A team of physicists has upended a major assumption in quantum computing: they solved a notoriously difficult quantum simulation problem using an ordinary laptop, contradicting claims that only quantum hardware could tackle it. Researchers at the Simons Foundation's Flatiron Institute and Boston University used advanced mathematics and specialized software to simulate hundreds of interacting qubits, the quantum building blocks that give quantum computers their power. The breakthrough suggests that classical computers may be far more capable than previously thought, and it raises important questions about where quantum advantage actually begins.

What Problem Did They Actually Solve?

The challenge involved modeling hundreds of qubits arranged in square, cubic, or diamond-shaped lattices. In March 2025, another research team published a paper in Science claiming they had used a quantum computer to calculate the dynamics of an especially complex qubit system, and that a classical computer could not match the achievement. The Flatiron Institute team decided to test that claim directly.

Qubits are fundamentally different from the bits in your laptop. A regular bit is either a 0 or a 1. A qubit, however, can exist in a superposition of multiple states simultaneously, which is what gives quantum systems their unusual capabilities. But this same feature makes their behavior extraordinarily difficult to reproduce on a classical computer. When qubits become entangled, their properties remain connected even when separated by large distances, forcing researchers to model the entire system together rather than each qubit independently.

"Whenever we see these kinds of claims, we're always a bit skeptical. Like, 'Did you try this? Did you try that?'" said Joseph Tindall, an associate research scientist at the Center for Computational Quantum Physics and first author on the new Science paper.

Joseph Tindall, Associate Research Scientist at the Center for Computational Quantum Physics

How Did They Compress the Impossible?

The core obstacle was the wave function, a mathematical object that describes the quantum system. As more qubits are added, the wave function grows exponentially in size, becoming impossible to store on a conventional computer. The Flatiron team overcame this barrier using tensor networks, mathematical structures that compress wave function information so it can be handled efficiently.

Tindall completed many of the initial calculations on a personal laptop using ITensor, a high-performance tensor network software library created at the Flatiron Institute. The compression approach works so effectively that Tindall compared it to "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 researchers also adapted an older algorithm called belief propagation, developed in the 1980s, for quantum systems. This method is less precise than some newer approaches but requires far fewer computing resources and can tackle much harder problems. The results reached state-of-the-art accuracy levels, matching both theoretical predictions and simulations performed with actual quantum computers.

Ways to Understand the Practical Impact of This Finding

• Classical-Quantum Collaboration: The findings suggest that classical and quantum computing are not simply competing technologies but can work together synergistically, with classical simulations helping researchers understand what quantum computers are capable of doing.
• Expanded Research Possibilities: By extracting more computing power from conventional hardware, the approach expands the range of quantum dynamics problems scientists can study without requiring access to expensive quantum machines.
• Optimization Problem Solving: The method may offer a useful strategy for optimization problems where researchers must identify the best answer among many possible solutions, opening new applications for classical computers.

What Does This Mean for Quantum Computing Claims?

The work adds fuel to an ongoing debate about where classical computing ends and quantum advantage begins. However, the researchers emphasize that the two fields are not simply competing. Miles Stoudenmire, a research scientist at the Flatiron Institute, noted that "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".

"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," explained Miles Stoudenmire.

Miles Stoudenmire, Research Scientist at the Center for Computational Quantum Physics

The findings published in Science demonstrate that claims about quantum supremacy, the idea that quantum computers can solve problems classical computers cannot, deserve scrutiny. When a research team makes such a claim, it is worth asking whether classical methods have truly been exhausted. The Flatiron team's success suggests that sophisticated algorithms and mathematical compression techniques can push classical computers far beyond their perceived limits.

What's Next for Quantum Simulation?

The researchers are now developing methods that go beyond systems made only of qubits. Their next goal is to model electrons that can move between different sites. These systems are significantly more difficult to simulate, but they are also directly relevant to understanding real quantum materials, including superconductors. The work represents a frontier in quantum physics research, where the boundary between what classical and quantum computers can achieve continues to shift.

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