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Classical laptop matches quantum computer in complex simulation — AI-generated representative image: A researcher uses a laptop to perform complex quantum simulations using classical algorithms at the Flatiron Institute.

Editorial Team

Tensor networks and 1980s algorithm enable qubit simulation on conventional hardware

Researchers at the Center for Computational Quantum Physics (CCQ) at the Simons Foundation's Flatiron Institute, in collaboration with Boston University, have demonstrated that a standard personal laptop can solve a quantum dynamics problem previously thought to require a quantum computer. The findings, published in the journal Science, show that simulations of hundreds of interacting qubits can be performed on classical hardware using advanced mathematical compression techniques, matching results that another team had earlier obtained using a quantum machine.

The achievement matters because it challenges assumptions about where the boundary between classical and quantum computing lies. By extracting greater performance from conventional hardware, the method could expand the range of quantum physics problems accessible to researchers without access to quantum computers. It also offers potential strategies for optimization problems where the best answer must be identified among many possible solutions.

Key Findings

The research team, led by CCQ associate research scientist Joseph Tindall and research scientist Miles Stoudenmire, set out to test whether classical methods could replicate a result from a March 2025 Science paper in which another group used a quantum computer to calculate the dynamics of a complex qubit system and claimed that a classical computer could not match the achievement.

The core challenge involved modeling hundreds of interacting qubits arranged in square, cubic or diamond-shaped lattices. Qubits, the quantum counterparts of classical bits, can exist in superpositions of multiple states, making their collective behavior extremely difficult to reproduce on conventional computers.

The researchers overcame this barrier using tensor networks, mathematical structures that compress wave function data in a manner Tindall likened to "a zip file for the wave function." Many of the initial calculations were performed on a personal laptop using ITensor, a high-performance tensor network software library developed at the CCQ.

Background and Previous Claims

In March 2025, a separate research team published findings in Science arguing that a classical computer could not reproduce the behavior of an especially complex qubit system they had simulated on quantum hardware. That claim caught the attention of the CCQ researchers, who routinely scrutinize such assertions.

"Whenever we see these kinds of claims, we're always a bit skeptical," Tindall said. "Like, 'Did you try this? Did you try that?'"

Stoudenmire described the challenge as an opportunity to take their tools "out for a test drive." He added, "We could have picked some more arbitrary target, but it was like 'Why not pick this one that has a big claim attached to it?'"

Quantum entanglement presented one of the greatest obstacles. When qubits become entangled, their properties remain connected even across large distances, meaning researchers cannot model each qubit independently. The wave function describing such systems grows exponentially in size as more particles are added, making direct storage on classical computers impossible.

Technical Approach and Validation

The researchers applied belief propagation, an algorithm developed in the 1980s that has recently been adapted for quantum systems. Stoudenmire noted that while the method is "a little more approximate than some of the other methods, it's way cheaper, and we can run it much more directly on lots of harder problems." He contrasted this with older techniques that "wouldn't be able to even start going for some of these three-dimensional problems, because they're so big."

The simulations produced solutions that aligned with theoretical predictions and performed well on smaller test problems where correct answers could be verified independently. Crucially, the results agreed with those previously obtained using a quantum computer, but without requiring quantum hardware.

"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," Tindall said. "I can just write some code and press 'run' on my personal computer."

What Lies Ahead

The researchers are now developing methods that extend beyond systems composed solely of qubits. Their next objective is to model electrons that can move between different sites, a significantly more complex problem that is directly relevant to understanding real quantum materials such as superconductors.

"They're really, quantitatively, a lot harder problems," Stoudenmire said. "So that's one of our next big bars that we want to clear."