Presented and implemented on the Quantinuum System Model H2 quantum processor, high-qubit peaked output circuits (HQAP circuits) demonstrate heuristic quantum advantage. The largest instance uses all-to-all connectivity, 2000 two-qubit gates, and generates the target bit string in 2 hours. Extrapolations from leading classical methods—tensor networks with belief propagation and Pauli path simulators—show that on exascale systems (Frontier, Summit) the solution would take years, pointing to a potentially exponential separation. A design protocol for such circuits is proposed, and numerical extrapolation results are given. Separately, the complexity of the decision problem for generalized peaked circuits is proven: determining peakedness with unknown input and output data is QCMA-complete, meaning it remains hard even for quantum polynomial-time machines. Based on this, quantum-resistant encryption is proposed. The circuits are openly published for community verification.
The task resembles a giant maze with a single exit among billions of dead ends. A conventional computer checks each corridor step by step—taking centuries. A quantum processor launches a wave that seeps through all paths at once. The correct route echoes back, amplifying, and the answer is found in hours. That’s exactly how the “peak” circuits worked in the new experiment.
With each additional fork, the quantum chip’s advantage grows not just quickly, but frighteningly so—like the expansion of the Universe accelerates galaxies. Surprisingly, the quantum device’s answer is probabilistic: it guesses the path with high accuracy but doesn’t guarantee it. Yet that accuracy is enough to make classical verification take years. In the experiment, the most complex circuit had 2,000 forks. H2 found the exit in two hours; supercomputers would need years.
🎯 The most complex circuit involved 2,000 operations—like an orchestra of 2,000 instruments playing in unison.