Quantum Supremacy Experiments
Milestone demonstrations that a quantum processor performed a sampling task infeasible for classical supercomputers.
What was claimed
Quantum supremacy (now more often called quantum advantage) is the demonstration that a programmable quantum device performs a well-defined computational task that no classical computer can perform in a feasible time. The landmark 2019 superconducting experiment ran random circuit sampling on around fifty-three qubits and argued the task would take a classical supercomputer far longer than the quantum run.
The two experimental families
- Superconducting random circuit sampling: deep random gate sequences on tens of qubits, verified with cross-entropy benchmarking.
- Photonic boson sampling: single-photon and Gaussian variants over many optical modes, tied to permanents and hafnians.
- Both are sampling tasks chosen for classical hardness, not for practical usefulness.
The moving target
Every supremacy claim is a snapshot in a contest. After each announcement, classical algorithm improvements (better tensor-network contraction, smarter simulation of noisy circuits, spoofing methods) reduced the estimated classical cost, sometimes dramatically. Meanwhile hardware groups increased qubit counts and depth. The frontier is a shifting boundary rather than a permanent victory, and honest reporting states both the quantum runtime and the best current classical estimate.
What it does and does not prove
These experiments provide strong evidence that quantum devices can outperform classical ones on some tasks, supporting the extended Church-Turing thesis being false in practice. They do not deliver useful computation: the sampled distributions have no known application, and the circuits lack error correction. The results are proofs of principle that motivate the harder goal of practical, fault-tolerant advantage.
Honest framing
Distinguishing a contrived sampling advantage from useful advantage matters. A demonstration on a purpose-built hard task says little about whether a device can solve chemistry, optimization, or simulation problems better than classical methods today. The distinction is developed in quantum advantage definitions.