The Art of Quantum Computing for Finance: Brief Overview and Prospects

  1. Orson Mengara

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Abstract

This review article discusses the application of quantum computing to financial problems while presenting current approaches and their future prospects. We also talk about quantum machine learning and deep learning in finance. In the banking industry (Figure 9), we look at the most recent developments and the state of the art in quantum computing. Following a quick introduction to financial derivatives, we go over the key models and techniques for estimating the effects of quantum computing. The most popular quantum financial algorithms and their quantum adversary are then described. Lastly, we discuss the main problems that must be solved in order for quantum algorithms to truly benefit the financial industry.

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  1. PREreview

    This Zenodo record is a permanently preserved version of a Structured PREreview. You can view the complete PREreview at https://prereview.org/reviews/17636532.

    Does the introduction explain the objective of the research presented in the preprint? Yes The Introduction, along with the Abstract, clearly explains the objective of the research presented in the preprint. The Abstract characterizes the paper as a review article that discusses the application of quantum computing to financial problems, detailing current approaches, future prospects, and specifically addressing quantum machine learning and deep learning in finance, along with key models and techniques. The Introduction further narrows this scope by stating that the study is interested in the application of quantum computing in the financial sphere in a very broad way. This broad objective is then distilled into three explicit research questions (RQs) that the paper seeks to answer: identifying the most commonly used methods in quantum finance (RQ1), evaluating how the contributions of quantum approaches to finance are measured (RQ2), and discussing the gaps, challenges, open questions, and future prospects of quantum computing (RQ3).
    Are the methods well-suited for this research? Highly appropriate The methods implemented are well suited for the research objectives because the study is explicitly presented as a review article or survey that seeks to provide an overview of quantum computing applications in the financial sphere. The primary objective is to answer three specific research questions (RQs) concerning the most commonly used methods, how contributions are evaluated, and the gaps, challenges, and future prospects of quantum computing in finance. To address these questions, the methodology involved conducting systematic literature searches across various academic databases including PubMed, MDPI, SCOPUS, Nature, Science Direct, IEEE Xplore, ACM, and Google Scholar. This approach, utilizing specific keyword combinations like "Finance AND ("Quantum Finance" OR "Quantum Computing")" and selecting articles based on their publication dates, is appropriate for systematically gathering and synthesizing the existing academic knowledge necessary for a comprehensive survey.
    Are the conclusions supported by the data? Highly supported The conclusions of the preprint are supported by the synthesized data derived from its comprehensive literature review, which is characteristic of a survey article. The conclusion states that the field of quantum computing for finance is expanding quickly, a finding substantiated by the numerous applications and references cited throughout the paper covering areas such as risk management, fraud detection, asset pricing, and portfolio optimization. Furthermore, the conclusion that conceptual advancements promise large speedups for broadly applicable algorithms is supported by specific examples detailed in the text, such as the proposed quantum algorithm for pricing multi asset derivatives which offers an exponential acceleration of dimensionality compared to classical algorithms. Lastly, the cautionary conclusion that more experimental work is required before a universal quantum processor can outperform existing supercomputers is reinforced by the discussion on current hardware challenges, including the strict operational limit imposed by decoherence and the current reliance on Noisy Intermediate Scale Quantum (NISQ) processors.
    Are the data presentations, including visualizations, well-suited to represent the data? Highly appropriate and clear The data presentations are well suited for this technical review, which aims to survey the landscape of quantum computing in finance, primarily relying on structured organization and mathematical notation rather than traditional visualizations. The manuscript includes a Table 1, which serves as an effective organizational tool, systematically listing various quantum finance application areas such as transaction settlement, risk management, fraud detection, asset pricing, and portfolio optimization, alongside their corresponding reference citations, thereby clearly summarizing the reviewed literature. Furthermore, for a study focused on quantitative finance, the inclusion of detailed mathematical formulae, such as the multiple-asset Black-Scholes Partial Differential Equation, geometric Brownian motion processes, and optimization problems for trading and arbitrage, is highly appropriate for communicating the technical foundations and complexity of the models discussed.
    How clearly do the authors discuss, explain, and interpret their findings and potential next steps for the research? Very clearly The authors clearly discuss, explain, and interpret their findings by systematically structuring the review to answer the stated research questions concerning quantum computing applications in finance. They interpret the rapid expansion of the field based on conceptual advancements that promise large speedups for broadly applicable algorithms and experimental breakthroughs in quantum hardware. For example, the text explains that a proposed quantum algorithm for pricing multi asset derivatives using the finite difference method offers an exponential acceleration of dimensionality compared to classical algorithms, illustrating the potential for speedup. Regarding challenges and future steps, the authors explicitly discuss the strict operational limit imposed by decoherence in quantum hardware, noting that this challenge necessitates the use of Noisy Intermediate Scale Quantum (NISQ) processors and requires the development of higher fidelity qubits and error correction techniques. The ultimate viewpoint presented is that while the field is expanding quickly, more experimental work remains necessary before a universal quantum processor can definitively outperform existing supercomputers.
    Is the preprint likely to advance academic knowledge? Highly likely It offers a comprehensive and systematic survey of the rapidly expanding field of quantum computing in finance, structured around answering three specific research questions. The study significantly contributes to the existing body of knowledge by reviewing current approaches and future prospects, synthesizing information on the most common methods, evaluating how contributions are currently measured, and identifying gaps, challenges, and future prospects. Specifically, the review highlights conceptual advancements that promise large speedups for broadly applicable algorithms, such as a proposed quantum algorithm for pricing multi asset derivatives using the finite difference method, which offers an exponential acceleration of dimensionality compared to classical methods. Furthermore, it clearly outlines critical challenges facing the academic community, including the strict operational limit imposed by decoherence and the reliance on Noisy Intermediate Scale Quantum (NISQ) processors, thereby guiding necessary future experimental research before quantum processors can universally outperform classical supercomputers.
    Would it benefit from language editing? No The authors explicitly define their scope, pose specific research questions, and organize the paper logically, indicating that the overall presentation is clear and functional for the academic audience
    Would you recommend this preprint to others? Yes, it's of high quality This preprint is highly recommended, particularly for researchers and professionals interested in the intersection of quantum computing and financial recommended, particularly for researchers and professionals interested in the intersection of quantum computing and financial applications, as it substantially advances academic knowledge by providing a comprehensive survey of the field.
    Is it ready for attention from an editor, publisher or broader audience? Yes, as it is

    Competing interests

    The author declares that they have no competing interests.

    Use of Artificial Intelligence (AI)

    The author declares that they did not use generative AI to come up with new ideas for their review.

  2. Version published to 10.20944/preprints202507.2609.v3
  3. Version published to 10.20944/preprints202507.2609.v2
  4. Version published to 10.20944/preprints202507.2609.v1