If you could run one experiment on a quantum computer today, what would it be & why?

[Hollow Coder]

Not asking about the biggest scientific problems quantum will eventually solve. Asking about what is actually accessible on current NISQ hardware with 50-200 qubits and the error rates that exist today.

The interesting constraint is that the most compelling quantum experiments for current hardware are not necessarily the ones that will matter most commercially in ten years. What would you actually run today and what would you hope to learn from it?

[Delulu66]

A variational quantum eigensolver on a small molecule that classical computers can also solve exactly, specifically to characterise the error profile of the hardware I am using. Understanding where and how my quantum computer fails is more useful than attempting something classically hard

[GoldbergFan_X]

The Fermi-Hubbard model on a 2D grid of qubits at a size where classical simulation is expensive but not impossible. Running both and comparing gives you a direct calibration of how much the quantum result is trusted

[Baz_26]

Quantum simulation of a specific reaction in nitrogen fixation at biological temperature. The Haber-Bosch process for making fertiliser consumes ~2% of global energy. If a quantum computer could help design a room-temperature catalyst the value would be extraordinary even on current hardware

[Ava_75]

A QAOA circuit for a logistics optimisation problem from a real supply chain where I know the classical optimal solution. Testing whether QAOA approaches the classical optimum as circuit depth increases would tell me something concrete about where the hardware actually is

[DarkMatter24]

A quantum error correction experiment on the surface code at a size where I can track individual error events and see whether the error rate improves or degrades as I add more qubits. The below-threshold demonstration from Google Willow suggests it should improve. I want to see it myself

[NatureBoy86]

Quantum random number generation benchmarked against the best classical PRNGs in a way that a statistician would find convincing. Not because I doubt quantum randomness but because the methodology for proving it is interesting