Abstract
This article outlines our point of view regarding the applicability, state-of-the-art, and potential of quantum computing for problems in finance. We provide an introduction to quantum computing as well as a survey on problem classes in finance that are computationally challenging classically and for which quantum computing algorithms are promising. In the main part, we describe in detail quantum algorithms for specific applications arising in financial services, such as those involving simulation, optimization, and machine learning problems. In addition, we include demonstrations of quantum algorithms on IBM Quantum back-ends and discuss the potential benefits of quantum algorithms for problems in financial services. We conclude with a summary of technical challenges and future prospects.
Highlights
In the financial services industry, there are many computationally challenging problems arising in applications across asset management, investment banking, and retail and corporate banking
The probability to sample near-optimal states with quantum approximate optimization algorithm (QAOA) are lower than for variational quantum eigensolver (VQE), which may indicate that deeper QAOA variational forms are needed [90] or that the Constrained Optimization By Linear Approximation (COBYLA) optimizer we used was trapped in a local minimum [68], [91]
The method of [11] leverages the alternating direction method of multipliers (ADMM) operator-splitting procedure to devise a decomposition for certain classes of mixed-binary optimization (MBO) into: 1) a quadratic unconstrained binary optimization (QUBO) subproblem to be solved by on the quantum device via variational algorithms, such as VQE or QAOA, described in Section IV-D; 2) a continuous convex constrained subproblem, which can be efficiently solved with classical optimization solvers [80]
Summary
In the financial services industry, there are many computationally challenging problems arising in applications across asset management, investment banking, and retail and corporate banking. In the near-term future, quantum computers will continue to rely on noisy qubits with relatively high error rates and limited coherence times In this era of noisy quantum devices [16], we will be confidently in the realm of Quantum Advantage once we are able to solve a good number of significant real-world problems more efficiently with the help of quantum devices than compared with solving them on a classical computers only. 2) The Compute Step: Once data are loaded, the solution must rapidly perform a computation on the loaded data within the quantum computer This involves manipulation of the qubits in a manner that changes the fundamental states in a way that reflects the outcome of a desired computation. It should be noted that the higher the number of qubits, the higher requirements on precision, and the higher the requirements on the number of measurements
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