In a groundbreaking development that blurs the lines between conventional and quantum computing, researchers have demonstrated that a complex quantum physics problem, previously deemed exclusively within the domain of quantum computers, can be tackled with remarkable efficiency using an everyday laptop. This achievement, spearheaded by scientists at the Center for Computational Quantum Physics (CCQ) at the Simons Foundation’s Flatiron Institute, in collaboration with Boston University, leverages advanced mathematical techniques and bespoke software to unlock computational power previously thought unattainable for classical hardware. The implications are far-reaching, promising to expand the scope of quantum dynamics research and offering novel strategies for optimization problems across various scientific disciplines. The full findings of this transformative work have been published in the prestigious journal Science.

The core of the challenge lay in simulating the intricate behavior of hundreds of interacting ‘qubits,’ the fundamental building blocks of quantum computers. Unlike classical bits, which can only represent a 0 or a 1, qubits possess the extraordinary ability to exist in a superposition of multiple states simultaneously. This quantum phenomenon, while the source of quantum computers’ immense potential, also renders their dynamics notoriously difficult to replicate on classical machines. The problem at hand involved arranging these qubits in various lattice structures – square, cubic, and diamond – and then modeling their complex, interdependent behavior. This difficulty was underscored by a recent study, also published in Science in March 2025, where another research team successfully used a quantum computer to calculate the dynamics of a particularly complex qubit system, asserting that classical computers were incapable of matching their feat.

This bold claim served as a powerful catalyst for the CCQ researchers. "Whenever we [at the CCQ] see these kinds of claims, we’re always a bit skeptical," admits Joseph Tindall, an associate research scientist at the CCQ and the lead author of the new Science paper. "Like, ‘Did you try this? Did you try that?’" This inherent skepticism fueled a desire to rigorously test the limits of their own computational methodologies. The challenging problem presented an ideal opportunity to "take their tools out for a test drive," as described by study co-author and CCQ research scientist Miles Stoudenmire. "We could have picked some more arbitrary target," Stoudenmire elaborates, "But it was like ‘Why not pick this one that has a big claim attached to it?’"

A significant hurdle in accurately simulating quantum systems is the phenomenon of quantum entanglement. When qubits become entangled, their fates are inextricably linked, their properties remaining correlated irrespective of the physical distance separating them. This means that each qubit cannot be modeled in isolation; rather, the entire entangled system must be described as a single, unified entity. "When you have lots of particles that interact by quantum physics, you have this wave function that describes the state of the system," explains Tindall. "It’s this huge object that rapidly gets bigger and bigger the more particles there are." The wave function encapsulates all the necessary information about the quantum system, but its size escalates exponentially with each additional particle. This exponential growth quickly overwhelms the memory capacity of conventional computers, making direct storage and manipulation of such wave functions an insurmountable challenge. This problem is a recurring obstacle in quantum physics, yet the accurate prediction of quantum material behavior, including that of superconductors, hinges on solving these calculations.

The breakthrough achieved by Tindall and Stoudenmire lies in their innovative application of tensor networks. These sophisticated mathematical structures act as powerful compression tools for wave functions. They effectively "zip" the vast information contained within the wave function into a more manageable data structure composed of interconnected tables of numbers. "It’s like a zip file for the wave function where you’ve taken all this information, and you’ve compressed it into this mathematical data structure full of these small tables of numbers that are interconnected to each other," Tindall illustrates. This compression made the simulation feasible on classical computers. Tindall himself was able to perform many of the initial calculations on a personal laptop, utilizing ITensor, a high-performance tensor network software library developed at the CCQ.

The new simulations also showcase the evolving capabilities of the ITensor team in adapting tensor techniques for novel problem types. In this instance, the researchers successfully modeled three-dimensional quantum dynamics by employing a 3D tensor network. "It’s this very powerful compression that can be very effective, but it’s a pretty complex mathematical object," Tindall notes. "This really is a bit of a frontier, because working with these objects — especially in three dimensions — is very untrodden. You need sophisticated codes and algorithms to deal with them; it’s a software engineering challenge in itself."

Interestingly, many of the simulations required relatively modest computing resources, benefiting from an older algorithm adapted for quantum applications. The researchers utilized belief propagation, an algorithm originally developed in the 1980s, which has recently found new utility in quantum systems. "It’s a little more approximate than some of the other methods, but it’s way cheaper, and we can run it much more directly on lots of harder problems," Stoudenmire explains. He contrasts this with "more sophisticated methods in the past of our field" that "wouldn’t be able to even start going for some of these three-dimensional problems, because they’re so big." Despite the seemingly modest hardware, the accuracy of the results was state-of-the-art, aligning precisely with theoretical predictions and performing exceptionally well on smaller, verifiable problems. Crucially, the simulated outcomes matched those previously obtained using a quantum computer, but without the need for specialized quantum hardware.

This remarkable achievement adds a significant new dimension to the ongoing discourse surrounding the boundaries of classical and quantum computing. However, Tindall and Stoudenmire are keen to emphasize that these two fields are not in direct competition but rather exist in a synergistic relationship. Classical simulations serve as invaluable tools for understanding the potential of quantum computers, while advancements in quantum hardware, in turn, inspire the development of new and more efficient classical methods. "The good side of the classical versus quantum computing debate is that there’s a lot of synergy between the kind of simulations we’re interested in and the codes we write and what can be realized on these quantum computers," Tindall states. "That can help guide us, and it can also help guide quantum computing researchers, because, obviously, the barrier for entry for us to simulate certain things is a lot easier than for them, because we don’t have to build a quantum computer. I can just write some code and press ‘run’ on my personal computer."

Looking ahead, the researchers are already charting their next ambitious course: developing methods to simulate systems beyond simple qubit arrangements, specifically focusing on electrons that can move between different sites. These systems represent a considerably greater simulation challenge but are directly relevant to understanding the fundamental properties of real-world quantum materials. "They’re really, quantitatively, a lot harder problems," Stoudenmire acknowledges. "So that’s one of our next big bars that we want to clear." The successful simulation of such complex systems on accessible hardware would represent another significant leap forward, further solidifying the power of advanced classical computation in unraveling the mysteries of the quantum realm.