A Survey of Quantum Computing for Finance

Abstract

Quantum computers are expected to surpass the computational capabilities of classical computers during this decade and have transformative impact on numerous industry sectors, particularly finance. 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. This survey paper presents a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on Monte Carlo integration, optimization, and machine learning, showing how these solutions, adapted to work on a quantum computer, can help solve more efficiently and accurately problems such as derivative pricing, risk analysis, portfolio optimization, natural language processing, and fraud detection. We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance. We hope this article will not only serve as a reference for academic researchers and industry practitioners but also inspire new ideas for future research.

Preparing Arbitrary Continuous Functions in Quantum Registers With Logarithmic Complexity

“…As the technology is scaled up, it will ultimately enable powerful quantum algorithms capable of both polynomial and exponential speedups over their classical counterparts. However, many of these algorithms require efficient state preparation procedures to achieve their speedup, as is the case in: option pricing [6][7][8], machine learning [9][10][11], matrix inversion [12], quantum chemistry [13,14], and quantum Monte Carlo based algorithms [15,16]. As such, it remains a crucial open question: can we efficiently prepare quantum states given a set of prespecified amplitudes?…”

Adaptive Algorithm for Quantum Amplitude Estimation

“…Although only achieving a quadratic speedup over a classical brute-force search, Grover's algorithm makes no assumption on the function other than the number of the solutions (later relaxed by Brassard et al (2002)), and therefore has a wide range of potential applications (Ambainis, 2004;Sun et al, 2014;Zhong et al, 2021). In recent years, quantum algorithms have been developed for various domains including finance (Hong et al, 2014;Herman et al, 2022), chemistry (Cao et al, 2019), optimization (Durr and Hoyer, 1996;Kochenberger et al, 2014;Wang et al, 2016;Hu and Wang, 2020), machine learning (Ramezani et al, 2020), and high-dimensional statistics (Zhong et al, 2021), among others.…”

Stochastic optimization algorithms for quantum applications

“…Thus, hybrid optimization algorithms are used whenever the objective function can be evaluated more efficiently on a quantum computer than on a classical one. This is the case for applications to quantum chemistry [6][7][8], quantum control [9][10][11], quantum simulation [12,13], entanglement detection [14][15][16], state estimation [17][18][19][20][21], quantum machine learning [22][23][24][25][26], error correction [27], graph theory [28][29][30], differential equations [31][32][33], and finances [34].…”