Sun. Feb 5th, 2023
Quantum computers reach deeper, find the ground state of simple hydrides

Whenever we talk about quantum computers, the headline is often that someone somewhere is going to use the quantum to break your encryption and steal your student loan. If only that were true. But it’s probably more realistic to think about quantum computers being used to solve quantum problems. And this has been shown with recent chemical calculations using a small quantum computer.

If solving quantum problems with quantum computers sounds a bit circular, well, it is, but it’s also practical. Think of it this way: every protein in your body has the structure it has thanks to quantum mechanics. And a physicist who is smart, but not intelligent, can write down an exact equation that describes that protein. But even the most intelligent cannot solve that equation.

Understanding molecules is difficult

A lazy physicist would write a computer script to solve the equation. But that doesn’t work either, because the time it takes to solve an exact description of the molecule will take longer than it takes to go from big bang to heat death. So we live with approximations. Approaches that are usually quite good, but sometimes fail spectacularly. And for some molecules, those approximations don’t speed up the calculations at all.

Quantum computers should solve this problem. The idea is that if each qubit represents an available state for an electron, you can build a model of a molecule and bounce the qubits on each other until they find the lowest energy state. That would then correspond to the molecule in its most relaxed and happy state.

But that’s quite a challenge. Every qubit is a swing, and the swings are all swinging. If everything is perfect, the swings will all stay with each other in time and the calculation will succeed. However, the noise from the environment causes the swings to stop and start randomly, changing their timing. This is called coherence, and quantum computers usually don’t do well without coherence. Calculations without coherence often produce nonsense.

So until the day we have perfect qubits, even quantum computers have to use approximations.

Let’s play a variation of that game

The optimization process is based on something called the variation principle. It is a very simple principle and very powerful. My molecule has a lowest energy state that corresponds to a certain configuration of electrons and distances between atoms (or rather a unique wave function). Now, if I’m smart (or, more likely, lucky) I can guess a configuration that’s pretty close. The energy for the configuration I think will be always greater than (or at best equal to) that of the ground state.

The researchers recommend a starting configuration. The quantum computer relaxes from its starting configuration to a near-lowest-energy configuration. The state and energy are read out and used to come up with a new estimate for the ground state configuration.

Repeat that a few times, and if you’re lucky you’ll get something close enough to the true ground state. In this case, “close enough” means you can use the results to accurately predict the properties of the molecule.

Using a six-qubit quantum computer, researchers were able to set up solvers to obtain the lowest energy state for molecular hydrogen, lithium hydride and beryllium hydride. This actually hides a lot of cool physics and math. The researchers have come up with a beautifully simple way to represent some rather complicated molecules. Its simplicity reduces computational power, and it’s really the only reason the researchers were able to solve a three-atom molecule on such a small quantum computer.

Beryllium hydride (BeH2) has three atoms and a more complicated electronic structure. That’s because beryllium has a full inner shell of electrons, and then the next shell has two orbitals that are very different in nature from each other (technically to model beryllium you need to have an ‘s’ and a ‘p’ orbital in the calculation). This extra complexity is also reflected in the calculations. The solution for molecular hydrogen – the simplest structure – corresponds almost perfectly to a numerical solution for the entire molecule. However, for lithium hydride and beryllium hydride, the solutions are less accurate.

The researchers think that the decreasing accuracy is not due to the simplifications, but because the qubits do not remain sufficiently coherent during the calculation.

However, this is not just a guess on the researchers’ part. Their quantum computer is so small that it can be modeled with a normal computer. The numerical model was able to reproduce the results of the quantum computer, showing that the researchers understand how their quantum computer works.

And that leads to a little disappointment. Given that, the researchers could also have adjusted the parameters slightly, including extending the time in which the qubits remain coherent. That would have allowed them to say how much they need to improve their device to get an accurate ground state for beryllium hydride, for example.

But as the number of qubits increases, I expect larger molecules to be modeled and the accuracy will only get better.

Nature2017, DOI: 10.1038/nature23879 (About DOIs).

By akfire1

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