How Many Shots Are Enough for a Quantum Circuit?

Quantum algorithms require repeated circuit executions – known as shots – to estimate output distributions accurately. Determining the minimal number of shots needed to meet a target accuracy is crucial to reduce costs and resource usage, especially on today’s noisy and expensive quantum hardware. In this paper, we address the shot optimisation problem in a black-box setting , where no assumptions are made about the structure of the quantum circuit or the noise model of the backend. We introduce IncrementalExecution , a novel online framework that dynamically determines when to stop executing shots based on the principle of point of diminishing returns : the point at which additional shots no longer significantly alter the empirical distribution of a fixed circuit. The framework supports customisable policies for shot management, enabling flexible trade-offs between execution cost and result fidelity within static execution scenarios. We assess our proposal through an extensive experimental evaluation spanning 33, 750 framework configurations across 180 unique static quantum circuit–backend combinations, for a total of 7.3M independent experiments. Unlike prior work that relies on problem-specific knowledge or algorithm-dependent assumptions (e.g., variational or adaptive workflows), our approach is applicable to a large set of static circuits and immediately deployable on current quantum cloud platforms.