Unconditional and exponentially large violation of classicality

Testing the predictions of quantum mechanics has been one of the main experimental endeavors for decades. Recent advancements in technology have led to a number of demonstrations that test non-classicality via specific computational tasks. Limitations of these experiments include dependence on complexity theory assumptions, susceptibility to hardware noise, and inefficient verification, raising questions about their scalability. We propose to test non-classicality using a game based on complement sampling, an efficiently verifiable problem that achieves the largest possible separation between quantum and classical computation when both input and output represent samples from probability distributions. When restricting the input to instances inspired by the Bernstein-Vazirani problem, our game admits an exponentially large violation of classicality unconditionally, i.e., without relying on computational hardness assumptions. We demonstrate the game on Quantinuum System Model H2 trapped-ion quantum computers, with experiments consisting of thousands of different circuits on up to 55 qubits. The observed scores can be explained by a systematic adoption of a quantum strategy, further corroborating the quantum nature of the hardware in an efficient and scalable way.