Classical code matches quantum computer on hard physics simulation
Researchers used tensor networks to simulate hundreds of entangled qubits, with some calculations running on a laptop, according to the Simons Foundation.
By Tom Brennan · Health & Medicine Correspondent
3 min read
Researchers have used classical computing methods to solve a quantum physics simulation that another team had described as beyond the reach of ordinary computers. The result matters because it tests where quantum computers may have an edge, and where better algorithms can still extend the power of existing hardware.
The work was carried out by scientists at the Center for Computational Quantum Physics at the Simons Foundation’s Flatiron Institute, with collaborators at Boston University, according to the Simons Foundation. The findings were published in Science in a paper led by Joseph Tindall, Antonio Francesco Mello, Matthew Fishman, E. Miles Stoudenmire and Dries Sels.
The problem involved simulating hundreds of interacting qubits arranged in square, cubic and diamond-shaped lattices, the Simons Foundation said. Qubits are the quantum version of classical bits, but they can exist in combinations of states, making their collective behavior difficult to reproduce on a conventional machine.
A March 2025 Science paper by a separate team reported quantum-computer calculations for a complex qubit system and argued that classical computers could not match the result. Tindall, an associate research scientist at the CCQ, said the new work grew out of skepticism about such claims and a desire to test the group’s own computational tools.
How the calculation was compressed
The main obstacle was entanglement, according to the Simons Foundation. When qubits are entangled, their properties must be treated as part of a connected system, so researchers cannot calculate each qubit separately.
That full system is described by a wave function, which grows rapidly as more particles are added. Tindall said the object becomes too large to store directly on a computer, even though such calculations are central to studying quantum systems and materials such as superconductors.
The team addressed the problem with tensor networks, mathematical tools that compress the information in a wave function into a more manageable form, the Simons Foundation said. Tindall compared the method to compressing a file, with the quantum information represented by linked tables of numbers.
Some of the early runs were performed on a personal laptop using ITensor, a tensor network software library developed at the CCQ, according to the Simons Foundation. The researchers also used a three-dimensional tensor network to model 3D quantum dynamics, an area Tindall described as technically demanding because the mathematical objects and software are complex.
Older algorithm, new role
For many simulations, the researchers used belief propagation, an algorithm developed in the 1980s that has recently been adapted for quantum systems, the Simons Foundation said. Stoudenmire said the method is more approximate than some alternatives but far less costly to run, making it useful for large three-dimensional problems.
The Simons Foundation said the classical simulations agreed with theoretical predictions, matched checks on smaller systems and aligned with results previously obtained on a quantum computer. The key difference was that the new calculations did not require quantum hardware.
Tindall and Stoudenmire said the result should not be read only as a contest between classical and quantum computing. According to the Simons Foundation, they see classical simulations as a way to test quantum-computer claims and help guide future quantum hardware work.
The group’s next target is harder: systems in which electrons can move between sites, according to the Simons Foundation. Stoudenmire said those problems are more difficult but more directly connected to real quantum materials.
This story draws on original reporting from ScienceDaily.