1. https://arxiv.org/pdf/2201.02773.pdf A Survey of Quantum Computing for Finance

Conclusion and Outlook

Quantum computers are expected to surpass the computational capabilities of classical computers and achieve disruptive impact on numerous industry sectors, such as global energy and materials, pharmaceuticals and medical products, telecommunication, travel, logistics, and finance. In particular, the finance sector has a history of creation and first adaptation of new technologies. This is true also when it comes to quantum computing. In fact, finance is estimated to be the first industry sector to benefit from quantum computing, not only in the medium and long terms, but even in the short term, because of the large number of financial use cases that lend themselves to quantum computing and their amenability to be solved effectively even in the presence of approximations.

A common misconception about quantum computing is that quantum computers are simply faster processors and hence speedups will be automatically achieved by porting a classical algorithm from a classical computer to a quantum one—just like moving a program to a system-upgraded hardware. In reality, quantum computers are fundamentally different from classical computers, so much so that the algorithmic process for solving an application has to be completely redesigned based on the architecture of the underlying quantum hardware. Most of the use cases that characterize the finance industry sector have high computational complexity, and for this reason they lend themselves to quantum computing. However, the computational complexity of a problem per se is not a guarantee that quantum computing can make a difference. To assess commercial viability, we must first answer a couple questions. First, is there in fact any need for improved speed of calculations or computational-accuracy for the given application? Determining whether there is a gap in what the current technology can provide us is essential and is a question that financial players typically ask when doing proof of concept projects. Second, when adapting a classical finance application to quantum computing, can that application achieve quantum speedup and, if so, when will that happen based on the estimated evolution of the underlying quantum hardware?

Today’s quantum computers are not yet capable of solving real-life-scale problems in the industry more efficiently and more accurately than classical computers can. Nevertheless, proofs of concept for quantum advantage and even quantum supremacy have already been provided (see Section 3). There is hope that the situation will change in the coming years with demonstrations of quantum advantage. It is crucial for enterprises, and particularly financial institutions, to use the current time to become quantum ready in order to avoid being left behind when quantum computers become operational in a production environment. We are in the early stages of the quantum revolution, yet we are already observing a strong potential for quantum technology to transform the financial industry. So far, the community has developed potential quantum solutions for portfolio optimization, derivatives pricing, risk modeling, and several problems in the realm of artificial intelligence and machine learning, such as fraud detection and NLP.

In this paper we have provided a comprehensive review of quantum computing for finance, specifically focusing on quantum algorithms that can solve computationally challenging financial problems. We have described the current landscape of the state of the industry. We hope this work will be used by the scientific community, both in industry and in academia, not only as a reference, but also as a source of information to identify new opportunities and advance the state of the art.

1.portfolio optimization (Section 6.4.1),

2.hedging and swap netting (Section 6.4.2),

3.optimal arbitrage (Section 6.4.3),

4.credit scoring (Section 6.4.4), and

5.financial crash prediction (Section 6.4.5).

Quantum advantage

Quantum supremacy