## Particle physics and quantum computing meet in an important new effort by young researchers at the Department of Applied Mathematics and Theoretical Physics.

Bipasha Chakraborty and Masazumi Honda are particle physicists: they study the fundamental particles of nature and how they interact to form our Universe and everything within it. Out of the four fundamental forces the one relevant here is the *strong nuclear force*: it binds together the smallest building blocks of matter, *quarks*, to form other particles, including the protons and neutrons within the nuclei of the atoms that we know and love.

"The methods have implications and applications beyond our specific problem — so now we would like to collaborate with people from other disciplines to learn about them all." Bipasha Chakraborty

But the strong force is a stubborn beast. Physicists have a mathematical framework to describe it, called *quantum chromodynamics* (QCD), which should enable them to calculate quantities such as the masses of particles that are formed by quarks. Only it doesn't. Some of the calculations are so hard, they defy even the fastest supercomputer. This is why it makes sense to look towards the revolution that's about to rock computer science: quantum computing. Chakraborty and Honda, two early career researchers at DAMTP, have done just that. Their prototype algorithm is inspired by QCD and can perform tricky calculations on a quantum device.

### What are we looking for?

Like all particle physicists, Chakraborty and Honda's ultimate goal is to understand all there is to know about the particles that make up our Universe. That's a tall order neither they nor anyone else is likely to achieve within our lifetimes, which is why the pair focus on slightly smaller aims that will serve as stepping stones along the way.

One is to calculate the masses of particles, called *hadrons*, made up of quarks. This involves much more than just adding up the masses of constituent quarks because much of a hadron's mass comes from the energetic processes that happen inside it — and these are complex. Messenger particles called *gluons* flit about mediating the strong force that hold the quarks together, and *virtual particles* continually pop in out of existence. Even the simplest hadron is really a seething mess of goings-on which all contribute to its mass. Being able to calculate this mass therefore constitutes a real triumph and is one of the main challenges of particle physics

Another aim is to predict what we expect to see in particle accelerators like the Large Hadron Collider at CERN: when hadrons are smashed together and break apart, what new particles emerge and in what percentages? Such predictions present the vital link between theory and experiment.

In an effort to make the calculations involved easier, physicists have developed something called *lattice QCD*, which is slightly more amenable than true QCD. "Instead of [working with] a four-dimensional continuous spacetime, [we] imagine that we have a grid of points and put the theory on that grid," explains Chakraborty. This is akin to weather forecasting, which also only foucusses on a grid of points placed across the Earth and on discrete time steps, as dealing with all of space and time would be too complex. But even within lattice QCD, calculations are still incredibly hard.

### Can quantum computing help in theory?

Quantum computing exploits some of the strange phenomena of quantum physics, the physics of the very small, which we don't observe in everyday life. The hope is that these phenomena will open the door to a whole new world of computing capabilities.

The field is still in its infancy, however. Since quantum phenomena are something we don't see in daily life, it's not surprising that they're also extremely hard to create in everyday settings, which is why no one has yet succeeded in building a universally useful quantum computer. And although Google famously claimed *quantum supremacy* last year, meaning that their quantum computer had solved a problem significantly faster than a classical computer could have done, the claim related to a particular problem specifically designed to fit the purpose. So for particle physicists the question remains of whether quantum computing has anything useful to offer them.

This is where Chakraborty and Honda's quantum computation provides an important proof of concept. "[Our work] shows that this sort of quantum computing is going to be very useful in the future, compared to the classical standard computations".

Chakraborty and Honda's algorithm doesn't tackle QCD itself, but something a little simpler. "The very first step is to take a prototype theory which is well-understood, but to which we can still add a little more knowledge," explains Chakraborty. The theory they used involves the mathematical framework that describes electromagnetism, which is similar but easier than QCD, but with an extra mathematical term added in. This term is designed to cause trouble: its analogue in conventional lattice QCD wreaks havoc with the calculations, leading to non-sensical results.

As it turns out, Chakraborty and Honda's algorithm is able to master the challenge beautifully. Among other things, it can calculate, for the first time ever using digital quantum computing, the lowest energy state of the system described by the underlying theory. Knowing the lowest energy state then enabled Chakraborty and Honda to compute the masses of particles (and reassuringly, for particles whose mass had previously been worked out, the new results agreed with existing ones).

Importantly, Chakraborty and Honda's algorithm can also cope with the fact that the lattice approach is only a simplification: when you try to get back to the true theory, by letting the grid the lattice theory is built on become finer and finer and the volume of spacetime it considers larger and larger, the answers you get still make sense. "Previous papers in this field did not take this *continuum limit* seriously," says Honda. "Ours is the first to do that."

### When will quantum computing help in practice?

That's a difficult question to answer. Perhaps surprisingly, Chakraborty and Honda tested their algorithm mostly on a classical computer. While suitable for a quantum computer, their algorithm can be implemented on a classical device called a *quantum simulator*, which checks if it would actually function on a quantum computer and can be used to estimate the computational cost involved. Once proper quantum computers come online, the algorithm can then be run on those, hopefully benefitting from dramatic speed-ups.

Chakraborty and Honda's algorithm performs admirably well on a quantum simulator, showing that quantum computing has real potential for particle physics. The switch to real quantum computers, however, does involve an extra challenge: unlike classical computers, quantum computers suffer from *noise*, small mistakes at each computational step, which can accumulate. A few runs on a real prototype quantum computer have shown that the algorithm will have to be tweaked to deal with that noise. It's a task Chakraborty and Honda will take on next.

More generally, there's the complex nature of algorithms in QCD, which tend to consist of a hierarchy of components, each using the parallel computing capabilities of classical supercomputers. To outperform such a supercomputer, a quantum computer would have to do so on every single component. We won't really know if it can do this until we have solved the hardware problem of building a quantum computer with a sufficient number of bits.

With this challenge still to be mastered, Chakraborty thinks it'll be "a few years" until quantum computing in particle physics will come into its own. For the near future, Honda suggests, it might be best to concentrate on hybrid approaches, involving both classical and quantum computing.

In the meantime Chakraborty and Honda will continue to branch out, not just into new areas of computing, but also into other areas of physics. "Our work can also be employed in many other areas, such as condensed matter physics, nuclear physics and cosmology," says Chakraborty.

"The methods have implications and applications beyond our specific problem — so now we would like to collaborate with people from other disciplines to learn about them all."