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.
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.
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.
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.
Quantum computing is progressing at a rapid pace, though still constrained by the limitations of Noisy Intermediate-Scale Quantum (NISQ) devices, such as restricted qubit counts and high susceptibility to noise. To address these constraints, researchers have begun adapting classical software engineering principles to the quantum realm, giving rise to the field of Quantum Software Engineering. Within this context, techniques like circuit cutting and shot- wise distribution have emerged as promising approaches to divide quantum circuits into smaller fragments and to improve the scalability and reliability of quantum computations. In this paper, we present our Cut&Shoot pipeline, which supports the cutting of quantum circuits and the flexible distribution of their shots across multiple quantum processing units (QPUs), in a unified execution strategy. We compare different policies to determine the number of shots for which each fragment should be executed on each QPU. Through 107,000+ experiments on simulated NISQ devices, we assess how circuit size, shot allocation, and QPU availability affect execution times and error rates. Our findings indicate that combining circuit cutting and shot- wise distribution provides a useful trade-off of execution times and error rates, while featuring high-qubit quantum computations as well as increased resilience and adaptiveness.
Despite significant progress in quantum computing in recent years, executing quantum circuits for practical problems remains challenging due to error-prone quantum hardware. Hence, quantum error correction becomes essential but induces significant overheads in qubits and execution time, often by orders of magnitude. Obviously, these overheads must be reduced. Since many quantum applications can tolerate some noise, end users can provide a maximum tolerated error, the error budget, to be considered during compilation and execution. This error budget, or, more precisely, its distribution, can be a key factor in achieving the overhead reduction. Conceptually, an errorcorrected quantum circuit can be divided into different parts that each have a specific purpose. Errors can happen in any of these parts and their errors sum up to the mentioned error budget-but how to distribute it among them actually constitutes a degree of freedom. This work is based on the idea that some of the circuit parts can compensate for errors more efficiently than others. Consequently, these parts should contribute more to satisfy the total error budget than the parts where it is more costly. However, this poses the challenge of finding optimal distributions. We address this challenge not only by providing general guidelines on distributing the error budget, but also a method that automatically determines resource-efficient distributions for arbitrary circuits by training a machine learning model on an accumulated dataset. The approach is evaluated by analyzing the machine learning model's predictions on so far unseen data, reducing the estimated space-time costs for more than 75% of the considered quantum circuits, with an average reduction of15.6%, including cases without improvement, and a maximum reduction of77.7%.
Randomized protocols are procedures that incorporate probabilistic choices during their execution and they play a central role in quantum algorithms, spanning Hamiltonian simulation, noise mitigation, and measurement tasks. In practical implementations, the dominant cost of such protocols typically arises from circuit execution and measurement, and depends on hardware-specific resources such as gate counts, circuit depth, runtime, or dissipated energy. We introduce a general framework for applying classical importance sampling to randomized quantum protocols. Given a cost function for running quantum circuits, the proposed approach minimizes a net-cost figure of merit that jointly captures the computational expense per circuit and the estimator variance. We further extend the framework to scenarios where the quantum computation is subject to errors arising either from algorithmic approximations or from physical noise, proving that importance sampling preserves estimator bias despite altering the sampling distribution, and to settings with error-detection schemes, where we characterize the resulting changes in the optimal sampling strategy and achievable net-cost reduction. Representative applications include the Qdrift protocol, dephasing channels, mixed-states simulation, composite observables estimation, classical shadows, and probabilistic error cancellation. Overall, our results establish a principled approach for reducing the computational resources required by randomized quantum protocols through classical sampling optimization.
Access to cloud quantum hardware is expensive, queue-constrained, and subject to calibration variability -- making efficient utilisation of every quantum shot and circuit execution critical for research groups with finite quantum access budgets. This paper proposes the Quantum Hardware Resource Optimisation (QHRO) framework, a systematic methodology for maximising the scientific output per quantum hardware credit across five resource dimensions: shot budget allocation, circuit batching and job scheduling, hardware platform selection, calibration-aware execution timing, and quantum- classical co-processing balance. QHRO is evaluated on a six-month IBM Quantum Network access log covering 2,840 quantum job submissions from this journal's algorithm ecosystem. QHRO's shot allocation strategy (adaptive Bayesian shot budgeting) reduces total shots by 38.4% at equal result quality. Circuit batching reduces queue wait time by 48.4% through intelligent job packing. Calibration-aware scheduling reduces effective error rate by 18.4% by submitting jobs during low-noise calibration windows. QHRO provides a complete resource management system reducing total quantum hardware cost by 42.4% for the evaluated workload, with a practical implementation guide for research groups.