Quantum Finance: Toward a Reconfiguration of Market Engineering?

The roll-out of quantum technologies (2) offers potential solutions to problems whose complexity overwhelms conventional processing capabilities. Financial institutions are hampered by the limitations of traditional computing architectures when it comes to optimising portfolios with a large number of assets and complex constraints (limits, exclusions, etc.), modelling sophisticated derivatives or projecting extreme risk scenarios (3).

These operations require a certain precision in execution and a level of computing power that is driving the industry towards alternative paradigms. By utilising superposition to process a variety of configurations, the interference between superimposed states to direct probabilities towards the most relevant configurations, and entanglement to synchronise the interdependencies between variables, this system could transform current decision-making methods (4).

However, this shift requires an assessment of the practical benefits in light of the technical and methodological constraints inherent in these new tools. In an interview with Polytechnique Insights (1), Lionel Martellini, Professor of Finance at EDHEC Business School and founder and director of the EDHEC Quantum Institute (5), shares his expertise on the integration of these algorithms into security selection, portfolio construction and risk management. His work focuses in particular on measuring the added value of these innovations within financial processes and on the conditions for their viability within market structures.

The question of how mature these technologies are within the financial ecosystem remains a key issue. It is important to distinguish between applications that are likely to deliver measurable progress, to identify the factors that are slowing down their roll-out, and to define the scientific steps required before they can be put into everyday use. The tension between current research capabilities and the reliability requirements specific to field operations thus constitutes the point of convergence between laboratory hypotheses and the imperatives of the sector (6).

High-Performance Computing: Tackling Financial Complexities

Financial markets involve operations whose computational intensity is constantly increasing. Whether structuring multi-asset portfolios, valuing derivatives with non-linear profiles or modelling stress scenarios, traditional architectures are reaching a saturation point as the scale of the problems grows (8).

In Quantum speedup of Monte Carlo methods, Ashley Montanaro demonstrates that the quantum amplitude estimation algorithm offers a significant theoretical acceleration of Monte Carlo methods, which are essential for the pricing of derivative assets and risk management (9). His work demonstrates that, for a given target level of accuracy, the volume of simulations required is reduced quadratically compared to conventional approaches. This efficiency gain makes it possible to envisage a reduction in the computational cost of complex financial calculations, provided that fault-tolerant quantum computers and models compatible with the algorithm’s requirements are available (10).

According to Lionel Martellini, “a true quantum advantage lies in improving a portfolio’s profitability, or reducing its risk, in such a way as to generate an economic gain that outweighs the additional costs incurred by the quantum solution”. He confirms the need to measure the concrete contribution of these technologies beyond mere gains in speed, noting that “it is essential to consider the costs before concluding that there is a quantum advantage”. Indeed, the investments required for these ecosystems remain substantial.

In portfolio optimisation, risk management models struggle to cope with the exponential growth in the number of asset combinations (11). Regarding valuation, Martellini points out that “the central problem is calculating the expected payoff under a risk-adjusted probability, often via Monte Carlo simulations” and that “the quantum amplitude estimation algorithm (QAI) offers a quadratic gain: the pricing error decreases more rapidly, which reduces the number of trajectories required”. However, financial viability remains the ultimate test: “Technologically speaking, the benefit is clear, but the economic advantage remains to be assessed in light of the costs of accessing quantum computers, including their energy consumption.”

Epistemology of usage: the relevance of models and algorithmic deviations

The value of quantum processors in portfolio optimisation is most evident in environments characterised by high dimensionality and changing data structures. “When there are few parameters and they are stationary, conventional methods suffice. Small problems can be solved with simple, inexpensive tools,” states the researcher. The usefulness of quantum approaches becomes apparent when the dynamic complexity of the flows overwhelms the capabilities of conventional methods (12).

Nevertheless, research must avoid use cases that are disconnected from real-world needs. Martellini warns against “combining security selection and the optimisation of the portfolio’s risk-adjusted return into a single problem. This creates a combinatorial complexity that artificially highlights a quantum advantage”. Asset selection must meet clear financial objectives: “It may be driven by performance, by comparing the market price to ‘fair value’, or by risk, for example by seeking a portfolio with low correlation.”

Quantum washing refers to a methodological pitfall that involves attributing a quantum advantage to problems formulated in an excessively complex manner. This trend undermines the credibility of solutions and, consequently, their adoption. Indeed, according to Lionel Martellini, “there is a tendency to artificially construct use cases to highlight the advantages of quantum computing. This gives the impression of a solution desperately seeking a problem, or a disproportionately large hammer looking for nails to hammer”.

This bias can lead to conclusions that are promising but impractical. “Even when a problem is real,” he continues, “there is a risk of exaggerating the supposed benefits. The benefits presented often depend on unstated assumptions regarding the maturity of the technology or the actual cost.”

Material realities and pathways towards the hybridisation of systems

The integration of quantum technology into finance faces constraints that go beyond mere raw power, notably technological maturity and cybersecurity. Current machines (NISQ – see box) operate using components that are still unstable. “Current quantum computers are still too limited for widespread use,” Martellini points out. The benefits in real-world conditions depend on a more stable technological landscape, known as fault-tolerant (6).

The financial aspect is just as crucial: “Some machines will cost tens of millions, others hundreds of millions, or even billions,” points out Martellini, adding that “the cost-effectiveness of these machines and their energy consumption, whether used in a shared or dedicated cloud environment, will be decisive factors. ” Furthermore, the processing of sensitive data requires stringent encryption protocols and meticulous monitoring of cloud infrastructures.

As a result, the technology is seen as a complementary layer to existing systems. “Today, hybrid approaches are the most realistic route,” says the professor of finance. He also mentions “quantum-inspired simulators, such as digital annealers or methods based on tensor networks”. These tools allow experimentation without the constraints of physical qubits. Furthermore, “whilst the standalone quantum computer remains a medium-term goal, in the short and medium term, it is classical-quantum hybrid architectures that represent the most realistic approach to achieving usable results”. This transition enables targeted gains to be realised and use cases to be explored whilst managing operational risks.

References

(1) Finance quantique : vers une reconfiguration de l’ingénierie de marché ? (mars 2026) Lionel Martellini, EDHEC, in Polytechnique Insights - https://www.polytechnique-insights.com/tribunes/science/finance-quantique-vers-une-reconfiguration-de-lingenierie-de-marche/

(2) Quantum finance: the experimental application of quantum computing principles and algorithms to complex financial problems, with the aim of processing a large number of scenarios simultaneously.

(3) Gorbanyov, Michael, Malaika, Majid, Sedik, Tahsin Saadi, 2021, Quantum Computing and the Financial System : Spooky Action at a Distance ?, IMF Working Paper 2021 071, International Monetary Fund - https://www.imf.org/en/publications/wp/issues/2021/03/12/quantum-computing-and-the-financial-system-spooky-action-at-a-distance-50159

(4) Nielsen, Michael A., Chuang, Isaac L., 2000, Quantum Computation and Quantum Information - https://michaelnielsen.org/qcqi/QINFO-book-nielsen-and-chuang-toc-and-chapter1-nov00.pdf

(5) The EDHEC Quantum Institute (EQI), founded and directed by Lionel Martellini, a professor at EDHEC and former director of the EDHEC-Risk Institute, aims to help organisations and society as a whole understand the transformations brought about by the second quantum revolution - https://www.edhec.edu/en/research-and-faculty/centres-and-chairs/edhec-quantum-institute

(6) OECD, 2025, A quantum technologies policy primer - https://www.oecd.org/content/dam/oecd/en/publications/reports/2025/01/a‑quantum-technologies-policy-primer_bdac5544/fd1153c3-en.pdf

(7) A qubit, or quantum bit, is the equivalent of a bit (the basic unit of information in classical computing) in quantum computing. Whilst a classical bit is either 0 or 1, a qubit can exist in a superposition of both states at the same time. This property enables quantum computers to explore multiple possibilities simultaneously during a calculation.

(8) Jiawei Zhou, 2025, Quantum Finance : Exploring the Implications of Quantum Computing on Financial Models Computational Economics, Springer - https://link.springer.com/article/10.1007/s10614-025-10894-4

(9) Quantum speedup of Monte Carlo methods, Proceedings of the Royal Society A, 2015 - https://royalsocietypublishing.org/rspa/article/471/2181/20150301/57575/Quantum-speedup-of-Monte-Carlo-methodsQuantum

(10) Abha Satyavan Naik, Glenda Cox, Colin de la Higuera, 2025, From portfolio optimization to quantum blockchain and security : a systematic review of quantum computing in finance, Financial Innovation, Springer Nature - https://link.springer.com/article/10.1186/s40854-025-00751-6

(11) Farhi, Edward ; Goldstone, Jeffrey ; Gutmann, Sam, 2014, A Quantum Approximate Optimization Algorithm, arXiv - https://arxiv.org/pdf/1411.4028. Techniques such as approximate quantum optimisation algorithms (QAOA) and QUBO formulations offer promising avenues for exploring these data spaces more intelligently, particularly for combinatorial problems where the objective is to identify optimal configurations subject to constraints, as these methods have been specifically developed to efficiently explore high-dimensional optimisation landscapes

(12) Preskill, John, 2018, Quantum Computing in the NISQ era and beyond, Quantum, Volume 2 https://quantum-journal.org/papers/q‑2018–08-06–79/pdf/