in terms of their metadata connectivity. If the set of data is large enough, a separate structure would be seen for the Wolf-Dog hybrid and according to your criteria can be included or excluded from the Wolf classifier as the constructor sees fit. In short, what topology is doing is allowing the construction of the training set to be discrete when across other variables it is continuous. So, as you can see, there are problems that will benefit greatly from topology calculations when moved to a quantum system. Ok, we’re far into the weeds at this point and the pollen is starting to make my nose run and I just got bit by a mosquito, so let’s get back on to more solid ground.
I think we’re going to see quantum computing as an adjunct to classical computes, taking a role similar to that of the GPU. It’s going to be a device for accelerating very large computes rather than for accelerating individual computes as it’s speed comes from being able to accelerate algorithms rather than the clock. Also, due to the size, expense and nature of the machines, they will almost exclusively be the domain of the cloud or the rent to compute areas. The quantum computer will have to be fronted by a large classical computer for data preparation and translating the data into states that can be represented by quantum states. At the moment Python has some libraries, such as PyQu for implementing quantum algorithms on classical hardware. The big issue I think we have to deal with is trying to determine what the useful problems will be in the future that will take advantage of the accelerative nature of quantum computing. What are the problems that need to be solved that have huge amounts of data that need to be computed upon in totality, cryptography, sure, machine learning certainly, database search, perhaps, but are there than many useful databases that are too big to compute upon as we currently stand? I think we’ll see the use cases start to shake out in the next couple of years.
One use case is the ability to calculate eigenvectors and eigenvalues of a Laplacian. This is used in Latent Semantic Analysis (LSA), one of the primary tools for natural language processing (NLP). Here is where quantum computing may begin to enable things we currently cannot do particularly well on large scale, specifically knowledge extraction from unstructured text. The LSA technique can infer meaning from words by means of a semantic averaging (http://lsa.colorado.edu/papers/dp1.LSAintro.pdf). Once we are able to do this, all printed material in a particular area or discipline can be used as an input and hidden relations can be computed and inferred (A -> B as B-> C; therefore A->C). Currently, to do this at any sort of useful scale is practically intractable. Once we have this all printed media, or media that can be reduced to print is fair game for analysis. How many genetic and metabolic pathways for diseases have been discovered in one context but not applied in another? The answer to that is thousands. How many diseases have cures that have been discovered but forgotten in the literature, uncountable.
Quantum computing the next big thing? Yes, but the revolution will be much different than what we saw with the move from doing things by hand to automating them with a computer. I think we’re looking at a revolution in how we use knowledge not how we automate repetive tasks.