OK, today’s blog post is going to be even weirder than usual – we’re going to wander off into quantum mechanics. And into a particular borderland of it where have been a lot of interesting hypotheses and speculations, but plenty of hand-waving hoo-hah, so it’s important to realize the risks up front. But here we go.
The talk about quantum computing has been impossible to miss over the years, and it’s not even near reaching a crescendo. Suffice it to say that directly taking advantage of quantum-mechanical phenomena can lead (potentially) to extraordinary accelerations in particular computing tasks. As I understand it, the situation will be a revved-up version of (for example) the situation you see when using Graphics Processing Units for other purposes than the high-end video and gaming that they were intended for. For GPUs, you have to identify the algorithms and approaches that best take advantage of their particular architecture, and the real-world problems that are best suited to being solved by them (as opposed to getting the glint of sunset light off a swinging ice ax to look right in the Yeti side-quest, which is what GPUs excel at in their natural state). Some calculations are just going to be intrinsically better suited from the beginning (more parallel and more easily broken down into smaller independent units), while other problems can be reworked to take advantage by emphasizing a different stage of the process or by coming at the problem from a different direction entirely.
And so it is (and will be) with quantum computing. If you’re going to go to the trouble and expense of building a quantum computer (and both of those are really formidable), you’ll want to get the most benefit out of it that you can. As it stands, there’s a (not extremely long) list of algorithms that have been mathematically proven to be faster via quantum techniques than they can be by classical ones, so everyone will be finding way to route their problems through those magic portals. The first example of such was Shor’s algorithm for factoring numbers, which is why if you manage to build a robust, capable quantum computer you can be sure that some intelligence agency will buy it from you. The widely-used RSA cryptography method depends on the multiplication of two huge prime numbers being immensely easier than factoring the resulting product back down from scratch, and Shor’s algorithm is almost exponentially faster than any known non-quantum method. At the moment the record (or at least the publicly known record) for the largest number that has been factored by Shor’s algorithm is (wait for it) 21 – told you the implementation was pretty steep. But things are moving right along. As an aside, it’s often been remarked that number theory was long considered the purest branch of mathematics, i.e. the one with the least possible reduction to any practical use, and the fact that the global economy now depends on things like the behavior of prime numbers would have horrified a pure-and-proud-of-it mathematician like G. H. Hardy beyond description.
The second quantum-advantage example was Grover’s algorithm for database searching (more properly, for inverting a function). If you have to root through a database of N entires, a linear search down column A in unstructured data, how many computational steps does it take? Well, it’s hard to get around the problem that it might take you up to N steps at the very least, because the answer you’re looking for might be in the last entry that you check. But Grover showed that quantum computation could shorten that to working in square-root-of-N time, and being quadratically faster is nothing to sneeze at, either, especially for really large problems. Grover’s algorithm is of great interest to the national security community as well, because it could brute-force its way through cryptographic hash functions, which also depend on algorithmic asymmetry: easy to run in one direction, viciously hard to reverse if you don’t know the trick.
Now what, you are asking yourself, does all this have to do with chemistry or biology? That’s where we get to this new paper from the CNRS in Marseille, written up here in Technology Review. It describes the behavior of electrons moving across two different sorts of surfaces – a quantum walk across a square grid and a triangular one (both of which are found, of course, in various crystalline materials). This paper seems to demonstrate that a quantum walk which recovers the Dirac equation also implements a Grover algorithm search – in this case, localizing around an electron hole in the grid with exactly the statistics that you’d expect from a Grover search process (when search may then, in fact, be natural electron behavior under such conditions). It’s already been shown that “quantum walks” can implement the Grover-style search, but under rather artificial conditions, because it typically requires an “oracle” step where you compare results to an expected value. But searching for an electron hole in this way effectively builds the oracle into the search itself, removing a substantial practical difficulty.
Now what, you are asking yourself, does all this have to do with chemistry, or biology? Well, a quick-and-easy answer is that it might lead to real quantum computing via a different route than we’ve been trying to date. If you can make electrons implement the Grover algorithm under the right circumstances, maybe you don’t have to build a general quantum computer to realize it yourself from the ground up. Just take advantage of what the electrons (or any other quantum particle) will be glad to do for you! The advent of large-scale quantum computing would have a bit of an effect on computational chemistry and structural biology, and it may have just gotten closer.
But there’s something else to think about, as mentioned in the Technology Review article linked to above. It directs the reader to this 2000 paper from Apoorva Patel. He showed that a quantum-computing system that implements the Grover algorithm is capable of distinguishing between four choices in a single computational step – in fact, four is the optimum number, giving the greatest computational efficiency. Similarly, he also showed that a three-step quantum search under these conditions can distinguish between 20 choices as the most efficient number.
Now what, you are asking yourself, does all this have to do with chemistry or biology? Well. . .if Grover-algorithmic processing is some sort of fundamental property of nature, then you might expect the genetic material to be synthesized most efficiently when the machinery has a choice of four different nucleotides. And when translating these into proteins, a triplet code (which requires three processing steps) would function most efficiently when working with a palette of 20 amino acids. I will admit to being unusually susceptible to ideas like this, but that makes the hair stand up on the back of my neck.
It has not escaped the attention of the authors of this new paper, to borrow a phrase. Recall that part about using the hole defect as a built-in “oracle” step in the search – the authors note: “Indeed, replacing the Grover oracle step by surface defects seems way more practical in terms of experimental realizations, whatever the substrate, possibly even in a biological setting“, and reference a later Patel paper at that link. Patel himself has speculated on just these possibilities with nucleotides and amino acids, but all this of course requires that the Grover algorithm be recapitulated by natural phenomena, and that such a quantum-mechanical process is actually somehow at the root of molecular biology. It looks like the first of those is being shown right now. Which makes the second, however weird and unlikely it may seem, worth taking more seriously. Now this is what I expected from the twenty-first century, not the rest of the garbage that we find ourselves surrounded with (current events, etc.) A research area for the brave!