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Archives of Computational Methods in Engineering

A Review of Quantum Scientific Computing Algorithms Relevant to Computational Mechanics

Osama M. Raisuddin, Suvranu De

Published Oct 1, 2025• 1 citation
Publisher
DOI
10.1007/s11831-025-10321-9

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Quantum physics has changed the way we understand our environment, and one of its branches, quantum mechanics, has demonstrated accurate and consistent theoretical results. Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles (photons, electrons, etc.) for subsequent use in performing calculations, as well as for large-scale information processing. These advantages are achieved through the use of quantum features, such as entanglement or superposition. These capabilities can give quantum computers an advantage in terms of computational time and cost over classical computers. Nowadays, scientific challenges are impossible to perform by classical computation due to computational complexity (more bytes than atoms in the observable universe) or the time it would take (thousands of years), and quantum computation is the only known answer. However, current quantum devices do not have yet the necessary qubits and are not fault-tolerant enough to achieve these goals. Nonetheless, there are other fields like machine learning, finance, or chemistry where quantum computation could be useful with current quantum devices. This manuscript aims to present a review of the literature published between 2017 and 2023 to identify, analyze, and classify the different types of algorithms used in quantum machine learning and their applications. The methodology follows the guidelines related to Systematic Literature Review methods, such as the one proposed by Kitchenham and other authors in the software engineering field. Consequently, this study identified 94 articles that used quantum machine learning techniques and algorithms and shows their implementation using computational quantum circuits or ansatzs. The main types of found algorithms are quantum implementations of classical machine learning algorithms, such as support vector machines or the k-nearest neighbor model, and classical deep learning algorithms, like quantum neural networks. One of the most relevant applications in the machine learning field is image classification. Many articles, especially within the classification, try to solve problems currently answered by classical machine learning but using quantum devices and algorithms. Even though results are promising, quantum machine learning is far from achieving its full potential. An improvement in quantum hardware is required for this potential to be achieved since the existing quantum computers lack enough quality, speed, and scale to allow quantum computing to achieve its full potential.

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MACHINE learning and Scientific Computing stand to gain significantly from Quantum Computing (QC), which holds promise to deliver new tools for solving complex and computationally demanding problems. Hardware-informed approaches, which attempt to lower the bar in resources required for the utilization of quantum paradigms, could accelerate such development. Simultaneously, as traditional workflows routinely employed in a number of applications evolve, so too do the opportunities for integrating quantum algorithms in the pipeline and unlock classical limitations. By developing the understanding for distinct advantages of quantum devices, new methods can emerge to enhance predictive accuracy, accelerate simulations, and uncover novel insights in scientific and industrial applications. However, limited resources offered by first generations of quantum devices typically necessitate of classical co-processing power, and require tailored software-hardware approach, often referred as ’co-design’. Furthermore, the nature of quantum computing and machine learning in science & technology applications increasingly call for methods that are physics-informed. This review explores the intersection of quantum computing and machine learning, with a particular emphasis on scientific machine learning (SciML). Unlike conventional machine learning, SciML is deeply rooted in formal and domain-specific constraints, making it an ideal candidate for quantum-enhanced approaches. Crucially, we argument how effective quantum algorithms need to both be aligned with the structures and requirements of targeted scientific problems, whilst carefully understanding the interplay between hardware and problem formulation. A key focus of this review is the role of neutral atomic quantum processors in advancing SciML. These platforms offer unique computational capabilities that remain under-explored compared to other quantum platforms. With their ability to naturally encode spatial and graph-based problems, neutral atom systems provide a promising avenue for tackling optimization and machine learning tasks that are particularly relevant in scientific computing. By highlighting in few examples the advantages and open questions surrounding these processors, we aim to present a forward-looking perspective on how quantum computing can reshape computational approaches in science and engineering.
Quantum physics has changed the way we understand our environment, and one of its branches, quantum mechanics, has demonstrated accurate and consistent theoretical results. Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles (photons, electrons, etc.) for subsequent use in performing calculations, as well as for large-scale information processing. These advantages are achieved through the use of quantum features, such as entanglement or superposition. These capabilities can give quantum computers an advantage in terms of computational time and cost over classical computers. Nowadays, scientific challenges are impossible to perform by classical computation due to computational complexity (more bytes than atoms in the observable universe) or the time it would take (thousands of years), and quantum computation is the only known answer. However, current quantum devices do not have yet the necessary qubits and are not fault-tolerant enough to achieve these goals. Nonetheless, there are other fields like machine learning, finance, or chemistry where quantum computation could be useful with current quantum devices. This manuscript aims to present a review of the literature published between 2017 and 2023 to identify, analyze, and classify the different types of algorithms used in quantum machine learning and their applications. The methodology follows the guidelines related to Systematic Literature Review methods, such as the one proposed by Kitchenham and other authors in the software engineering field. Consequently, this study identified 94 articles that used quantum machine learning techniques and algorithms and shows their implementation using computational quantum circuits or ansatzs. The main types of found algorithms are quantum implementations of classical machine learning algorithms, such as support vector machines or the k-nearest neighbor model, and classical deep learning algorithms, like quantum neural networks. One of the most relevant applications in the machine learning field is image classification. Many articles, especially within the classification, try to solve problems currently answered by classical machine learning but using quantum devices and algorithms. Even though results are promising, quantum machine learning is far from achieving its full potential. An improvement in quantum hardware is required for this potential to be achieved since the existing quantum computers lack enough quality, speed, and scale to allow quantum computing to achieve its full potential.