Quantum circuits are probabilistic. Each time you run one you get a sample from an unknown distribution. Repeating the run many times — called shots — builds up an estimate of that distribution. Shots cost time and money on today’s noisy quantum processors, so knowing how many are enough is important.

The authors present IncrementalExecution, an online, iterative way to decide when to stop taking shots for a fixed (static) quantum circuit. The idea is simple: run a small number of shots, look at the empirical distribution (the observed frequencies of measurement outcomes), and stop when more shots no longer change that distribution in any meaningful way. This stopping point is called the point of diminishing returns. The framework supports different stop rules or “policies” so users can trade off cost against result fidelity.

They tested the idea extensively. The experimental campaign covered 33,750 framework configurations over 180 unique static circuit–backend combinations, for a total of 7.3 million independent experiments. According to the paper, the framework can effectively approximate the best number of shots in a black-box setting and lets users control the balance between execution cost and statistical accuracy.

This work differs from earlier methods that rely on known noise models or that target variational or adaptive algorithms where the circuit changes over time. Here no assumptions are made about the circuit structure or the noise of the quantum processing unit (QPU). The authors also define an “a posteriori optimality” notion — the minimal number of shots that would have been sufficient for a given run if you had access to all outputs — and they publish a benchmark dataset to support reproducible evaluation.

There are important limitations. The approach is built for static, non-variational circuits whose output distribution stays the same across shots. It does not handle non-stationary cases where the circuit or its parameters change (for example, during a variational optimisation). Hardware noise can be time dependent, which complicates any black-box strategy, and the paper leaves extensions to adaptive or variational workloads to future work. The experimental results are promising but apply to the tested static circuits and backends only, so more work would be needed to generalise beyond that setting.