The Quantinuum quantum computer outperformed any classical strategies in a game where classical systems cannot win in principle, and this is mathematically proven rather than based on assumptions.
A team led by Marcello Benedetti and Harry Buhrman from Quantinuum in the UK developed a game based on complement sampling. Each possible solution to the problem is secretly divided into two equal groups, A and B. The computer is given an answer from group A and asked to provide an answer from group B. A classical machine can only exclude the received answer but does not know how the others are distributed, and the task becomes exponentially more difficult as the number of options grows.
The quantum computer holds the entire set A in superposition—a state where all options exist simultaneously—and uses a special "swapper" circuit to directly transform it into the complement, after which it measures an answer from group B. The ceiling for classical performance here is strictly mathematically proven, without relying on unproven hypotheses about computational complexity.
The experiment was conducted on Quantinuum's H2 ion quantum processors. Thousands of circuits scaled up to 55 qubits were used. Despite the noise of real hardware, the quantum system consistently outperformed the best possible classical result, and the gap grew exponentially with the size of the problem—in exact accordance with theoretical predictions.
Unlike tests based on Bell inequalities, this method is effectively verifiable, does not depend on unproven assumptions, and maintains its advantage as the scale increases. Noise, which usually hinders the demonstration of quantum supremacy, did not interfere here: the advantage only intensified.
The results were published in Nature Communications in 2026. They pave the way for reliable verification of quantum computers as they grow and for future experiments involving data exchange between physically separated quantum systems via a quantum communication channel.
This shows that quantum computing can be not only faster but also fundamentally unattainable for classical systems in strictly defined tasks.
