Quantum chemistry

The Green Revolution of the twentieth century increased the production of food worldwide. Hunger, in most countries, is now more a matter of economic inequality, poverty and weak governance rather than global inability to produce enough food. One of the key factors in this success has been the widespread adoption of synthetic fertilizers, which are created by pulling nitrogen out of the air and “fixing” it into a form more easily useable by plants. This process, known as the Haber-Bosch process, uses 1-2% of all of the energy humanity generates! Finding lower-energy alternatives to this process would be an enormous benefit to all of mankind.

Chemists study, among other things, the shape of molecules and the energy of each configuration. With this information, they can predict what shape molecules will take under different conditions and how they form larger structures, which helps them to understand how chemical reactions occur, and how much energy is either released or absorbed in a particular reaction.

Improvements in our ability to calculate these behaviors have the potential to improve our ability to make those agricultural fertilizers, and quantum computers may be able to contribute. They will also help us understand photosynthesis, and create new materials with desirable properties such as strength or flexibility.

Many of those calculations from the subfield known as quantum chemistry present an opportunity for quantum computers. As we will see when we begin discussing key concepts in quantum mechanics in order to understand quantum computers, the accurate description of quantum systems such as a molecule grow exponentially in the number of electrons and atoms involved. This makes the necessary calculations tedious for a classical computer.

Fortunately, we have a solution to this exponential growth in possible states we have to analyze: using a quantum computer. In many cases, what we want to learn is some aggregate fact about the possible states (such as the average energy, or how the molecule behaves when a group of possible vibrations are all happening at the same time) or to find some specific state among the set (such as the lowest energy).

The exact difficulty of problems in this domain depends on the precision to which we want to calculate the answer. Problems like factoring, which we just discussed, have a single, specific answer. But many computations aim to make predictions about the real world, which is messy and never corresponds fully to the idealized model we put into a computer. We have to pick a point at which to stop the computation, when it has enough digits in the answer.

That question aside, quantum chemistry ideally meets our criteria for a problem that is well suited to a quantum computer: the amount of memory required and the amount of data we have to read and write is small, and the space of possible answers we must explore grows exponentially as the size of the molecule grows.

In fact, quantum chemistry was the first application that Caltech professor and Nobel laureate Richard Feynman envisioned when he proposed something like a quantum computer in the early 1980s. It is now considered to be one of the most attractive applications for quantum computers, both because it seems relatively tractable, and because of its obvious benefits to humanity.