Quantum optimisation is emerging as a promising approach alongside classical heuristics and specialised hardware, yet its performance is often difficult to assess fairly. Traditional benchmarking methods, rooted in digital complexity theory, do not directly capture the continuous dynamics, probabilistic outcomes, and workflow overheads of quantum and hybrid systems. This paper proposes principles and protocols for fair benchmarking of quantum optimisation, emphasising end-to-end workflows, transparency in tuning and reporting, problem diversity, and avoidance of speculative claims. By extending lessons from classical benchmarking and incorporating application-driven and energy-aware metrics, we outline a framework that enables practitioners to evaluate quantum methods responsibly, ensuring reproducibility, comparability, and trust in reported results.
Quantum optimisation is emerging as a promising approach alongside classical heuristics and specialised hardware, yet its performance is often difficult to assess fairly. Traditional benchmarking methods, rooted in digital complexity theory, do not directly capture the continuous dynamics, probabilistic outcomes, and workflow overheads of quantum and hybrid systems. This paper proposes principles and protocols for fair benchmarking of quantum optimisation, emphasising end-to-end workflows, transparency in tuning and reporting, problem diversity, and avoidance of speculative claims. By extending lessons from classical benchmarking and incorporating application-driven and energy-aware metrics, we outline a framework that enables practitioners to evaluate quantum methods responsibly, ensuring reproducibility, comparability, and trust in reported results.
Quantum AI is a new way to think about the future of Artificial Intelligence through the merging of two technologies: quantum computing and advanced machine learning. Quantum AI has the potential to provide solutions to computationally difficult problems that traditional systems cannot solve. Quantum AI's continued success will rely on advancements in hybrid quantum-classical solutions, as well as the expansion of quantum hardware; hence, research remains necessary to conduct systematic benchmarks as well as performance analysis in order to determine both how well quantum AI algorithms perform practically, and where their limitations lie. In this chapter, detailed examinations of benchmarks that have been developed specifically for quantum AI are presented alongside evaluative metrics across various key areas of performance including algorithmic efficiency, scalability, noise immunity, and resource use for various types of quantum architectures. The chapter integrates dialogue between theory and practice to demonstrate ways in which performance metrics (i.e., quantum circuit depth, fidelity, convergence behaviour and computational complexity) can effectively compare Quantum AI algorithms to classical algorithms. Particular attention is given to hybrid variational algorithms, quantum-enhanced optimization algorithms, and quantum machine learning. Using benchmark datasets, simulation frameworks and new evaluation methods, there are several challenges in terms of reproducibility, hardware variability and algorithm/hardware co-design that emerge through analysis of the above metrics as well. Aside from focusing on a more broad view of how Performance Evaluation relates to developing more effective Quantum AI Solutions. In addition to viewing Benchmarking as a technical exercise solely, this chapter provides a more holistic view in relation to a human perspective of the situation. This paper outlines how performance evaluation practices can be used as a considerable and well-designed means of bridging the gap between the promise of Quantum Technology at an abstract level, and the ability of Quantum Technology to produce tangible outcomes in the real world by adopting a more comprehensive Governance-oriented approach to Benchmarking Quantum AI Systems. The purpose of this chapter is to assist the growing community of researchers, practitioners, and Strategic Technology Professionals by providing them with a clear and structured framework for Evaluation of Quantum AI Algorithms. There is a significant focus of the chapter on establishing important reference points that organizations can use to determine when an intelligent system has successfully achieved a true and validated quantum advantage. The ultimate goal is to assist in guiding the responsible development and implementation of Quantum AI to enable the Potential Benefits of Quantum AI to be realized, in ways that are meaningful and impactful.
Abstract Quantum optimization has become a leading application for near-term quantumcomputing, and yet many publications compare algorithms against idealizedassumptions and small toy benchmarks. This limits the interpretability, reproducibility,and practical relevance of reported performance gains, particularlyin the noisy intermediate-scale quantum (NISQ) era. In this work, we presenta systematic literature review that investigate quantum optimization beyondtoy benchmarks. Following established SLR protocols, we analyze the literaturealong multiple methodological dimensions, including algorithmic approach,benchmark realism, encoding strategies, hybrid quantum-classical workflows,hardware and noise modeling, evaluation metrics, and reporting practices. Weintroduce a unified taxonomy that captures the interaction between problemformulation, encoding overhead, noise-aware execution, and hybrid optimizationloops. In addition, we propose a reproducibility checklist and scoring rubric toassess reporting completeness and experimental rigor across studies. Instead ofdeveloping new quantum optimization algorithms or making theoretical quantumadvantage claims, the main contribution of this work is that it providesa methodological analysis on benchmarking realism and encoding or evaluationpractices as well as reproducibility rigor in NISQ-era quantum optimization studies.Our review uncovers a continued chasm between algorithmic innovation andevaluation maturity, with the number of publications and diversity of methodsgrowing without corresponding growth in standardized benchmarks, strongclassical baselines, noise-consistent evaluation, or reproducibility.
Combinatorial optimisation is a main topic for real-world applications, where fast solutions are required. Optimisation algorithms are incredibly powerful, but still face bottlenecks for certain problems. In recent years, quantum algorithms have been proposed as a potential candidate for solving such problems. The question that naturally arises is whether they could provide meaningful speed-ups over classical approaches. The study of asymptotic complexity has become central in the development of quantum algorithms. Nevertheless, having a promising asymptotic improvement does not directly translate into good practical performance. This is already well known for classical algorithms, which can be executed and evaluated directly. When it comes to quantum algorithms, the situation is more nuanced, as solving practically relevant instances would require a fully fault-tolerant quantum computer. In this thesis, we address the challenge of assessing the practical performance of a quantum algorithm without access to quantum hardware. Our strategy is to evaluate how these algorithms would perform under idealised fault-tolerant assumptions and to identify parameter regimes in which quantum approaches could potentially become useful. Our goal is to guide algorithmic development long before implementation becomes possible. We first give a general overview of the quantum (sub)routines that serve as building blocks for more advanced algorithms, as well as of the three hybrid benchmarking techniques used throughout this thesis. Then, we elaborate on each method: we start with the algorithmic descriptions, proceed to the methodology, and conclude with their hybrid evaluation on practically relevant datasets. Within the hybrid benchmarking method 1 (gate count analysis), we analytically derive the minimum number of gates that a quantum version of the classical simplex algorithm would require to solve realistic instances. By executing classical counterparts of the quantum subroutines, we infer the execution speed required per gate for the quantum simplex to outperform its classical counterpart. Within the hybrid benchmarking method 2 (query count analysis), we benchmark functional quantum linear solvers by analytically deriving a precise number of query calls made to the same oracles as a function of problem parameters. This provides insight into which algorithm might be more suitable in a given parameter regime. It allows for a direct comparison only between different quantum algorithms and is independent of classical runtime measurements. Within the hybrid benchmarking method 3 (cycle count analysis), we develop a runtime estimation framework tailored to the quantum tree generator–based search for solving 0-1-knapsack problems. We evaluate its performance on large scale instances beyond the reach of general simulation. We compare it with state-of-the-art classical linear programming solvers in terms of processor cycle counts. Hybrid benchmarking provides a fair, systematic benchmarking methodology, ensuring reproducible and relevant comparisons not only between classical and quantum approaches, but also among different quantum algorithms.
As quantum processors continue to scale in size and complexity, the need for well-defined, reproducible, and technology-agnostic performance metrics becomes increasingly critical. Here we present a suite of scalable quantum computing benchmarks developed as key performance indicators (KPIs) within the EU Quantum Flagship. These proposed benchmarks are designed to assess holistic system performance rather than isolated components, and to remain applicable across both noisy intermediate-scale quantum (NISQ) devices and future fault-tolerant architectures. We introduce four core benchmarks addressing complementary aspects of quantum computing capability: large multi-qubit circuit execution via a Clifford Volume benchmark, scalable multipartite entanglement generation through GHZ-state preparation, a benchmark based on the application of Shor's period-finding subroutine to simple functions, and a protocol quantifying the benefit of quantum error correction using Bell states. Each benchmark is accompanied by clearly specified protocols, reporting standards, and scalable evaluation methods. Together, these KPIs provide a coherent framework for transparent and fair performance assessment across quantum hardware platforms and for tracking progress late-NISQ toward early fault-tolerant quantum computation.
As quantum computing systems continue to mature, there is an increasing need for benchmarking methodologies that capture performance in terms of meaningful, application-level metrics. In this work, we present a scalable framework for application-level quantum benchmarking that is designed to support internal system evaluation and cross-platform comparison across technology providers. Our framework is guided by a set of core principles, including measurability, simplicity, scalability, and extensibility. We present 13 benchmark families that reflect realistic workloads across multiple domains. This enables the systematic evaluation of the quality of solutions, the total execution time, total used energy, as well as Time-to-Solution. The benchmarks are designed to be reproducible, interpretable across stakeholder groups, and adaptable to evolving system capabilities. The framework aims to bridge the gap between low-level performance metrics and real-world value, providing a unified approach to assessing quantum systems. The resulting benchmarks support development and validation and contribute to the foundation of industry-wide benchmarking standards.
Abstract The technological development of increasingly larger quantum processors on different quantum platforms raises the problem of how to fairly compare their performance, known as quantum benchmarking of quantum processors. This is a challenge that computer scientists have already faced when comparing classical processors, leading to the development of various mathematical tools to address it, but also to the identification of the limits of this problem. In this work, we briefly review the most important aspects of both classical processor benchmarks and the metrics comprising them, providing precise definitions and analyzing the quality attributes that they should exhibit. Subsequently, we analyze the intrinsic properties that characterize the paradigm of quantum computing and hinder the naive transfer of strategies from classical benchmarking. However, we can still leverage some of the lessons learned such as the quality attributes of a good benchmark such as relevance, reproducibility, fairness, verifiability and usability. Additionally, we review some of the most important metrics and benchmarks for quantum processors proposed in the literature, assessing what quality attributes they fulfill. Finally, we propose general guidelines for quantum benchmarking. These guidelines aim to pave the way for establishing a roadmap towards standardizing the performance evaluation of quantum devices, ultimately leading to the creation of an organization akin to the Standard Performance Evaluation Corporation (SPEC).