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arXiv:2408.03613 · IEEE International Conference on Quantum Computing and Engineering (QCE)

A Predictive Approach for Selecting the Best Quantum Solver for an Optimization Problem

Deborah Volpe, Nils Quetschlich, Mariagrazia Graziano, Giovanna Turvani, Robert Wille

Published Sep 15, 2024• 5 citations
arXivHTMLPDF

Abstract

Leveraging quantum computers for optimization problems holds promise across various application domains. Nevertheless, utilizing respective quantum computing solvers requires describing the optimization problem according to the Quadratic Unconstrained Binary Optimization (QUBO) formalism and selecting a proper solver for the application of interest with a reasonable setting. Both demand significant proficiency in quantum computing, QUBO formulation, and quantum solvers, a background that usually cannot be assumed by end users who are domain experts rather than quantum computing specialists. While tools aid in QUBO formulations, support for selecting the best-solving approach remains absent. This becomes even more challenging because selecting the best solver for a problem heavily depends on the problem itself. In this work, we are accepting this challenge and propose a predictive selection approach, which aids end users in this task. To this end, the solver selection task is first formulated as a classification task that is suitable to be solved by supervised machine learning. Based on that, we then propose strategies for adjusting solver parameters based on problem size and characteristics. Experimental evaluations, considering more than 500 different QUBO problems, confirm the benefits of the proposed solution. In fact, we show that in more than 70% of the cases, the best solver is selected, and in about 90% of the problems, a solver in the top two, i.e., the best or its closest suboptimum, is selected. This exploration proves the potential of machine learning in quantum solver selection and lays the foundations for its automation, broadening access to quantum optimization for a wider range of users. The pre-trained classifier is integrated into the MQT Quantum Auto Optimizer (MQT QAO) framework, publicly available on GitHub (https://github.com/cda-tum/mqt-qao) as part of the Munich Quantum Toolkit (MQT).

DOI
10.1109/qce60285.2024.00121

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Leveraging quantum computers for optimization problems holds promise across various application domains. Nevertheless, utilizing respective quantum computing solvers requires describing the optimization problem according to the Quadratic Unconstrained Binary Optimization (QUBO) formalism and selecting a proper solver for the application of interest with a reasonable setting. Both demand significant proficiency in quantum computing, QUBO formulation, and quantum solvers, a background that usually cannot be assumed by end users who are domain experts rather than quantum computing specialists. While tools aid in QUBO formulations, support for selecting the best-solving approach remains absent. This becomes even more challenging because selecting the best solver for a problem heavily depends on the problem itself. In this work, we are accepting this challenge and propose a predictive selection approach, which aids end users in this task. To this end, the solver selection task is first formulated as a classification task that is suitable to be solved by supervised machine learning. Based on that, we then propose strategies for adjusting solver parameters based on problem size and characteristics. Experimental evaluations, considering more than 500 different QUBO problems, confirm the benefits of the proposed solution. In fact, we show that in more than 70% of the cases, the best solver is selected, and in about 90% of the problems, a solver in the top two, i.e., the best or its closest suboptimum, is selected. This exploration proves the potential of machine learning in quantum solver selection and lays the foundations for its automation, broadening access to quantum optimization for a wider range of users. The pre-trained classifier is integrated into the MQT Quantum Auto Optimizer (MQT QAO) framework, publicly available on GitHub (https://github.com/cda-tum/mqt-qao) as part of the Munich Quantum Toolkit (MQT).
Optimizing objective functions stands to benefit significantly from leveraging quantum computers, promising enhanced solution quality across various application domains in the future. However, harnessing the potential of quantum solvers necessitates formulating problems according to the Quadratic Unconstrained Binary Optimization (QUBO) model, demanding significant expertise in quantum computation and QUBO formulations. This expertise barrier limits access to quantum solutions. Fortunately, automating the conversion of conventional optimization problems into QUBO formulations presents a solution for promoting accessibility to quantum solvers. This article addresses the unmet need for a comprehensive automatic framework to assist users in utilizing quantum solvers for optimization tasks while preserving interfaces that closely resemble conventional optimization practices. The framework prompts users to specify variables, optimization criteria, as well as validity constraints and, afterwards, allows them to choose the desired solver. Subsequently, it automatically transforms the problem description into a format compatible with the chosen solver and provides the resulting solution. Additionally, the framework offers instruments for analyzing solution validity and quality. Comparative analysis against existing libraries and tools in the literature highlights the comprehensive nature of the proposed framework. Two use cases (the knapsack problem and linear regression) are considered to show the completeness and efficiency of the framework in real-world applications. Finally, the proposed framework represents a significant advancement towards automating quantum computing solutions and widening access to quantum optimization for a broader range of users. The framework is publicly available on GitHub (https://github.com/cda-tum/mqt-qao) as part of the Munich Quantum Toolkit (MQT).
With the applications of quantum computing becoming more and more widespread, finding ways that allow end users without experience in the field to apply quantum computers to solve their individual problems is becoming a crucial task. However, current optimization algorithms require problem instances to be posed in complex formats that are challenging to formulate, even for experts. In particular, the Quadratic Unconstrained Binary Optimization (QUBO) formalism employed by many quantum optimization algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA), involves the mathematical rewriting of constraints under strict conditions. To facilitate this process, we propose a framework to automatically generate QUBO formulations for pathfinding problems. This framework allows users to translate their specific problem instances into formulations that can be passed directly to quantum algorithms for optimization without requiring any expertise in the field of quantum computing. It supports three different encoding schemes that can easily be compared without requiring manual reformulation efforts. The resulting QUBO formulations are robust and efficient, reducing the previously tedious and error-prone reformulation process to a task that can be completed in a matter of seconds. In addition to an open-source Python package available on https://github.com/munich-quantum-toolkit/problemsolver, we also provide a graphical user interface accessible through the web (https://munich-quantum-toolkit.github.io/problemsolver/), which can be used to operate the framework without requiring the end user to write any code.
Any potential application of quantum computing, once encoded as a quantum circuit, needs to be compiled in order to be executed on a quantum computer. Deciding which qubit technology, which device, which compiler, and which corresponding settings are best for the considered problem—according to a measure of goodness—requires expert knowledge and is overwhelming for end-users from different domains trying to use quantum computing to their advantage. In this work, we treat the problem as a statistical classification task and explore the utilization of supervised machine learning techniques to optimize the compilation of quantum circuits. Based on that, we propose a framework that, given a quantum circuit, predicts the best combination of these options and, therefore, automatically makes these decisions for end-users. Experimental evaluations show that, considering a prototypical setting with 3000 quantum circuits, the proposed framework yields promising results: for more than three quarters of all unseen test circuits, the best combination of compilation options is determined. Moreover, for more than 95% of the circuits, a combination of compilation options within the top-three is determined—while the median compilation time is reduced by more than one order of magnitude. Furthermore, the resulting methodology not only provides end-users with a prediction of the best compilation options, but also provides means to extract explicit knowledge from the machine learning technique. This knowledge helps in two ways: it lays the foundation for further applications of machine learning in this domain and, also, allows one to quickly verify whether a machine learning algorithm is reasonably trained. The corresponding framework and the pre-trained classifier are publicly available on GitHub (https://github.com/cda-tum/MQTPredictor) as part of the Munich Quantum Toolkit (MQT).
Fueled by recent accomplishments in quantum computing hardware and software, an increasing number of problems from various application domains are being explored as potential use cases for this new technology. Similarly to classical computing, realizing an application on a particular quantum device requires the corresponding (quantum) circuit to be compiled so that it can be executed on the device. With a steadily growing number of available devices—each with their own advantages and disadvantages—and a wide variety of different compilation tools, the number of choices to consider when trying to realize an application is quickly exploding. Due to missing tool support and automation, especially end-users who are not quantum computing experts are easily left unsupported and overwhelmed. In this work, we propose a methodology that allows one to automatically select a suitable quantum device for a particular application and provides an optimized compiler for the selected device. The resulting framework—called the MQT Predictor —not only supports end-users in navigating the vast landscape of choices, it also allows mixing and matching compiler passes from various tools to create optimized compilers that transcend the individual tools. Evaluations of an exemplary framework instantiation based on more than 500 quantum circuits and seven devices have shown that—compared with both Qiskit’s and TKET’s most optimized compilation flows for all devices—the MQT Predictor produces circuits within the top-3 out of 14 baselines in more than 98% of cases while frequently outperforming any tested combination by up to 53% when optimizing for expected fidelity . Additionally, the framework is trained and evaluated for critical depth as another figure of merit to showcase its flexibility and generalizability—producing circuits within the top-3 in 89% of cases while frequently outperforming any tested combination by up to 400%. MQT Predictor is part of the Munich Quantum Toolkit (MQT) and publicly available as open-source on GitHub ( https://github.com/cda-tum/mqt-predictor ) and as an easy-to-use Python package ( https://pypi.org/p/mqt.predictor ).
The Quantum Approximate Optimization Algorithm (QAOA) requires considered optimization problems to be translated into a compatible format. A popular transformation step in this pipeline involves the quadratization of higher-order binary optimization problems, translating them into Quadratic Unconstrained Binary Optimization (QUBO) formulations through the introduction of auxiliary variables. Conventional algorithms for the selection of auxiliary variables often aim to minimize the total number of required variables without taking the constraints of the underlying quantum computer-in particular, the connectivity of its qubits-into consideration. This quickly results in interaction graphs that are incompatible with the target device, resulting in a substantial compilation overhead even with highly optimized compilers. To address this issue, this work presents a novel approach for the selection of auxiliary variables tailored for architectures with limited connectivity. By specifically constructing an interaction graph with a regular structure and a limited maximal degree of vertices, we find a way to construct QAOA circuits that can be mapped efficiently to a variety of architectures. We show that, compared to circuits constructed from a QUBO formulation using conventional auxiliary selection methods, the proposed approach reduces the circuit depth by almost 40%. An implementation of all proposed methods is publicly available at https://github.com/munich-quantum-toolkit/problemsolver.
Optimization is a crucial challenge across various domains, including finance, resource allocation, and mobility. Quantum computing has the potential to redefine the way we handle complex problems by reducing computational complexity and enhancing solution quality. Optimization, particularly of objective functions, stands to benefit significantly from quantum solvers, which leverage principles of quantum mechanics like superposition, entanglement, and tunneling. The Ising and Quadratic Unconstrained Binary Optimization (QUBO) models are the most suitable formulations for these solvers, involving binary variables and constraints treated as penalties within the overall objective function. To harness quantum approaches for optimization, two primary strategies are employed: exploiting quantum annealers—special-purpose optimization devices—and designing algorithms based on quantum circuits. This review provides a comprehensive overview of quantum optimization methods, examining their advantages, challenges, and limitations. It demonstrates their application to real-world scenarios and outlines the steps to convert generic optimization problems into quantum-compliant models. Lastly, it discusses available tools and frameworks that facilitate the exploration of quantum solutions for optimization tasks.