In a study published in Physical Review Letters, researchers at the Center for Computational Quantum Physics (CCQ) at the Flatiron Institute have revealed that the quantum problem they solved, which involved a specific two-dimensional quantum system of flipping magnets, exhibits a behavior known as confinement. This problem explains why they defeated the quantum computer in its own game. Only one-dimensional systems had previously exhibited this behavior in quantum condensed matter physics.
An illustration of a quantum system that was simulated by both classical and quantum computers. The highlighted sections show how the influence of the system’s components is confined to nearby neighbors. Image Credit: Lucy Reading-Ikkanda/Simons Foundation
The researchers revealed earlier this year that they had completely surpassed a quantum computer at a task that some believed could only be completed by quantum computers by using a classical computer and complex mathematical models.
According to lead author Joseph Tindall, a research fellow at the CCQ, this surprising discovery is giving researchers a framework for evaluating novel quantum simulations and aiding in their understanding of the boundary between quantum and classical computers' capabilities.
There is some boundary that separates what can be done with quantum computing and what can be done with classical computers. At the moment, that boundary is incredibly blurry. I think our work helps clarify that boundary a bit more.
Joseph Tindall, Study Lead Author and Research Fellow, Center for Computational Quantum Physics
Quantum computers, which use the concepts of quantum mechanics, promise to outperform classical computers in terms of speed and processing power. Quantum computers can process information in a fundamentally different way by using qubits, which can represent both 0 and 1 simultaneously, whereas classical computations are restricted by the binary operations of ones and zeros.
However, quantum technology is still in its early stages and has not yet proven to be a viable alternative to classical computers. Scientists are developing challenging problems that push the boundaries of both classical and quantum computing as they try to determine where quantum computers might be superior.
In June 2023, IBM researchers published a paper in the journal Nature detailing the findings of a recent test of quantum computers. An experiment that simulated a system with a collection of tiny flipping magnets changing over time was described in their study.
The researchers asserted that only a quantum computer, not a classical one, could perform this simulation. Tindall chose to accept the challenge after reading about the new paper in the press.
Over the past few years, Tindall has been collaborating with others to create more effective codes and algorithms for using classical computers to solve challenging quantum problems. In just two weeks, he demonstrated that he could solve the problem using a smartphone and very little processing power by applying these techniques to IBM's simulation.
Tindall added, “We didn’t really introduce any cutting-edge techniques. We brought a lot of ideas together in a concise and elegant way that made the problem solvable. It was a method that IBM had overlooked and was not easily implemented without well-written software and codes.”
In January 2024, Tindall and his associates published their research in the journal PRX Quantum, but Tindall did not stop there. Motivated by the results’ simplicity, he and his co-author Dries Sels from New York University and the Flatiron Institute set out to find out why this system, which at first glance seemed to be a very complex problem, could be solved so simply with a classical computer.
“We started thinking about this question and noticed a number of similarities in the system’s behavior to something people had seen in one dimension called confinement,” Tindall stated.
Similar to quark confinement in particle physics, confinement is a phenomenon that can occur in closed quantum systems under specific conditions.
An individual magnet on a quantum scale can be either up or down, or it can be in a "superposition," which is a quantum state where it points both up and down at the same time. When a magnet is in a magnetic field, its energy depends on how up or down it is.
The magnets were all pointing in the same direction when the system was first set up. A small magnetic field was then applied to the system, which caused some of the magnets to want to flip and prompted other nearby magnets to do the same.
Entanglement, or the linking of the magnets’ superpositions, can result from this behavior, in which the magnets affect one another's flipping. As the system becomes more entangled over time, it becomes difficult for a traditional computer to simulate.
However, there is only so much energy available in a closed system. Tindall and Sels demonstrated that the energy available in their closed system was limited to flipping small, sparsely separated clusters of orientations, thereby directly limiting the growth of entanglement. The two-dimensional geometry of the system naturally led to this energy-based restriction on entanglement, which is called confinement.
“In this system, the magnets won’t just suddenly scramble up; they will actually just oscillate around their initial state, even on very long timescales. It is quite interesting from a physics perspective because that means the system remains in a state which has a very specific structure to it and isn’t just completely disordered,” Tindall added.
Coincidentally, IBM had created a scenario in their first test where confinement resulted from the arrangement of the magnets in a closed two-dimensional array. Tindall and Sels discovered that the system's confinement kept the problem straightforward enough to be explained using classical techniques because it decreased the amount of entanglement. Tindall and Sels developed a straightforward, precise mathematical model that explains this behavior through simulations and mathematical computations.
Tindall added, “One of the big open questions in quantum physics is understanding when entanglement grows rapidly and when it doesn’t. This experiment gives us a good understanding of an example where we don’t get large-scale entanglement due to the model used and the two-dimensional structure of the quantum processor.”
The findings suggest that confinement could appear in a variety of two-dimensional quantum systems. If it does, Tindall and Sels’ mathematical model will be a valuable tool for understanding the physics at work in these systems. Furthermore, the codes used in the paper can serve as a benchmarking tool for experimental scientists as they create new computer simulations of other quantum problems.
Journal Reference:
Tindall, J..and Sels, D. (2024) Confinement in the Transverse Field Ising Model on the Heavy Hex Lattice. Physical Review Letters. doi.org/10.1103/PhysRevLett.133.180402