Prospects and challenges of quantum finance

Abstract

Quantum computers are expected to have substantial impact on the finance industry, as they will be able to solve certain problems considerably faster than the best known classical algorithms. In this article we describe such potential applications of quantum computing to finance, starting with the state-of-the-art and focusing in particular on recent works by the QC Ware team. We consider quantum speedups for Monte Carlo methods, portfolio optimization, and machine learning. For each application we describe the extent of quantum speedup possible and estimate the quantum resources required to achieve a practical speedup. The near-term relevance of these quantum finance algorithms varies widely across applications -some of them are heuristic algorithms designed to be amenable to near-term prototype quantum computers, while others are proven speedups which require larger-scale quantum computers to implement. We also describe powerful ways to bring these speedups closer to experimental feasibility -in particular describing lower depth algorithms for Monte Carlo methods and quantum machine learning, as well as quantum annealing heuristics for portfolio optimization. This article is targeted at financial professionals and no particular background in quantum computation is assumed.

Quantum algorithm for calculating risk contributions in a credit portfolio

“…Note that X 0 is common for all the obligors but X 1 , ..., X N obl affect only the first, ..., N obl th obligors, respectively. X 0 is called a systematic risk factor, which reflects the situation of macro economy, and X 1 , ..., X N obl are called idiosyncratic risk factors, which reflect the matters unique to the credit of the individual obligor 3 . Z k is the linear combination of X 0 and X k as (3), and follows the standard normal distribution too.…”

An Efficient Quantum Readout Error Mitigation for Sparse Measurement Outcomes of Near-term Quantum Devices

“…We conducted two experiments on the 65-qubit IBM Quantum Brooklyn system: the expectation values of GHZ states and the fidelity of GHZ states. The circuits are executed on IBM Quantum Brooklyn by mapping the virtual circuit qubits to physical qubits with [33,32,25,31,34,19,39,30,35,18,45,20,29,40,17,46,36,44,21,28,49,16,47,24,11,37,43,12,27,50,15,53,22,48,4,26,52,8,38,51,14,60,42,23,3,56,7,41,54,13,59, 5, 9, 61, 2, 55, 6, 64, 10, 58, 57, 62, 1, 63, 0] as shown in FIG. 7.…”

“…Furthermore, the estimation error of the maximum likelihood amplitude estimation (MLAE) algorithm [32] with modified Grover iterator [33] is investigated by numerical simulation on Qiskit [24]. The amplitude estimation problem has essential applications in finance and machine learning using quantum devices [34,35]. The MLAE method [32,36] avoids the phase estimation in the original amplitude estimation [37] and is expected to be realized earlier than the Shor's algorithm as estimated in [35].…”

“…The amplitude estimation problem has essential applications in finance and machine learning using quantum devices [34,35]. The MLAE method [32,36] avoids the phase estimation in the original amplitude estimation [37] and is expected to be realized earlier than the Shor's algorithm as estimated in [35]. Experimental results imply that the proposed methods successfully improve the estimation errors in the order of O(1/N ) for N Grover oracle iterations.…”

Pricing multi-asset derivatives by finite difference method on a quantum computer

“…In fact, some recent papers have already discussed applications of quantum algorithms to concrete problems in financial engineering: for example, derivative pricing [4][5][6][7][8][9][10][11][12][13][14][15][16], risk measurement [17][18][19], portfolio optimization [20][21][22], and so on. See [23][24][25] as comprehensive reviews.…”