Quantum Computing

Quantum computing for multidimensional option pricing: End-to-end pipeline ArXiv ID: 2601.04049 “View on arXiv” Authors: Julien Hok, Álvaro Leitao Abstract This work introduces an end-to-end framework for multi-asset option pricing that combines market-consistent risk-neutral density recovery with quantum-accelerated numerical integration. We first calibrate arbitrage-free marginal distributions from European option quotes using the Normal Inverse Gaussian (NIG) model, leveraging its analytical tractability and ability to capture skewness and fat tails. Marginals are coupled via a Gaussian copula to construct joint distributions. To address the computational bottleneck of the high-dimensional integration required to solve the option pricing formula, we employ Quantum Accelerated Monte Carlo (QAMC) techniques based on Quantum Amplitude Estimation (QAE), achieving quadratic convergence improvements over classical Monte Carlo (CMC) methods. Theoretical results establish accuracy bounds and query complexity for both marginal density estimation (via cosine-series expansions) and multidimensional pricing. Empirical tests on liquid equity entities (Credit Agricole, AXA, Michelin) confirm high calibration accuracy and demonstrate that QAMC requires 10-100 times fewer queries than classical methods for comparable precision. This study provides a practical route to integrate arbitrage-aware modelling with quantum computing, highlighting implications for scalability and future extensions to complex derivatives. ...

Variational Quantum Eigensolver for Real-World Finance: Scalable Solutions for Dynamic Portfolio Optimization Problems ArXiv ID: 2512.22001 “View on arXiv” Authors: Irene De León, Danel Arias, Manuel Martín-Cordero, María Esperanza Molina, Pablo Serrano, Senaida Hernández-Santana, Miguel Ángel Jiménez Herrera, Joana Fraxanet, Ginés Carrascal, Escolástico Sánchez, Inmaculada Posadillo, Álvaro Nodar Abstract We present a scalable, hardware-aware methodology for extending the Variational Quantum Eigensolver (VQE) to large, realistic Dynamic Portfolio Optimization (DPO) problems. Building on the scaling strategy from our previous work, where we tailored a VQE workflow to both the DPO formulation and the target QPU, we now put forward two significant advances. The first is the implementation of the Ising Sample-based Quantum Configuration Recovery (ISQR) routine, which improves solution quality in Quadratic Unconstrained Binary Optimization problems. The second is the use of the VQE Constrained method to decompose the optimization task, enabling us to handle DPO instances with more variables than the available qubits on current hardware. These advances, which are broadly applicable to other optimization problems, allow us to address a portfolio with a size relevant to the financial industry, consisting of up to 38 assets and covering the full Spanish stock index (IBEX 35). Our results, obtained on a real Quantum Processing Unit (IBM Fez), show that this tailored workflow achieves financial performance on par with classical methods while delivering a broader set of high-quality investment strategies, demonstrating a viable path towards obtaining practical advantage from quantum optimization in real financial applications. ...

Portfolio construction using a sampling-based variational quantum scheme ArXiv ID: 2508.13557 “View on arXiv” Authors: Gabriele Agliardi, Dimitris Alevras, Vaibhaw Kumar, Roberto Lo Nardo, Gabriele Compostella, Sumit Kumar, Manuel Proissl, Bimal Mehta Abstract The efficient and effective construction of portfolios that adhere to real-world constraints is a challenging optimization task in finance. We investigate a concrete representation of the problem with a focus on design proposals of an Exchange Traded Fund. We evaluate the sampling-based CVaR Variational Quantum Algorithm (VQA), combined with a local-search post-processing, for solving problem instances that beyond a certain size become classically hard. We also propose a problem formulation that is suited for sampling-based VQA. Our utility-scale experiments on IBM Heron processors involve 109 qubits and up to 4200 gates, achieving a relative solution error of 0.49%. Results indicate that a combined quantum-classical workflow achieves better accuracy compared to purely classical local search, and that hard-to-simulate quantum circuits may lead to better convergence than simpler circuits. Our work paves the path to further explore portfolio construction with quantum computers. ...

Monte-Carlo Option Pricing in Quantum Parallel ArXiv ID: 2505.09459 “View on arXiv” Authors: Robert Scriba, Yuying Li, Jingbo B Wang Abstract Financial derivative pricing is a significant challenge in finance, involving the valuation of instruments like options based on underlying assets. While some cases have simple solutions, many require complex classical computational methods like Monte Carlo simulations and numerical techniques. However, as derivative complexities increase, these methods face limitations in computational power. Cases involving Non-Vanilla Basket pricing, American Options, and derivative portfolio risk analysis need extensive computations in higher-dimensional spaces, posing challenges for classical computers. Quantum computing presents a promising avenue by harnessing quantum superposition and entanglement, allowing the handling of high-dimensional spaces effectively. In this paper, we introduce a self-contained and all-encompassing quantum algorithm that operates without reliance on oracles or presumptions. More specifically, we develop an effective stochastic method for simulating exponentially many potential asset paths in quantum parallel, leading to a highly accurate final distribution of stock prices. Furthermore, we demonstrate how this algorithm can be extended to price more complex options and analyze risk within derivative portfolios. ...

Quantum Computing for Multi Period Asset Allocation ArXiv ID: 2410.11997 “View on arXiv” Authors: Unknown Abstract Portfolio construction has been a long-standing topic of research in finance. The computational complexity and the time taken both increase rapidly with the number of investments in the portfolio. It becomes difficult, even impossible for classic computers to solve. Quantum computing is a new way of computing which takes advantage of quantum superposition and entanglement. It changes how such problems are approached and is not constrained by some of the classic computational complexity. Studies have shown that quantum computing can offer significant advantages over classical computing in many fields. The application of quantum computing has been constrained by the unavailability of actual quantum computers. In the past decade, there has been the rapid development of the large-scale quantum computer. However, software development for quantum computing is slow in many fields. In our study, we apply quantum computing to a multi-asset portfolio simulation. The simulation is based on historic data, covariance, and expected returns, all calculated using quantum computing. Although technically a solvable problem for classical computing, we believe the software development is important to the future application of quantum computing in finance. We conducted this study through simulation of a quantum computer and the use of Rensselaer Polytechnic Institute’s IBM quantum computer. ...

Decomposition Pipeline for Large-Scale Portfolio Optimization with Applications to Near-Term Quantum Computing ArXiv ID: 2409.10301 “View on arXiv” Authors: Unknown Abstract Industrially relevant constrained optimization problems, such as portfolio optimization and portfolio rebalancing, are often intractable or difficult to solve exactly. In this work, we propose and benchmark a decomposition pipeline targeting portfolio optimization and rebalancing problems with constraints. The pipeline decomposes the optimization problem into constrained subproblems, which are then solved separately and aggregated to give a final result. Our pipeline includes three main components: preprocessing of correlation matrices based on random matrix theory, modified spectral clustering based on Newman’s algorithm, and risk rebalancing. Our empirical results show that our pipeline consistently decomposes real-world portfolio optimization problems into subproblems with a size reduction of approximately 80%. Since subproblems are then solved independently, our pipeline drastically reduces the total computation time for state-of-the-art solvers. Moreover, by decomposing large problems into several smaller subproblems, the pipeline enables the use of near-term quantum devices as solvers, providing a path toward practical utility of quantum computers in portfolio optimization. ...

PO-QA: A Framework for Portfolio Optimization using Quantum Algorithms ArXiv ID: 2407.19857 “View on arXiv” Authors: Unknown Abstract Portfolio Optimization (PO) is a financial problem aiming to maximize the net gains while minimizing the risks in a given investment portfolio. The novelty of Quantum algorithms lies in their acclaimed potential and capability to solve complex problems given the underlying Quantum Computing (QC) infrastructure. Utilizing QC’s applicable strengths to the finance industry’s problems, such as PO, allows us to solve these problems using quantum-based algorithms such as Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA). While the Quantum potential for finance is highly impactful, the architecture and composition of the quantum circuits have not yet been properly defined as robust financial frameworks/algorithms as state of the art in present literature for research and design development purposes. In this work, we propose a novel scalable framework, denoted PO-QA, to systematically investigate the variation of quantum parameters (such as rotation blocks, repetitions, and entanglement types) to observe their subtle effect on the overall performance. In our paper, the performance is measured and dictated by convergence to similar ground-state energy values for resultant optimal solutions by each algorithm variation set for QAOA and VQE to the exact eigensolver (classical solution). Our results provide effective insights into comprehending PO from the lens of Quantum Machine Learning in terms of convergence to the classical solution, which is used as a benchmark. This study paves the way for identifying efficient configurations of quantum circuits for solving PO and unveiling their inherent inter-relationships. ...

Towards A Post-Quantum Cryptography in Blockchain I: Basic Review on Theoretical Cryptography and Quantum Information Theory ArXiv ID: 2407.18966 “View on arXiv” Authors: Unknown Abstract Recently, the invention of quantum computers was so revolutionary that they bring transformative challenges in a variety of fields, especially for the traditional cryptographic blockchain, and it may become a real thread for most of the cryptocurrencies in the market. That is, it becomes inevitable to consider to implement a post-quantum cryptography, which is also referred to as quantum-resistant cryptography, for attaining quantum resistance in blockchains. ...

Time series generation for option pricing on quantum computers using tensor network ArXiv ID: 2402.17148 “View on arXiv” Authors: Unknown Abstract Finance, especially option pricing, is a promising industrial field that might benefit from quantum computing. While quantum algorithms for option pricing have been proposed, it is desired to devise more efficient implementations of costly operations in the algorithms, one of which is preparing a quantum state that encodes a probability distribution of the underlying asset price. In particular, in pricing a path-dependent option, we need to generate a state encoding a joint distribution of the underlying asset price at multiple time points, which is more demanding. To address these issues, we propose a novel approach using Matrix Product State (MPS) as a generative model for time series generation. To validate our approach, taking the Heston model as a target, we conduct numerical experiments to generate time series in the model. Our findings demonstrate the capability of the MPS model to generate paths in the Heston model, highlighting its potential for path-dependent option pricing on quantum computers. ...

Quantum Computational Algorithms for Derivative Pricing and Credit Risk in a Regime Switching Economy ArXiv ID: 2311.00825 “View on arXiv” Authors: Unknown Abstract Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both realistic in terms of mimicking financial market risks as well as more amenable to potential quantum computational advantages. The type of models we study are based on a regime switching volatility model driven by a Markov chain with observable states. The basic model features a Geometric Brownian Motion with drift and volatility parameters determined by the finite states of a Markov chain. We study algorithms to estimate credit risk and option pricing on a gate-based quantum computer. These models bring us closer to realistic market settings, and therefore quantum computing closer the realm of practical applications. ...