Róbert Izsák

4 Oct 2023

Modelling molecules: How quantum computers simulate at the atomic level

At Riverlane, we have a core focus on building the quantum error correction stack that every useful quantum computer will need. This quantum error correction stack sits between the application and qubit layers, correcting the errors that quantum computers are prone to.

Simply put, without quantum error correction we cannot do anything useful with quantum computers.

The Discover team, where I work, is unique at Riverlane as we’re not working directly on the quantum error correction stack. We’re focused on writing the quantum algorithms that will support the applications to unlock the promise of quantum computing.

Quantum computing and materials science is a key research area for our group because quantum computers are suited to “think” at the molecular level. We have had several exciting breakthroughs and it is widely expected that materials science will be one of the early applications of quantum computing.

In this post, I will explain why we need quantum computers to simulate molecules and materials.

The prediction of chemical properties from quantum mechanics is a very complicated task. Molecules and materials consist of atoms, each of which in turn consists of nuclei and electrons.

The interactions of these particles – and predominantly the interactions between electrons – determine the properties of chemicals. Unfortunately, the large number of electrons in industrially relevant materials makes their precise quantum mechanical characterisation nearly impossible since each pair of electrons needs to be accounted for.

Typically, such a characterisation involves solving equations that describe electrons moving around fixed nuclei. As a result, the total energy and other useful molecular properties are obtained directly from subatomic contributions, which requires a quantum mechanical treatment.

Classical computers are not well suited to this problem because they cannot perfectly solve these equations in molecules with any more than a few electrons. Classical computations are simply too large and time-consuming as we try to model larger molecules and, instead, approximations are used to try and determine these chemical properties. But these approximations are often not accurate enough and limit the ability of chemists to use them as an aid in their everyday laboratory work.

To simplify the task, we usually assume an “averaged relationship” between electrons during a classical computation in which each electron swims in the “cloud” of all the others. It doesn’t matter where exactly the other electrons are in this cloud only that they can be found there with some likelihood. We often refer to this approximate solution by saying that each electron is associated with a spin-orbital. This is a good start, allowing classical computers to calculate such states for many chemical properties, even for large molecules.

The problem starts with the fact that the results obtained in this manner are not good enough for practical purposes. This is because in such an approach the electrons don’t see each other well or, in other words, they are not correlated.

The challenge is then to calculate these correlation effects that we need to make our chemical predictions accurate. On classical computers, the solution is to use many of the average interaction states, but this makes the calculation very expensive due to their large number.

The big advantage of quantum computers is that there is no need to represent molecules and materials in terms of such average interaction states, we can simply use other quantum systems (qubits) to represent them.

A qubit can map onto an electron’s spin orbitals and the quantum computer can use quantum phenomena such as entanglement to describe electron-electron interactions without any approximations.

Unfortunately, the problem about the large number of electrons still remains. This has motivated researchers to use various models for which quantum computers could produce a breakthrough earlier than for the full-scale chemistry problem discussed so far.

For our purposes, a model is a simplified version of a chemical that is simple enough to use in calculations but also retains enough complexity to capture the most interesting properties of materials.

It turns out that electrons like to pair up when they have the chance and if such paired electrons remain close to the same site in a molecule they can be neglected in models. Thus, important families of models focus on the interactions between single electrons at different sites in materials and they are especially relevant in studying magnetic materials and high-temperature superconductors.

From the perspective of quantum computers, such models require fewer physical qubits than full-scale chemical calculations, and thus, the industrial areas where they can be most beneficially employed are expected to be among the first to benefit from quantum computing.

As you can see, unlocking useful applications in quantum computing is a complex undertaking. From the qubits to the quantum error correction and applications layers, we need improvements across the quantum computing stack.

But quantum computers are the only machines capable of simulating molecules and materials with the accuracy required to do everything from development of new drugs to discover novel fuels and other materials.

If you’d like to find out more about the work we do and would like to help advance this exciting field, click here.