Limitation of a Classical Computer - The Second Problem in Chemistry

The second problem is that of chemistry. What follows below is the picture of a nitrogenase enzyme. 

It is an important catalyst for creation of ammonia, which is of paramount importance and forms an integral part of food, fertilizer, pharmaceuticals and many more. The image above represents the iron sulphide cluster (FexSy) with three molecules of different sizes. The one on the left is a cluster of 4 iron atoms and 4 sulphur atoms. This is one of the biggest molecules we can simulate using some of the largest compute intensive supercomputers in the world. It is extremely small and one of the biggest molecule we can simulate on a classical machine. In order to simulate what is going on in the molecule, one must account for every electron – electron attraction and every electron-electron repulsion to the nuclei. Every single electron exerts an electrostatic force on every other electron upon adding another electron, one needs to recalculate all the electron energies. That number grows exponentially as the molecule grows bigger and bigger. The other two bigger clusters look so small; however, we cannot simulate them. There are many problems with similar characteristics and the commonality is the idea of exponential scaling.

There is this classic fable about the power of an exponential. The story goes that the creator of the game of chess bought the chess board to the emperor, the emperor loved the game and asked the creator of the game what he can give him as a reward. The craftsman/creator said there are 64 squares on the chess board. On day one, give me one grain of rice and each day thereafter, double the grain of rice. After a week he had a teaspoon full of rice but after a month he had the rice production of a small country. After 64 days he had mount Everest of rice. It grows fast. The number 64 does not sound that big but two to the power of 64 is an enormous number.

In the next article will understand what is being done to overcome the problem of exponential scaling.