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.
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.
Quantum circuit execution estimates output distributions by repeated measurements, yet developers commonly choose a fixed shot budget before execution. This static choice is brittle: low budgets can under-sample the distribution, while high budgets waste measurements. In this paper, we present StableShots, a black-box online stopping rule for static quantum circuits. The method executes a fixed circuit in small batches, monitors the total-variation distance between cumulative empirical distributions, and stops after repeated evidence of local stability. We evaluate StableShots on 180 QSimBench traces spanning six circuit families, six sizes from 4 to 14 qubits, and five noisy IBM simulated backends. With validation-only calibration and 100 repeated backend-holdout splits, the selected configuration reaches TVD <= 0.05 on all held-out test evaluations with median 7,650 shots, whereas fixed-shot baselines either fail more often or spend substantially more shots.
Any algorithm execution on quantum computers requires several repeated and costly executions (known as shots) to obtain reliable results. In this work, we propose a closed-form accurate analytical expression to determine optimal number of shots required for reliable execution of any algorithm on a quantum computer. We also present a theoretically grounded technique to distribute fixed shot budget across different partitions in a quantum circuit minimizing the total error. Our proposed analytical model helps to reduce the shots associated with reliable execution of quantum algorithms by about 58\% compared to current practice, in turn reducing the energy consumption by upto 62\%. Furthermore, our proposed optimal shot allocation technique across different partitions reduces total error by up to 73\% compared to conventional approaches.
Context: Quantum computing is rapidly evolving, offering new opportunities for solving problems in optimization, cryptography, and simulation. However, the limited availability of quantum resources makes efficient utilization of quantum hardware a current challenge. Today’s paradigms often lead to under-utilization of qubits, increased costs, and execution delays, especially in the NISQ era. Objective: This work aims to improve the utilization of quantum hardware by introducing an execution model that integrates multiprogramming at circuit level with quantum shot-wise distribution in a single policy-driven pipeline. Methods: An architecture has been implemented that combines circuit scheduling and shot distribution techniques to aggregate multiple circuits and distribute their shots across heterogeneous QPUs. The approach was empirically validated on actual IBM Quantum devices using a diverse set of reference circuits. Results: The proposal achieved a reduction in cost of 95% and a reduction in tasks 92%. Moreover, the fidelity analysis of the results showed an increase in noise, with an average increase of approximately 20% using different statistical distances. Conclusions: This research provides a usable and extensible solution to increase the efficiency, cost effectiveness, and resilience of quantum workload execution in heterogeneous and dynamic cloud environments. These results obtained suggest that users should weigh the implications of fidelity versus cost (and time) savings based on the application requirements and their goals.
Variational quantum algorithms (VQAs) have attracted remarkable interest over the past few years because of their potential computational advantages on near-term quantum devices. They leverage a hybrid approach that integrates classical and quantum computing resources to solve high-dimensional problems that are challenging for classical approaches alone. In the training process of variational circuits, constructing an accurate probability distribution for each epoch is not always necessary, creating opportunities to reduce computational costs through shot reduction. However, existing shot allocation methods that capitalize on this potential often lack adaptive feedback or are tied to specific classical optimizers, which limits their applicability to common VQAs and broader optimization techniques. Our observations indicate that the information entropy of a quantum circuit’s output distribution exhibits an approximately exponential relationship with the number of shots needed to achieve a target Hellinger distance. In this work, we propose a distribution-adaptive dynamic shot (DDS) framework that efficiently adjusts the number of shots per iteration in VQAs using the entropy distribution from the prior training epoch. Our results demonstrate that the DDS framework sustains inference accuracy while achieving an ∼ 50 % reduction in average shot count compared to fixed-shot training, and ∼ 60 % higher accuracy than recently proposed tiered shot allocation methods. Furthermore, in noisy simulations that reflect the error rates of actual IBM quantum systems, DDS achieves an ∼ 30 % reduction in the total number of shots compared to the fixed-shot method with minimal degradation in accuracy and offers ∼ 70 % higher computational accuracy than tiered shot allocation methods.
NISQ (Noisy Intermediate-Scale Quantum) era constraints, high sensitivity to noise and limited qubit count, impose significant barriers on the usability of QPUs (Quantum Process Units) capabilities. To overcome these challenges, researchers are exploring methods to maximize the utility of existing QPUs despite their limitations. Building upon the idea that the execution of a quantum circuit’s shots does not need to be treated as a singular monolithic unit, we propose a methodological framework, termed shot-wise, which enables the distribution of shots for a single circuit across multiple QPUs. Our framework features customizable policies to adapt to various scenarios. Additionally, it introduces a calibration method to pre-evaluate the accuracy and reliability of each QPU’s output before the actual distribution process and an incremental execution mechanism for dynamically managing the shot allocation and policy updates. Such an approach enables flexible and fine-grained management of the distribution process, taking into account various user-defined constraints and (contrasting) objectives. Demonstration results show that shot-wise distribution consistently and significantly improves the execution performance, with no significant drawbacks and additional qualitative advantages. Overall, the shot-wise methodology improves result stability and often outperforms single QPU runs, offering a robust and flexible approach to managing variability in quantum computing.
Quantum Computing is advancing from isolated prototypes toward heterogeneous, cloud-accessed quantum processors that are noisy, capacity-limited, and operationally diverse. In this landscape, the prevalent device-centric execution model (i.e., compiling a circuit for a single backend and running all shots monolithically) constrains scale, reliability, and cost-effectiveness. This thesis argues for and instantiates a system-centric paradigm of distributed execution, which treats execution as an engineered process that orchestrates spatial and temporal distribution across multiple devices and time scales, guided by explicit Quality-of-Service (QoS) objectives. Spatial distribution aggregates multiple, heterogeneous Quantum Processing Units and supporting classical services into a shared resource pool, placing circuits, subcircuits, and workloads where their algorithmic needs best align with hardware characteristics and availability. Temporal distribution adapts execution over time, modulating sampling depth, pacing, and scheduling in response to drift, queue dynamics, and evidence of statistical convergence. Together, these dimensions are governed by policy-driven orchestrations that reconciles fidelity, latency, and cost, and that elevates user intent above device idiosyncrasies. This thesis delivers five main contributions: (1) a shot-wise execution methodology that distributes measurement shots across heterogeneous QPUs under policy control, reducing output variance and matching or surpassing single-device averages; (2) Quantum Broker, a QoS-aware orchestration framework with the Quantum QoS Specification Language (QQSpec) that consistently finds feasible, high-quality allocations and outperforms single-backend and uniform-shot baselines under competing fidelity/latency/cost goals; (3) Cut&Shoot, an integrated circuit-cutting + shot-wise pipeline that executes large circuits across multiple devices with significantly lower error than monolithic, cutting-only, or shot-wise-only baselines, at negligible time overhead relative to standard cutting; (4) a hybrid orchestration architecture, QCRAFT Scheduler–Shotwise, which combines high-level circuit scheduling with shot-wise distribution to achieve up to 95% cost reduction and 92% fewer job submissions while improving robustness to hardware variability; and (5) IncrementalExecution, an adaptive, evidence-seeking shot manager that approximates optimal allocations with minimal overhead and high fidelity across unseen circuits and backends. Evaluations on simulated and real cloud backends demonstrate practicality across heterogeneous providers. Situated within Quantum Software Engineering, this thesis promotes abstractions and runtime mechanisms that make distribution a first-class program property rather than a backend option. The resulting perspective embraces hardware diversity as an optimization opportunity, improves portability across providers, and lays a path from today’s Noisy Intermediate-Scale Quantum (NISQ) platforms to future networked and fault-tolerant regimes. The overarching vision is that, by engineering execution as a principled, evidence-seeking process, heterogeneous quantum resources become the substrate for scalable, reliable, and efficient Quantum Computing.