Researchers at the Flatiron Institute cracked a quantum physics problem that a separate team had declared impossible for classical computers — using nothing more than a laptop and clever math. The breakthrough challenges assumptions about quantum supremacy and opens new directions for simulating quantum materials.
A team of physicists has pulled off something the quantum computing world said couldn’t be done: solving a complex quantum dynamics problem on an ordinary classical computer — and, in some cases, a personal laptop. The work, published May 21 in Science, directly counters a high-profile claim made just months earlier that a quantum computer had achieved a feat beyond the reach of conventional machines.
The Claim They Set Out to Challenge
In March 2025, a separate group of quantum computing researchers published findings in Science asserting they had simulated the behavior of hundreds of interacting qubits — the quantum equivalent of classical computing bits — in a way that no classical computer could replicate. Physicists at the Center for Computational Quantum Physics (CCQ) at the Simons Foundation’s Flatiron Institute, along with collaborators at Boston University, were not convinced.
“Whenever we [at the CCQ] see these kinds of claims, we’re always a bit skeptical,” Joseph Tindall, an associate research scientist at the CCQ and first author of the new study, said in a news release. “Like, ‘Did you try this? Did you try that?'”
Rather than selecting an abstract benchmark, the team decided to take their tools “out for a test drive” on the very problem the quantum computing group had flagged as classically impossible.
“We could have picked some more arbitrary target,” co-author and CCQ research scientist Miles Stoudenmire said in the news release. “But it was like ‘Why not pick this one that has a big claim attached to it?'”
Why Quantum Systems Are So Hard to Simulate
The core difficulty lies in something called quantum entanglement. Unlike classical bits, which are either 0 or 1, qubits can exist in a superposition of states simultaneously. When hundreds of qubits interact, they become entangled — meaning you can’t analyze them in isolation, even if they’re physically distant from one another.
This interdependence produces what physicists call a wave function: a mathematical object that encodes the full state of a quantum system.
“When you have lots of particles that interact by quantum physics, you have this wave function that describes the state of the system,” Tindall added. “It’s this huge object that rapidly gets bigger and bigger the more particles there are.”
The wave function grows exponentially with each additional particle, making direct storage on any computer a practical impossibility.
“I just can’t directly store it on my computer,” added Tindall.
The Tensor Network Trick
The CCQ team’s solution was to use tensor networks — a mathematical framework that compresses enormously complex wave functions into a manageable form. Tindall describes it as “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.”
The approach is powerful but technically demanding.
“It’s this very powerful compression that can be very effective, but it’s a pretty complex mathematical object,” Tindall said. “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.”
Much of the heavy lifting was done using ITensor, a high-performance tensor network software library developed at the CCQ. The simulations extended tensor methods into three dimensions, a significant technical leap for the field. An older algorithm called belief propagation — originally developed in the 1980s and recently adapted for quantum systems — made many of the computations accessible even on modest hardware.
“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 said of the approach, contrasting it 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.”
Why It Matters for Students and Researchers
For students studying physics, computer science or materials science, the implications of this work are far-reaching. The ability to simulate quantum materials — including superconductors — using classical computers could dramatically lower the barrier to entry for quantum research. You don’t need access to a multimillion-dollar quantum machine to make progress; in some cases, a well-written algorithm running on a laptop will do.
The finding also reframes the relationship between classical and quantum computing, which is often portrayed as a rivalry. Tindall sees it differently.
“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 said. “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.”
The team’s simulations produced results that matched theoretical predictions and aligned with what the quantum computing group had reported — but without requiring any quantum hardware at all.
What Comes Next
The CCQ researchers are already looking beyond qubits to a harder class of problems involving electrons that can hop between atomic sites — a challenge directly relevant to understanding real quantum materials.
“They’re really, quantitatively, a lot harder problems,” Stoudenmire said. “So that’s one of our next big bars that we want to clear.”
Source: Simons Foundation