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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.
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This is a brief review of the experimental and theoretical quantum computing. The hopes for eventually building a useful quantum computer rely entirely on the so-called threshold theorem. In turn, this theorem is based on a number of assumptions, treated as axioms, i.e. as being satisfied exactly. Since in reality this is not possible, the prospects of scalable quantum computing will remain uncertain until the required precision, with which these assumptions should be approached, is established. Some related sociological aspects are also discussed. .
We discuss how quantum computation can be applied to financial problems, providing an overview of current approaches and potential prospects. We review quantum optimization algorithms, and expose how quantum annealers can be used to optimize portfolios, find arbitrage opportunities, and perform credit scoring. We also discuss deep-learning in finance, and suggestions to improve these methods through quantum machine learning. Finally, we consider quantum amplitude estimation, and how it can result in a quantum speed-up for Monte Carlo sampling. This has direct applications to many current financial methods, including pricing of derivatives and risk analysis. Perspectives are also discussed.
This article aims to review the developments, both theoretical and experimental, that have in the past decade laid the ground for a new approach to solid state quantum computing. Measurement-based quantum computing (MBQC) requires neither direct interaction between qubits nor even what would be considered controlled generation of entanglement. Rather it can be achieved using entanglement that is generated probabilistically by the collapse of quantum states upon measurement. Single electronic spins in solids make suitable qubits for such an approach, offering long coherence times and well defined routes to optical measurement. We will review the theoretical basis of MBQC and experimental data for two frontrunner candidate qubits -- nitrogen-vacancy (NV) centres in diamond and semiconductor quantum dots -- and discuss the prospects and challenges that lie ahead in realising MBQC in the solid state.
Molecular science is governed by the dynamics of electrons, atomic nuclei, and their interaction with electromagnetic fields. A reliable physicochemical understanding of these processes is crucial for the design and synthesis of chemicals and materials of economic value. Although some problems in this field are adequately addressed by classical mechanics, many require an explicit quantum mechanical description. Such quantum problems represented by exponentially large wave function should naturally benefit from quantum computation on a number of logical qubits that scales only linearly with system size. In this perspective, we focus on the potential of quantum computing for solving relevant problems in the molecular sciences -- molecular physics, chemistry, biochemistry, and materials science.
The quantum computer is supposed to process information by applying unitary transformations to the complex amplitudes defining the state of N qubits. A useful machine needing N=1000 or more, the number of continuous parameters describing the state of a quantum computer at any given moment is much greater than the number of protons in the Universe. However, the theorists believe that the feasibility of large-scale quantum computing has been proven via the threshold theorem. Like for any theorem, the proof is based on a number of assumptions considered as axioms. However, in the physical world none of these assumptions can be fulfilled exactly. Any assumption can be only approached with some limited precision. So, the rather meaningless error-per-qubit-per-gate threshold must be supplemented by a list of the precisions with which all assumptions behind the threshold theorem should hold. Such a list still does not exist. The theory also seems to ignore the undesired free evolution of the quantum computer caused by the energy differences of quantum states entering any given superposition. Another important point is that the hypothetical quantum computer will be a system of at least a thousand of qubits plus an extremely complex and monstrously sophisticated classical apparatus. This huge and strongly nonlinear system will generally exhibit instabilities and chaotic behavior.
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