By Andre Costa, CAIA, MCSI, CFP®, ERP®, SCR, FDP & Oswaldo Zapata, PhD
In the dynamic environment of the modern financial industry, characterized by intense competition and evolving regulations, quantum computing holds great promise, as it is expected to surpass classical systems in both efficiency and security. We previously discussed some of the important foundations of quantum computing here. Some experts predict that finance may be one of the first industries to undergo a transformation driven by quantum computing. However, the timeline for the availability of fully functional quantum computers remains uncertain.
Remember that fully reliable, fault-tolerant quantum computers are still many years from being realized. We are in the so-called NISQ era, characterized by quantum devices that are relatively noisy and support only a limited number of quantum gates. As a result, researchers have focused on hybrid quantum-classical algorithms, which combine the strengths of both classical and quantum computing. In these hybrid models, quantum computers tackle the most computationally demanding parts of a problem, while classical computers handle the remaining tasks. This approach offers practical advantages, as the quantum subroutines require only a limited number of coherent qubits and shallow circuits, making them feasible with today’s quantum technology.
Quantum Portfolio Optimization
One of the key areas where quantum computing can improve upon classical methods is portfolio optimization. Traditional portfolio optimization techniques can struggle with large datasets, particularly when the portfolios are vast and require the processing of complex data. Variational quantum algorithms (VQAs), such as the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA), are believed to offer improvements by processing large datasets more efficiently than classical algorithms.
The VQE is an algorithm that leverages the variational principle of quantum mechanics to approximate solutions to the time-independent Schrödinger equation. This equation describes the behavior of complex quantum systems, such as molecules or the electronic configurations of materials. While VQE was originally developed for quantum chemistry applications, researchers have explored adapting it to represent the quantized version of certain classical problems, including portfolio optimization, by reformulating them as Hamiltonian minimization tasks. The QAOA is another variational algorithm, specifically designed to solve classical combinatorial optimization problems, such as portfolio optimization. What makes VQAs particularly compelling is that they are designed for hybrid classical-quantum computers. The quantum subroutine prepares quantum states and computes the Hamiltonian expectation values, while the classical computer performs the optimization process.
This hybrid approach makes VQAs suitable for solving complex problems that are challenging for purely classical systems, especially in domains like portfolio optimization. Although it is still uncertain whether VQAs will outperform classical algorithms, the potential for significant improvements in processing massive datasets and performing optimization tasks at a faster rate could open up new avenues in financial modeling and analysis.
It is widely believed that quantum computing will transform industries that rely on machine learning, and finance is one of the sectors most likely to experience this change. We have previously explored the foundational concepts of classical ML. In this section, we briefly address the main challenges quantum computing faces in enhancing and potentially revolutionizing classical ML techniques.
The primary challenge in quantum machine learning (QML) today lies in effectively encoding classical data into qubits so that the quantum computer can process it efficiently. Several methods have been developed to facilitate this encoding process, enabling quantum computers to perform computations on classical data.
Let us illustrate this with the simplest example. Suppose you have two classical data points, for example, two positive numbers, and you want to insert this information into a quantum computer to process them using the quantum algorithm you have designed. These classical data points must be transformed into quantum information that the quantum computer can understand. Perhaps the simplest way to encode these classical data points into a quantum state is by using the angles of a single qubit, a process known as angle encoding. As we mentioned when discussing qubits, a single qubit generally requires two complex numbers, which corresponds to four real numbers to fully specify it. However, by the principles of quantum mechanics, these four real numbers can be reduced to only two. The single qubit can thus be represented as a vector on the surface of a unit sphere. Since the position of any point on the sphere is completely determined by two angles, the azimuthal and polar angles, the single qubit is determined by these two angles. By properly rescaling if necessary, the original two classical data points can be encoded in the single qubit by rotating it accordingly. That is, the two data points can be encoded in the rotation angles of the single qubit. For more complex situations with many more classical data points, general multi qubits are necessary, but the principle remains the same. The real challenge lies in the implementation of these ideas in real-world scenarios.
In quantum machine learning, several algorithms have been developed to speed up learning tasks by processing vast amounts of data more efficiently than classical systems. These algorithms can be applied to a variety of ML problems, ranging from classification and regression to clustering and optimization. In the context of finance, quantum machine learning holds the potential to improve financial applications, as we discussed earlier when reviewing machine learning in finance.
It is worth noting that ML is a technology that was only recently incorporated into the financial sector, and QML is still in the early stages of research. As quantum technology progresses, it is expected that quantum algorithms will become increasingly capable of handling more complex data and providing substantial advantages over classical approaches.
As mentioned in the introduction, quantum computing is much more than the acceleration of computationally expensive problems; it also encompasses secure communication.
The issue is that sufficiently powerful quantum computers could break the current encryption methods used by most public institutions and private organizations, potentially gaining access to sensitive data, such as military and financial information. The threat posed by quantum computers is a reality that governments and financial institutions are taking very seriously. Let us discuss these concepts.
An encryption method is a process that transforms information into a form that is not easily linked to the original. The original form is referred to as plaintext, while the transformed version is known as ciphertext. Most contemporary digital encryption standards are based on mathematical problems that are difficult for classical computers to solve. However, quantum algorithms have the potential to solve some of these problems efficiently. For example, RSA, widely used to secure digital data over the internet, relies on the difficulty of integer factorization, while ECC (Elliptic Curve Cryptography) is based on the discrete logarithm problem. The concern is that Shor’s algorithm, a quantum algorithm, can efficiently solve both of these problems. Once sufficiently large quantum computers become available—potentially within the next 5 to 10 years—these encryption systems could be broken in a relatively short period of time. These two examples represent some of the most vulnerable encryption standards in the quantum era. This is why governments worldwide are enacting laws to secure sensitive data.
Post-quantum cryptography (PQC) is one potential solution. It involves the development and implementation of a set of encryption methods based on mathematical problems designed to remain secure against both classical computers and quantum algorithms running on quantum computers. These algorithms are based on mathematical problems that are not known to be efficiently solvable by quantum algorithms such as Shor’s and Grover’s. Examples of such problems include lattice problems, multivariate polynomials, code-based schemes, and hash-based signatures. The National Institute of Standards and Technology (NIST) has recently standardized several PQC algorithms to either supplement or completely replace existing cryptographic systems. NIST has determined that, by 2030, federal agencies should treat current standard encryption methods as vulnerable, and by 2035, these methods are expected to be phased out. However, financial institutions have not yet established a timeline for transitioning to post-quantum cryptography.
Quantum Key Distribution (QKD) is considered among the most secure ways to share encryption keys—not because it depends on the difficulty of solving large mathematical problems, but because it leverages the fundamental principles of quantum physics. Two features are central to its security: the no-cloning theorem, which prevents perfect copying of a quantum state, and the fact that any measurement inevitably alters the state being measured. Together, these properties make eavesdropping detectable in theory.
Despite its robust theoretical foundations, QKD faces practical hurdles. It demands costly, specialized equipment and is limited in range, making it impractical for widespread use. For now, it is most applicable in highly sensitive environments—such as government communications or specialized segments of the financial industry—where dedicated infrastructure is both justified and affordable.
For large-scale financial institutions, moving entirely to quantum-secure systems will require significant investment and time. A practical first step is the adoption of hybrid cryptography—systems that combine today’s established classical encryption methods with quantum-resistant algorithms designed to withstand attacks from future quantum computers. This approach provides a bridge between current capabilities and full quantum readiness, offering protection against both existing threats and those on the horizon.
The Trajectory of Quantum Computing
Quantum computing remains in the research phase, but its trajectory is unmistakable. While today’s practical advantages are modest, the technology holds immense promise for tackling the most computationally demanding problems in fields ranging from pharmaceuticals to logistics—and, importantly, finance.
In finance, quantum methods could accelerate portfolio optimization and enhance a wide range of services currently powered by machine learning. One particularly active research avenue is quantum-enhanced Monte Carlo simulation. While performance gains for variational quantum algorithms and quantum machine learning are still unproven, quantum Monte Carlo is backed by mathematical proofs that it can enhance crucial parts of the process.
Still, the road ahead isn’t without obstacles. Quantum systems remain sensitive to noise, and error rates are a persistent challenge. Yet, advances in both hardware and algorithms are arriving steadily, and the momentum is undeniable. Quantum computation and quantum communication are evolving in parallel, not only in theory but in the push toward real-world applications.
As quantum hardware grows more powerful in the coming years, finance will likely be among the industries leading its adoption. The future for quantum technology in this sector isn’t just promising—it’s thrilling.
About the Contributors
André Costa, CAIA and Oswaldo Zapata, PhD in Theoretical Physics are the Founders of The Quantum Finance Boardroom (TQFB Community). André Costa, CAIA, is the co-founder of The Quantum Finance Boardroom (TQFB Community), as well as the founder of Free Enterprise Advisors in Brazil. Born in 1968, in Brazil, Costa graduated in veterinary medicine from Universidade Federal de Goiás in Goiânia, GO, in 1992. He is a CTA - Commodity Trading Advisor, registered with the CFTC and a member of the NFA, is registered as Investment Advisor with both the SEC in the U.S. and the CVM in Brazil.
Dr. Oswaldo Zapata is a specialist in quantum computing for finance, passionate about bridging the gap between theoretical financial solutions and their practical applications for finance professionals. This passion has led him to author several eBooks on the topic and educational materials, from introductory to advanced levels. He actively engages with professionals worldwide on LinkedIn and co-founded The Quantum Finance Boardroom, an online community where leading finance and quantum experts exchange ideas, collaborate, and explore new business opportunities. He holds a PhD in theoretical physics and lives in Dubai.
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