An Ordinary Laptop Solved a Problem Thought Impossible Without a Quantum Computer
Physicists at the Center for Computational Quantum Physics (CCQ) at the Simons Foundation's Flatiron Institute have used an ordinary computer, advanced mathematics, and specialized software to solve a difficult quantum physics problem that had been described as beyond the reach of classical machines.
Their method proved so efficient that some of the calculations ran on a personal laptop.
The Challenge
The problem involved modeling hundreds of interacting 'qubits' — the quantum counterparts of classical bits — arranged in square, cubic, or diamond-shaped lattices. A qubit can exist in a superposition of states, giving quantum systems unusual capabilities but also making their behavior extremely difficult to reproduce on a classical computer.
In a March 2025 paper also published in Science, another research team had used a quantum computer to calculate the dynamics of an especially complex qubit system, arguing that a classical computer could not match the achievement.
"Whenever we see these kinds of claims, we're always a bit skeptical," says Joseph Tindall, associate research scientist at the CCQ and first author on the new paper. "Like, 'Did you try this? Did you try that?'"
Tensor Networks: A 'Zip File' for Quantum Wave Functions
The researchers overcame the exponential complexity barrier by developing new tools based on tensor networks — mathematical structures that compress the information contained in a quantum wave function so it can be handled more efficiently.
Tindall compares the approach 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."
That compression made the simulation manageable on classical computers. Tindall completed many of the first calculations on a laptop using ITensor, a high-performance tensor network software library created at the CCQ. The team also adapted belief propagation — an algorithm developed in the 1980s — for quantum systems.
Results That Match Quantum Hardware
Although the hardware was modest, the results reached state-of-the-art accuracy. The simulations aligned with theoretical predictions and agreed with those previously obtained using an actual quantum computer. The difference: the new calculations did not require any quantum hardware.
"The good side of the classical versus quantum computing debate is that there's a lot of synergy," says Tindall. "I can just write some code and press 'run' on my personal computer."
What This Means
The findings add to the ongoing debate over where classical computing ends and quantum advantage begins. Rather than undermining quantum computing research, the researchers emphasize that classical simulations help us understand what quantum computers are capable of — and vice versa.
Their next challenge: modeling electrons that can move between different sites, a significantly harder problem directly relevant to understanding real quantum materials.
"They're really, quantitatively, a lot harder problems," says co-author Miles Stoudenmire. "So that's one of our next big bars that we want to clear."
The study was published in the journal Science.
