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arXiv:2507.06758 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Predict and Conquer: Navigating Algorithm Trade-Offs with Quantum Design Automation

Simon Thelen, Wolfgang Mauerer

Published Aug 30, 2025• 2 citations
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Abstract

Combining quantum computers with classical compute power has become a standard means for developing algorithms and heuristics that are, eventually, supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or runtime are expected for increasingly many approaches, substantial challenges remain: Non-functional properties like runtime or solution quality of many suggested approaches are not yet fully understood, and need to be explored empirically. This, in turn, makes it unclear which approach is best suited for a given problem. Accurately predicting behaviour and properties of quantum-classical algorithms opens possibilities for software abstraction layers, which in turn can automate decisionmaking for algorithm selection and parametrisation. While such techniques find frequent use in classical high-performance computing, they are still mostly absent from quantum software toolchains. In this paper, we present a methodology (accompanied by a reproducible reference implementation) to perform algorithm selection based on desirable non-functional requirements. This greatly simplifies decision-making processes for end users. Based on meta-information annotations at the source code level, our framework traces key characteristics of quantum-classical heuristics and algorithms, and uses this information to predict the most suitable approach and its parameters for given computational challenges and their non-functional requirements. As combinatorial optimisation is a very extensively studied aspect of quantumclassical systems, we perform a comprehensive case study based on numerical simulations of algorithmic approaches to implement and validate our ideas. We develop statistical models to quantify the influence of various factors on non-functional properties, and establish predictions for optimal algorithmic choices without manual user effort. We argue that our methodology generalises to problem classes beyond combinatorial optimisation, such as Hamiltonian optimisation, and lays a foundation for integrated software layers for quantum design automation.

DOI
10.1109/qce65121.2025.00071

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Combining quantum computers with classical compute power has become a standard means for developing algorithms and heuristics that are, eventually, supposed to beat any purely classical alternatives. While in-principle advantages for solution quality or runtime are expected for increasingly many approaches, substantial challenges remain: Non-functional properties like runtime or solution quality of many suggested approaches are not yet fully understood, and need to be explored empirically. This, in turn, makes it unclear which approach is best suited for a given problem. Accurately predicting behaviour and properties of quantum-classical algorithms opens possibilities for software abstraction layers, which in turn can automate decisionmaking for algorithm selection and parametrisation. While such techniques find frequent use in classical high-performance computing, they are still mostly absent from quantum software toolchains. In this paper, we present a methodology (accompanied by a reproducible reference implementation) to perform algorithm selection based on desirable non-functional requirements. This greatly simplifies decision-making processes for end users. Based on meta-information annotations at the source code level, our framework traces key characteristics of quantum-classical heuristics and algorithms, and uses this information to predict the most suitable approach and its parameters for given computational challenges and their non-functional requirements. As combinatorial optimisation is a very extensively studied aspect of quantumclassical systems, we perform a comprehensive case study based on numerical simulations of algorithmic approaches to implement and validate our ideas. We develop statistical models to quantify the influence of various factors on non-functional properties, and establish predictions for optimal algorithmic choices without manual user effort. We argue that our methodology generalises to problem classes beyond combinatorial optimisation, such as Hamiltonian optimisation, and lays a foundation for integrated software layers for quantum design automation.
Combining quantum and classical computing is expected to beat purely classical approaches for specific use cases. Howver, non-functional properties like runtime or solution quality of many quantum-classical algorithms can only be measured empirically, which makes finding the best approach for a given problem difficult. Predicting behaviour of quantum-classical algorithms opens possibilities for software abstraction layers, which in turn can automate decision-making for algorithm selection and parametrisation. These techniques are common in classical computing but still mostly absent in quantum toolchains. This work, originally published at the IEEE Conference on Quantum Computing and Engineering (QCE) 2025 [TM25], presents a methodology for automatic quantum algorithm selection based on non-functional requirements, simplifying decision-making for end users. Based on meta-information annotations at the source code level, our framework traces key characteristics of quantum-classical algorithms to predict the best approach and its parameters for a given problem and non-functional requirements. To validate our ideas, we perform a comprehensive case study for combinatorial optimisation and develop statistical predictors for algorithmic behaviour to automatically choose the best algorithm for a given scenario.
The quantum approximate optimisation algorithm (QAOA) and its variants are at the core of many scenarios that aim at combining the power of quantum computers (QC) and classical high-performance computing (HPC) appliances for combinatorial optimisation. Several obstacles challenge concrete benefits now and in the foreseeable future: Imperfections quickly degrade algorithmic performance below practical utility; over-heads arising from alternating between classical and quantum primitives can counter any advantage; and the choice of parameters or algorithmic variant can substantially influence runtime and result quality. Selecting the appropriate combination is a non-trivial issue, as it not only depends on end-user requirements, but also on details of the hardware and software stack. Appropriate automation can alleviate the burden of choosing optimal combinations for end-users: They should not be required to understand technicalities like detail differences between QAOA variants, required number of QAOA layers, or necessary measurement samples. Yet, they should receive the best possible satisfaction of their non-functional requirements, be it performance or other. We determine factors that influence approximation quality and temporal behaviour of four QAOA variants using comprehensive density-matrix-based numerical simulations targeting three widely studied optimisation problems. Our simulations consider ideal quantum computation, and a continuum of scenarios troubled by realistic imperfections. Our quantitative results, accompanied by a comprehensive reproduction package, show strong performance differences between QAOA variants that can be pinpointed to narrow and specific effects. We identify influential co-variables and relevant non-functional quality goals that, as we argue, mark the rele-vant ingredients for designing appropriate software engineering abstraction mechanisms and automated tool-chains for devising quantum solutions from higher-level problem specifications.
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Solving real-world optimization problems with quantum computing requires choosing between a large number of options concerning formulation, encoding, algorithm and hardware. Finding good solution paths is challenging for end users and researchers alike. We propose a framework designed to identify and recommend the best-suited solution paths in an automated way. This introduces a novel abstraction layer that is required to make quantum-computing-assisted solution techniques accessible to end users without requiring a deeper knowledge of quantum technologies. State-of-the-art hybrid algorithms, encoding and decomposition techniques can be integrated in a modular manner and evaluated using problem-specific performance metrics. Equally, tools for the graphical analysis of variational quantum algorithms are developed. Classical, fault tolerant quantum and quantum-inspired methods can be included as well to ensure a fair comparison resulting in useful solution paths. We demonstrate and validate our approach on a selected set of options and illustrate its application on the capacitated vehicle routing problem (CVRP). We also identify crucial requirements and the major design challenges for the proposed abstraction layer within a quantum-assisted solution workflow for optimization problems.
This paper presents a comprehensive theoretical framework that unifies various hybrid quantumclassical optimization approaches for combinatorial problems. Building upon recent advances in Quantum Approximate Optimization Algorithm (QAOA) and quantum-enhanced heuristics, we establish a mathematical foundation that connects amplitude amplification, counterdiabatic annealing, and classical relaxation techniques. We derive general convergence criteria and performance bounds for hybrid algorithms, demonstrating how quantum subroutines can be systematically integrated with classical optimization methods. The framework encompasses both unconstrained and constraint-preserving formulations, providing theoretical guarantees for problem classes including graph optimization, scheduling, and resource allocation. We analyze the trade-offs between quantum circuit depth, classical preprocessing overhead, and solution quality, establishing conditions under which exponential or polynomial speedups can be achieved. Our theoretical analysis reveals fundamental limitations and opportunities in hybrid algorithm design, offering guidelines for selecting appropriate quantum-classical decompositions based on problem structure. This work contributes to the growing understanding of quantum advantage in optimization and provides a roadmap for developing provably efficient hybrid algorithms across diverse application domains.
Recent progress has brought benchmarking of (heuristic) quantum algorithms at scale within reach. Particularly in combinatorial optimization, it is key to empirically analyze and track progress towards quantum advantage. This work introduces a systematic, fair and comparable benchmarking framework for quantum optimization methods by presenting ten model-independent problem classes that are challenging for classical methods. Track records of specific instances and solutions are given in an accompanying open-source repository. While the individual properties of the problem classes vary, they all become challenging from less than 100 to, at most, an order of 100,000 decision variables. We reference results from state-of-the-art solvers for instances across all problem classes and demonstrate exemplary baseline results obtained with quantum solvers for selected problems, which illustrate standardized benchmark reporting. The presented problem instances may be approached with classical or quantum algorithms executed on varying hardware platforms to drive the field towards quantum advantage.