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Yuan Yang

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Recent Progress in Quantum Finance.

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Abstract

New development in Quantum Finance

Quantum computational quantitative trading:

high-frequency statistical arbitrage algorithm

概述
  • Quantitative trading is an integral part of financial markets with high calculation speed requirements, while no quantum algorithms have been introduced into this field yet. We propose quantum algorithms for high-frequency statistical arbitrage trading by utilizing variable time condition number estimation and quantum linear regression. The algorithm complexity has been reduced from the classical benchmark O(N2d) to $O(\sqrt{dN}{\kappa }{0}^{2}\,\mathrm{log}{(1/{\epsilon})}^{2})\left.\right)$, where N is the length of trading data, and d is the number of stocks, κ0 is the condition number and epsilon is the desired precision. Moreover, two tool algorithms for condition number estimation and cointegration test are developed. (量化交易是金融市场不可分割的组成部分， 对计算速度要求很高，但目前还没有量子算法引入该领域。 我们利用可变时间条件数估计和量子线性回归提出了高频统计套利交易的量子算法。 算法复杂度已从经典基准O ( N 2 d ) 降低到$O(\sqrt{dN}{\kappa }{0}^{2}\,\mathrm{log}{(1/{\epsilon})}^{2})\left.\right)$， 其中N是交易数据的长度，d是股票数量，κ 0是条件数，ε是所需的精度。 此外，还开发了两种用于条件数估计和协整检验的工具算法。)

Future of Quantum Finance

概述
  • Many problems in finance center on optimization issues, and the authors note, “These are tasks which are particularly hard for classical computers but find a natural formulation using quantum optimization methods. In recent years, this field has known a tremendous growth, partly due to the commercial availability of quantum annealers.” Quantum annealing is a computing method that provides a way to find solutions when the problems can present large numbers of solutions. The authors point out that quantum annealers can be used to optimize portfolios, find arbitrage opportunities, and perform credit scoring. (金融中的许多问题都集中在优化问题上， 作者指出，“这些任务对于经典计算机来说特别困难， 但可以使用量子优化方法找到一个自然的公式。 近年来，该领域取得了巨大的增长，部分原因是量子退火炉的商业可用性。 ” 量子退火是一种计算方法，当问题可以呈现大量解决方案时， 它提供了一种找到解决方案的方法。作者指出，量子退火器可用于优化投资组合、 寻找套利机会和进行信用评分。)

The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

概述
  • The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (martingale). In this paper, we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock markets. (应用于量子金融的自发对称破缺现象认为，如果我们以哈密顿形式表示金融方程， 则股票市场中的鞅状态对应于基（真空）状态。 对这种现象的原始分析完全忽略了势项最小值附近的动力学项。 这在大多数情况下是正确的。然而，当我们处理鞅条件时，发现动力学项也可以表现为势项， 然后再现真空有效位置的变化（鞅）。 在本文中，我们分析了这些特殊情况下有效的对称破缺模式和相关的真空简并。)

A Survey of Quantum Computing for Finance

概述
  • 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 stochastic modeling, optimization, and machine learning, describing how these solutions, adapted to work on a quantum computer, can potentially help to solve financial problems, such as derivative pricing, risk modeling, portfolio optimization, natural language processing, and fraud detection, more efficiently and accurately. 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. (在这十年中，量子计算机有望超越经典计算机的计算能力，并对众多行业产生变革性影响， 尤其是金融业。事实上，金融估计是第一个受益于量子计算的行业，不仅在中长期，甚至在短期内也是如此。 这份调查报告全面总结了金融应用中量子计算的最新技术， 特别强调了随机建模、优化和机器学习，描述了这些适用于量子计算机的解决方案如何潜在地帮助更高效、 更准确地解决金融问题，例如衍生品定价、风险建模、投资组合优化、自然语言处理和欺诈检测。 我们还讨论了这些算法在具有各种硬件实现的近期量子计算机上的可行性， 并展示了它们如何与金融领域的广泛用例相关联。 我们希望这篇文章不仅可以作为学术研究人员和行业从业者的参考， 也可以为未来的研究提供新的思路。)

Fintech Frontiers in Quantum Computing, Fractals, and Blockchain Distributed Ledger: Paradigm Shifts and Open Innovation

概述
  • Among the hot research topics, Fintech is leading the trend in terms of the newest technology applications. The relatively new emerging paradigms in various sciences, such as geometry (fractals), physics (quantum), and database systems (distributed ledger—blockchain), seem to potentially contribute to a greater shift in the framework of the finance industry, bringing also some concerns (cyber-threats). Consistent and extensive investigation of the reasonable potential impact of these new models (and their underlying technologies) is performed, and then tested through a SWOT analysis, as the main objective of this research. Threats and opportunities are always intrinsically driven by the introduction of technological advancements (revolutions). This research confirms that information availability and the increasing interconnection of crosswise applications of each discovery to the different fields of science is determining the rapid succession of revolutions identified by evident large shifts in economic paradigms. The growing computing capacity and the development of increasingly powerful predictive software are leading to a competitive, extremely dynamic, and challenging system. In this context, as shown by history, there is a high possibility of market concentration in which, however, only a few corporations—digital giants—can afford to develop these technologies, consolidating their dominance (在热点研究课题中，金融科技在最新技术应用方面处于领先地位。 各种科学中相对较新的范式，例如几何（分形）、物理学（量子）和数据库系统（分布式账本——区块链）， 似乎可能有助于金融业框架的更大转变，也带来一些担忧（网络威胁）。 对这些新模型（及其基础技术）的合理潜在影响进行一致和广泛的调查， 然后通过 SWOT 分析进行测试，作为本研究的主要目标。 威胁和机遇总是由技术进步（革命）的引入驱动的。这项研究证实， 信息可用性和每个发现在不同科学领域的交叉应用的日益相互联系 正在决定经济范式明显大转变所确定的革命的快速连续性。 不断增长的计算能力和越来越强大的预测软件的开发正在导致一个具有竞争力、 极其动态和具有挑战性的系统。在这种情况下，正如历史所表明的那样，市场集中的可能性很高， 然而，只有少数公司——数字巨头——有能力开发这些技术，巩固它们的主导地位。)

Quantum Machine Learning for Finance ICCAD Special Session Paper

概述
  • Quantum computers are expected to surpass the computational capabilities of classical computers during this decade, and achieve disruptive 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 review paper presents the state of the art of quantum algorithms for financial applications, with particular focus to those use cases that can be solved via Machine Learning. (量子计算机有望在这十年内超越经典计算机的计算能力， 并对众多行业产生颠覆性影响，尤其是金融领域。 事实上，金融估计是第一个从量子计算中受益的行业，不仅在中长期， 甚至在短期内。这篇评论论文介绍了用于金融应用的量子算法的最新技术， 特别关注那些可以通过机器学习解决的用例。).

Quantum Computing for Supply Chain Finance

概述
  • Applying quantum computing to real world applications to assess the potential efficacy is a daunting task for non-quantum specialists. This paper shows an implementation of two quantum optimization algorithms applied to portfolios of trade finance portfolios and compares the selections to those chosen by experienced underwriters and a classical optimizer. The method used is to map the financial risk and returns for a trade finance portfolio to an optimization function of a quantum algorithm developed in a Qiskit tutorial. The results show that whilst there is no advantage seen by using the quantum algorithms, the performance of the quantum algorithms has no statistically significant degradation. Therefore, it is promising that in the future, with expected improvements in quantum hardware, the theoretically superior processing speeds, and data volumes that quantum offers, will also be applicable to trade finance. (将量子计算应用于现实世界的应用以评估潜在功效对于非量子专家来说是一项艰巨的任务。 本文展示了应用于贸易融资投资组合的两种量子优化算法的实现， 并将选择与经验丰富的承销商和经典优化器的选择进行比较。 使用的方法是将贸易金融投资组合的金融风险和回报映射到 Qiskit 教程中开发的量子算法的优化函数。 结果表明，虽然使用量子算法没有看到任何优势， 但量子算法的性能在统计上没有显着下降。 因此，很有希望的是，在未来，随着量子硬件的预期改进，理论上优越的处理速度)

A Structured Survey of Quantum Computing for the Financial Industry

概述
  • Quantum computers can solve specific problems that are not feasible on “classical” hardware. Harvesting the speed-up provided by quantum computers therefore has the potential to change any industry which uses computation, including finance. First quantum applications for the financial industry involving optimization, simulation, and machine learning problems have already been proposed and applied to use cases such as portfolio management, risk management, and pricing derivatives. This survey reviews platforms, algorithms, methodologies, and use cases of quantum computing for various applications in finance in a structured way. It is aimed at people working in the financial industry and serves to gain an overview of the current development and capabilities and understand the potential of quantum computing in the financial industry. (量子计算机可以解决在“经典”硬件上不可行的特定问题。 因此，利用量子计算机提供的加速功能有可能改变任何使用计算的行业，包括金融业。 金融行业涉及优化、模拟和机器学习问题的第一个量子应用已经被提出， 并应用于投资组合管理、风险管理和衍生品定价等用例。 本调查以结构化的方式回顾了量子计算在金融领域的各种应用的平台、算法、方法和用例。 本课程面向金融行业的工作人员，旨在全面了解当前的发展和能力，并了解量子计算在金融行业的潜力。)

Quantum versus classical generative modelling in finance

概述
  • Finding a concrete use case for quantum computers in the near term is still an open question, with machine learning typically touted as one of the first fields which will be impacted by quantum technologies. In this work, we investigate and compare the capabilities of quantum versus classical models for the task of generative modelling in machine learning. We use a real world financial dataset consisting of correlated currency pairs and compare two models in their ability to learn the resulting distribution—a restricted Boltzmann machine, and a quantum circuit Born machine. We provide extensive numerical results indicating that the simulated Born machine always at least matches the performance of the Boltzmann machine in this task, and demonstrates superior performance as the model scales. We perform experiments on both simulated and physical quantum chips using the Rigetti QCSTM platform, and also are able to partially train the largest instance to date of a quantum circuit Born machine on quantum hardware. Finally, by studying the entanglement capacity of the training Born machines, we find that entanglement typically plays a role in the problem instances which demonstrate an advantage over the Boltzmann machine. (在短期内找到量子计算机的具体用例仍然是一个悬而未决的问题， 机器学习通常被吹捧为受量子技术影响的首批领域之一。 在这项工作中，我们研究并比较了量子模型与经典模型在机器学习中生成建模任务的能力。 我们使用由相关货币对组成的真实世界金融数据集， 并比较两个模型学习结果分布的能力——受限玻尔兹曼机和量子电路玻恩机。 我们提供了广泛的数值结果，表明模拟的 Born 机器在该任务中始终至少与 Boltzmann 机器的性能相匹配， 并且随着模型的扩展表现出卓越的性能。 TM平台，并且还能够在量子硬件上部分训练迄今为止最大的量子电路 Born 机器实例。 最后，通过研究训练 Born 机器的纠缠能力，我们发现纠缠通常在问题实例中发挥作用， 这证明了玻尔兹曼机器的优势).

Quantum Computing for Financial Risk Measurement

概述
  • Quantum computing allows a significant speed-up over traditional CPU- and GPU-based algorithms when applied to particular mathematical challenges such as optimisation and simulation. Despite promising advances and extensive research in hard- and software developments, currently available quantum systems are still largely limited in their capability. In line with this, practical applications in quantitative finance are still in their infancy. This paper analyses requirements and concrete approaches for the application to risk management in a financial institution. On the examples of Value-at-Risk for market risk and Potential Future Exposure for counterparty credit risk, the main contribution lies in going beyond textbook illustrations and instead exploring must-have model features and their quantum implementations. While conceptual solutions and small-scale circuits are feasible at this stage, the leap needed for real-life applications is still significant. In order to build a usable risk measurement system, the hardware capacity - measured in number of qubits - would need to increase by several magnitudes from their current value of about 10^2. Quantum noise poses an additional challenge, and research into its control and mitigation would need to advance in order to render risk measurement applications deployable in practice. Overall, given the maturity of established classical simulation-based approaches that allow risk computations in reasonable time and with sufficient accuracy, the business case for a move to quantum solutions is not very strong at this point. (当应用于优化和模拟等特定数学挑战时，量子计算允许比传统的基于CPU和GPU的算法显著提高速度。 尽管在硬件和软件开发方面取得了有前途的进展和广泛的研究， 但目前可用的量子系统在很大程度上仍受到其能力的限制。与此相一致， 定量金融的实际应用仍处于初级阶段。 本文分析了应用于金融机构风险管理的要求和具体方法。 在市场风险的风险价值和交易对手信用风险的潜在未来敞口的例子中， 主要贡献在于超越教科书中的插图，而是探索必备的模型功能及其量子实现。 虽然概念解决方案和小规模电路在现阶段是可行的，但实际应用所需的飞跃仍然是巨大的。 为了构建一个可用的风险测量系统，硬件容量（以量子位为单位）需要从当前约10^2的值增加几个数量级。 量子噪声带来了另一个挑战，需要推进对其控制和缓解的研究，以使风险测量应用程序能够在实践中部署。 总的来说，鉴于成熟的基于模拟的经典方法允许在合理的时间内以足够的精度进行风险计算， 目前转向量子解决方案的商业理由并不十分充分。)

Pricing Multi-Asset Derivatives by Finite-Difference Method on a Quantum Computer

概述
  • Following the recent great advance of quantum computing technology, there are growing interests in its applications to industries, including finance. In this article, we focus on derivative pricing based on solving the Black–Scholes partial differential equation by the finite-difference method (FDM), which is a suitable approach for some types of derivatives but suffers from the curse of dimensionality , that is, exponential growth of complexity in the case of multiple underlying assets. We propose a quantum algorithm for FDM-based pricing of multi-asset derivative with exponential speedup with respect to dimensionality compared with classical algorithms. The proposed algorithm utilizes the quantum algorithm for solving differential equations, which is based on quantum linear system algorithms. Addressing the specific issue in derivative pricing, that is, extracting the derivative price for the present underlying asset prices from the output state of the quantum algorithm, we present the whole of the calculation process and estimate its complexity. We believe that the proposed method opens the new possibility of accurate and high-speed derivative pricing by quantum computers (随着最近量子计算技术的巨大进步，人们对其在金融等行业的应用越来越感兴趣。在本文中，我们专注于基于有限差分法 (FDM) 求解 Black-Scholes 偏微分方程的衍生品定价，该方法适用于某些类型的衍生品，但存在维数灾难，即在多个基础资产的情况下，复杂性呈指数增长。我们提出了一种基于 FDM 的多资产衍生品定价的量子算法，与经典算法相比，该算法在维度方面具有指数加速。所提出的算法利用基于量子线性系统算法的量子算法求解微分方程。解决衍生品定价的具体问题，即从量子算法的输出状态中提取当前标的资产价格的衍生品价格，呈现整个计算过程并估计其复杂度。我们相信，所提出的方法为量子计算机准确和高速的衍生品定价开辟了新的可能性。)