Quantum Computing in Financial Risk Management

Emerging discipline

Quantum computing has recently emerged as a key driving force behind the modern technological change, revolutionising the approach to solving tremendously complex problems. By harnessing the mechanics of subatomic particles, it offers incredible opportunities with respect to navigating through massively complicated systems as well as speeding up existing algorithms. Its high efficiency, which outperforms even that of supercomputers, has grasped the attention of the scientific milieu and found a wide variety of applications in different disciplines, including pharmaceuticals, chemistry and, of course, finance. One particular application which is a source of great excitement in the financial industry is that related to risk management. From more precise pricing of financial derivatives to more reliable quantifications of risk, quantum computing carries an abundance of possibilities for boosting the financial risk oversight in today's increasingly interconnected and complex markets.

The fundamentals of quantum computing

Quantum computing relies on basic units of information called quantum bits, in short referred to as qubits. Qubits, unlike regular bits, which store information strictly in a binary system, can assume the state of superposition of 0 and 1 (representing a combination of possibilities). This property makes it possible for quantum computers to perform parallel computations on a vast scale, considerably improving efficiency of operations and reducing the time needed to solve complex problems. Another characteristic of quantum mechanics which boosts the appeal of quantum computing is entanglement, which refers to the interdependence of states of qubits belonging to the same system. More precisely, it means that the states of the two qubits cannot be described individually, but rather remain intrinsically linked - entangled, as the name suggests. Regardless of the separation of qubits, the measurement of one collapses the entire system into a definite state. Hence, what Einstein once dubbed "the spooky action at a distance", today makes it possible to process highly interconnected and complex information.

One other advantage of quantum computing over its classical form is its property of reversibility. While classical computing relies on binary operations, such as NOT or AND gates, making inputs irretrievable, quantum computing utilises unitary gates, which are necessarily reversible. This condition is necessitated by the Schrödinger equation and has vital implications for techniques of the amplitude amplification and phase kickback. These concepts prove crucial, inter alia, for Grover's algorithm intended for searching unordered databases or Shor's algorithm for factoring large composite numbers. Consequently, the state of the art computers leveraging the physics of quantum mechanics offer substantial speedups with respect to the classical ones. Perhaps the best proof behind this thesis is that Grover's algorithm alone offers a quadratic speedup to classical computing, which makes solving multiplex optimization problems dramatically more efficient.

Quantum computing hardware

When it comes to quantum computing hardware, it can be currently categorised into two main branches: quantum annealers and gate-based quantum computers. Quantum annealers are specifically intended for solving optimization and sampling problems. They begin with qubits in a superposition of states and gradually evolve the system in such a way that the qubits eventually settle on the lowest energy state, representing the most optimal solution. Accordingly, quantum annealers take advantage of the principle of quantum adiabatic evolution; the adiabatic theorem states that if a quantum system is initially in the ground state of a Hamiltonian (a function describing the total energy of a system), and the system evolves slowly enough to a another Hamiltonian, then it will remain in its ground state. Thanks to their efficiency in solving optimization problems, quantum annealers have found multiple applications in financial risk management, especially in the area of dynamic portfolio optimization.

The other category of quantum computing hardware is gate-based, meaning it relies on unitary gates to manipulate qubits in a controlled sequence. Due to its possibility of controlling and manipulating the evolution of the quantum states, the gate-based computing can be applied to a bigger class of problems than quantum annealing. It is also the gate-based computers which are able to run the previously mentioned Shor's and Grover's algorithm, underscoring their tremendous computational power. However, greater complexity comes along with more significant limitations in use; in particular, gate-based quantum computers are more demanding to scale due to the need for error correction and are highly sensitive to noise. To provide some perspective on the issue, the latest quantum annealers developed by D-Wave systems are able to process up to 5000 qubits, whereas the most advanced gate-based processor, the IBM Eagle, has 127 qubits.

Applications of quantum computing in finance

Although to this day the real-world application of quantum computing in risk management has been rather limited in scope, the technology has the potential to revolutionise the field in 3 key aspects: optimization, machine learning and quantum-accelerated Monte Carlo.

Quantum annealers, thanks to their intrinsic efficiency in solving optimization problems, seem particularly suitable to dynamic risk optimization. In fact, a recent study showed that by formulating generalised dynamic portfolio optimization problems as integer optimization problems, these can be solved by quantum computers. A D-Wave quantum processor, provided with a cost function and constraint to the sum of holdings, solved the optimization problem with a higher success rate than classical hardware. This offers a highly enthusiastic outlook on the future applications of quantum annealing in finding optimal trading trajectories.

Quantum computing has also led to significant developments in machine learning by making the training process much more efficient. This can prove perfectly beneficial to the problem of credit scoring, which relies on the machine-learning method of classification. Each data point representing the object of credit scoring is expressed as a vector in the space of its attributes. The program receives a training set of such points, each assigned to a specific credit class, and by the means of machine learning it ought to learn how to classify the remaining vectors. Thanks to the efficiencies brought about by quantum computing this process can become much more precise, especially with respect to pattern recognition.

Lastly, quantum computing generates considerable speedup to the Monte Carlo method, typically used in finance to simulate the effect of uncertainties on financial objects. In order to generate reliable results by Monte Carlo, a huge number of simulations must be carried out in the process, which makes quantum computing an especially potent tool. Its benefits can be observed, for example, in using Monte Carlo in calculation of Value at Risk (VaR), a key measure in risk management. A study by Woerner and Egger showed that a quantum-accelerated Monte Carlo can determine the values of VaR and CVaR with high accuracy and quadratic speedup compared with classical methods. This highly satisfactory outcome serves as a valid promise of further improvements in risk management thanks to quantum computing.

Economic implications

The application of quantum computing in finance could completely revolutionise the sector in the near future, improving market efficiency and risk oversight. Thanks to the previously mentioned qualities, quantum algorithms can process large volumes of data in record times, enabling the optimization of trading strategies, enhancement of risk analysis, and improvement in supply chain management. The technology also promises to reduce transaction costs by requiring faster settlement times, decreasing energy consumption, and strengthening cybersecurity through enhanced encryption. Nevertheless, these changes also bear the risk of causing labour market disruptions: routine jobs involving trading and data analysis may become automated, while higher demand for quantum computing professionals might spring up. Although one should not expect increased unemployment in the finance sector as a result, the need for an upskilling workforce is more than likely. The key take-away is that the integration of quantum computing can bring significant economic benefits but its full potential can only be realised by careful management of its societal issues.

Regulatory challenges

The integration of quantum computing into global financial systems presents huge regulatory challenges not only due to its expected labour market impacts but also because of its unparalleled data processing and encryption-breaking capabilities. Quantum computers, with a power to break the latest encryption systems and decipher sensitive financial data, render existing cybersecurity measures obsolete. In addition, they generate a risk of stark inequality between companies in terms of their technological advancement, which could lead to market-disrupting competitive advantages for those who decide to invest in the new technology. This potentially means further market consolidation and higher industry concentration, raising inevitable antitrust issues. Therefore, widespread application of quantum computing warrants the enactment of quantum-specific compliance standards by regulators, imposition of quantum-resistant encryption systems, and increased international cooperation to ensure a uniform legal framework. Precariously navigating this increasingly complex regulatory environment requires a delicate balance between fostering innovation on one end and safeguarding the stability of global markets on the other. All in all, making sure that the power of quantum computing is responsibly harnessed across the financial sector should be a priority.

Barriers to widespread application

Despite the potential benefits of quantum computing in finance, there are still unavoidable obstacles which need to be surpassed for optimal results to be achieved. Firstly, the technology is still in its infancy stage, and it may take years until reliable quantum computers become easily accessible to businesses. McKinsey has recently conducted a survey among tech experts, which reveals that 72% believe that by 2035 we should see the first fully fault-tolerant quantum computer, while the rest predict that the milestone will not be reached until 2040 or later. Nonetheless, some businesses should be able to benefit from quantum computing even before that, specifically thanks to quantum cloud offerings which continue to proliferate.

Another barrier to widespread adoption of quantum computing comes in the form of technological inequality between world regions. The World Economic Forum reports that in January 2021 only 17 countries across the globe had implemented any kind of national initiative aimed at supporting the development of quantum technologies. For instance, the UK National Quantum Technologies Programme had contributed £1 billion to promote cooperation between the industry, academia and government on the topic of quantum computing. In general, worldwide public spending on quantum technology in 2022 was estimated at $30 billion, with China accounting for half and the EU for almost a quarter. Furthermore, a growing number of private startups dedicated to quantum tech could be observed in the US and EU in recent years. In this investment environment, South America and Africa are considerably lagging behind, presenting a risk of a growing quantum divide. The discrepancies in quantum advancement between countries could possibly lead to future disintegration of financial markets and growing development gap, which is why the governments worldwide should urgently commit to bridging the divide.

Future prospects

Quantum technology carries unparalleled computational capabilities and promises to solve complex financial problems at speeds unattainable by classical computers. Advanced algorithms, involving quantum annealing or quantum-accelerated Monte Carlo, can dramatically improve up-to-date financial practices by boosting effectiveness of risk assessment and dynamic portfolio optimization. However, the path leading to widespread and efficient application of quantum computing is not a one without obstacles. Governments as well as independent financial institutions and intermediaries will need to carefully navigate through complex technical requirements and uncertain regulatory environments to manage the transition properly. These efforts will surely demand concerted research, universal education, and strong collaboration between various industries. Despite the challenges, quantum computing offers tremendous potential to be successfully integrated into the financial sector. It will remain, without a doubt, an overarching theme of financial risk management in the decades to come and its comprehensive application, once in place, shall satisfy the growing needs of the ever more interconnected world.

Bibliography

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McKinsey & Company. "What Is Quantum Computing? | McKinsey." Www.mckinsey.com, 1 May 2023, www.mckinsey.com/featured-insights/mckinsey-explainers/what-is-quantum-computing;

Orús, Román, et al. "Quantum Computing for Finance: Overview and Prospects." Reviews in Physics, vol. 4, Nov. 2019, www.sciencedirect.com/science/article/pii/S2405428318300571, https://doi.org/10.1016/j.revip.2019.100028;

Schneider, Josh, and Ian Smalley. "What Is Quantum Computing?" IBM, 5 Aug. 2024, www.ibm.com/topics/quantum-computing;

Van Biljon, Peet. "Closer than You Think – Quantum Computing in Finance." Financier Worldwide, May 2021, www.financierworldwide.com/closer-than-you-think-quantum-computing-in-finance;

Woerner, Stefan, and Daniel J. Egger. "Quantum Risk Analysis." Npj Quantum Information, vol. 5, no. 1, 8 Feb. 2019, https://doi.org/10.1038/s41534-019-0130-6.

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