New study expands types of physics, engineering problems that can be solved by quantum computers

A well-known quantum algorithm that is useful in studying and solving problems in quantum physics can be applied to problems in classical physics, according to a new study in the journal Physical Review A from University of Wisconsin–Madison assistant professor of physics Jeff Parker.

Quantum algorithms – a set of calculations that are run on a quantum computer as opposed to a classical computer – used for solving problems in physics have mainly focused on questions in quantum physics. The new applications include a range of problems common to physics and engineering, and expands on the types of questions that can be asked in those fields.

profile photo of Jeff Parker
Jeff Parker

“The reason we like quantum computers is that we think there are quantum algorithms that can solve certain kinds of problems very efficiently in ways that classical computers cannot,” Parker says. “This paper presents a new idea for a type of problem that has not been addressed directly in the literature before, but it can be solved efficiently using these same quantum computer types of algorithms.”

The type of problem Parker was investigating is known as generalized eigenvalue problems, which broadly describe trying to find the fundamental frequencies or modes of a system. Solving them is crucial to understanding common physics and engineering questions, such as the stability of a bridge’s design or, more in line with Parker’s research interests, the stability and efficiency of nuclear fusion reactors.

As the system being studied becomes more and more complex — more components moving throughout three-dimensional space — so does the numerical matrix that describes the problem. A simple eigenvalue problem can be solved with a pencil and paper, but researchers have developed computer algorithms to tackle increasingly complex ones. With the supercomputers available today, more and more difficult physics problems are finding solutions.

“If you want to solve a three-dimensional problem, it can be very complex, with a very complicated geometry,” Parker says. “You can do a lot on today’s supercomputers, but there tends to be a limit. Quantum algorithms may be able to break that limit.”

The specific quantum algorithm that Parker studied in this paper, known as quantum phase estimation, had been previously applied to so-called standard eigenvalue problems. However, no one had shown that they could be applied to the generalized eigenvalue problems that are also common in physics. Generalized eigenvalue problems introduce a second matrix that ups the mathematical complexity.

Parker took the quantum algorithm and extended it to generalized eigenvalue problems. He then looked to see what types of matrices could be used in this problem. If the matrix is sparse ­— meaning, if most of the numerical components that make it up are zero — it means this problem could be solved efficiently on a quantum computer.

The study shows that quantum algorithms could be applied to classical physics problems, such as nuclear fusion mirror machines. | Credit: Cary Forest

“What I showed is that there are certain types of generalized eigenvalue problems that do lead to a sparse matrix and therefore could be efficiently solved on a quantum computer,” Parker says. “This type includes the very natural problems that often occur in physics and engineering, so this study provides motivation for applying these quantum algorithms more to generalized eigenvalue problems, because it hasn’t been a big focus so far.”

Parker emphasizes that quantum computers are in their infancy, and these classical physics problems are still best approached through classical computer algorithms.

“This study provides a step in showing that the application of a quantum algorithm to classical physics problems can be useful in the future, and the main advance here is it shows very clearly another type of problem to which quantum algorithms can be applied,” Parker says.

The study was completed in collaboration with Ilon Joseph at Lawrence Livermore National Laboratory. Funding support was provided by the U.S. Department of Energy to Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and U.S. DOE Office of Fusion Energy Sciences “Quantum Leap for Fusion Energy Sciences” (FWP SCW1680).

Welcome, Assistant Professor Jeff Parker!

profile photo of Jeff Parker

Have you heard the joke about the lawyer who became a physics professor? Jeff Parker has, but rather than be the punchline, he was always in on the joke. After earning his Ph.D. in plasma physics from Princeton in 2014, Parker enrolled at Stanford Law School to pursue a career in energy and climate policy. “I lasted one year in law school, decided I really didn’t like it and just loved physics, and I wanted to get back to physics research,” Parker says.

After that one year, Parker accepted a postdoctoral fellowship at Lawrence Livermore National Lab, and two years later became a staff scientist there. On July 1, 2020, Parker joined the UW–Madison Physics Department as its newest assistant professor. Here, he will focus his research interests in theoretical plasma astrophysics. To welcome Professor Parker, we sat down for a (virtual) Q+A with him.

What are the main topics or projects that you will focus your research on?

My immediate research program has two main directions.

One area of research is going to be in plasma astrophysics and astrophysical fluid dynamics. This concerns plasmas in space or in the universe, like in the sun, or the origin of magnetic fields in the cosmos and how they shape what we see in the universe.  I will be investigating angular momentum transport by magnetic fields, which can occur in stars, accretion disks around black holes, and planetary interiors.

Another area is topological phases of matter in plasma physics, related to the 2016 Nobel prize on topological insulators, which came out of condensed matter physics. I am applying these ideas for the first time to plasma physics and plasma waves. This is a brand-new field in plasmas and I’m just getting into it, but I think it’s really, really interesting.

You’re in Madison now, and you’re getting started with your research. What is the first thing you’re doing?

One particular project I’m very interested in is the astrophysical fluid dynamics involving angular momentum transport due to magnetic fields. I have developed theory on something that I call magnetic eddy viscosity, which could be important where there are magnetic fields and rotation. This can occur in astrophysical objects like stars or accretion discs or planets. And so where I studied this was in a pretty idealized system, and I’d really like to extend this into more realistic models that are closer to reality that would help us say something more about real object like stars or accretion discs, or potentially could be measured in the laboratory. So, there are these experiments, Prof. Forest has one, and there are other experiments throughout the country or the world that have rotating plasmas or liquid metals. This effect could potentially be seen in those experiments as well, and that is something I’d love to do right away.

Your work is primarily theory and computation. Do you see your work as predicting ideas that would be tested with collaborators in the department?

That is one thing I do hope to do. But I do also enjoy developing theory to better understand plasmas, even if those theories cannot be tested immediately in an experiment. I’m a theoretical physicist at heart, but there are so many great plasma physics experiments at Madison, which enable a close collaboration of theory and experiment. Progress is truly made when you can measure, observe, analyze, and use theory to understand what you see.

What’s one thing you hope students who take a class with you will come away with?

I want students to take away how plasma physics is everywhere, how most of the universe is plasma, and so if we want to understand the universe, we need to understand plasma physics.

What is your favorite element and/or elementary particle?

For elementary particle, I’ll say the neutrino because it’s so mysterious, and mysterious is good for physics. For favorite element, hydrogen and its isotopes because they’re what’s important for fusion.

What hobbies/other interests do you have?

I like to hike, run, and travel.