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.

翻译：量子算法需要重复执行电路（即测量次数或称shots）来准确估计输出分布。确定满足目标精度所需的最小测量次数，对于降低成本和资源消耗至关重要，尤其是在当前噪声大且成本高昂的量子硬件上。本文在无假设的黑箱设置下解决测量优化问题，不对量子电路结构或后端的噪声模型做任何假设。我们提出IncrementalExecution这一新颖的在线框架，基于收益递减原则动态决定何时停止执行测量：即当额外测量不再显著改变固定电路的经验分布时，便停止执行。该框架支持可定制的测量管理策略，在静态执行场景中实现执行成本与结果保真度之间的灵活权衡。我们通过涵盖180种独特静态量子电路-后端组合的33,750种框架配置（总计730万次独立实验）的广泛实验评估来验证所提方案。与依赖问题特定知识或算法相关假设（如变分或自适应工作流）的已有工作不同，我们的方法适用于大量静态电路，并可直接部署于当前量子云平台。