A surprising challenge to quantum supremacy. Physicists from the Center for Computational Quantum Physics at the Flatiron Institute, Simons Foundation, along with colleagues from Boston University, have demonstrated that a problem previously considered intractable for classical computers can be simulated on a regular machine – and even on a laptop.
The dispute began in March 2025 when a research group published a revolutionary claim in the journal Science: they had succeeded in simulating the behavior of a complex quantum system on a quantum computer, a feat they asserted was impossible to replicate with classical means. Joseph Tindall, a scientist at Flatiron, raised a skeptical eyebrow upon hearing this assertion. He and his colleagues decided to test whether the problem was indeed unsolvable.
The research focuses on simulating systems of hundreds of interacting qubits arranged in square, cubic, and other regular lattices. It was precisely this task that opponents deemed impossible for classical computations, claiming it would require tens of thousands of years of continuous calculation.
The solution was found in tensor networks – a mathematical tool that literally "compresses" the enormous wave function of a quantum system, much like a ZIP archive compresses files. This drastically reduces the amount of information that needs to be processed. Tindall performed the initial calculations on his laptop, using the ITensor library developed by his colleagues at the Center. The result was astonishing: a task that a quantum computer took hours to complete was solved by a regular laptop in 30 minutes. On some laptops, the calculations took up to two hours and required only 40 megabytes of RAM – less than the size of a simple social media video.
The key technique is an adapted belief propagation algorithm, dating back to the 1980s. Tindall and his team re-engineered this old method for quantum systems, managing to extract a potential that had gone unnoticed for decades. The approach is cheaper and faster than alternative methods, though slightly less accurate – but acceptably accurate for practical tasks.
What is particularly impressive is that the results not only matched theoretical predictions but also agreed with data obtained from a real quantum computer. The accuracy reached a level that classical science considered unattainable. This implies that quantum advantage in this particular task is either very narrow or simply non-existent.
The scientists emphasize the main takeaway: classical and quantum computing are not rivals but allies. Classical simulations help to debunk exaggerated claims of quantum supremacy and better understand what quantum devices are truly useful for. Simultaneously, every breakthrough in quantum hardware inspires developers to create new classical methods and algorithms.
Tindall's team is now moving on to a more complex challenge: simulating electrons that can move between lattice nodes. These systems are even more intricate and closer to real quantum materials – magnets, superconductors, and exotic substances that physicists aim to synthesize and understand. The research indicates that the boundary between the classical and quantum worlds is more blurred than previously thought, and both approaches will aid each other on the path to true breakthroughs.
