Abstract Quantum computing is increasingly discussed as a possible source of new computational methods for economics, but its relevance depends on whether economic bottlenecks match quantum algorithmic primitives. This critical review evaluates that match for computational economics. It synthesizes work on quantum amplitude estimation and quantum Monte Carlo for simulation and risk measurement; quadratic unconstrained binary optimization (QUBO), Ising formulations, quantum annealing, and the quantum approximate optimization algorithm for discrete optimization; and quantum linear-algebra and machine-learning primitives for econometrics and model solution. The review argues that there is no general-purpose quantum algorithm for economics analogous to Shor's algorithm for factoring. Credible claims are problem-class specific and depend on state preparation, output requirements, conditioning, hardware noise, embedding overhead, and comparison with strong classical and quantum-inspired baselines. The most mature economic applications are derivative pricing and financial risk, payment-system liquidity optimization, quantum Monte Carlo for stress testing, and early quantum-annealing formulations of dynamic programming. Transportation and infrastructure applications are relevant mainly as networked economic optimization problems. The article proposes an evidence ladder for quantum computational economics and a research agenda centered on reproducible benchmarks, economically meaningful objective functions, end-to-end resource accounting, and evaluation by economic value rather than hardware novelty. JEL Classification: C02; C15; C61; C63; C88; E37; G11; G17; R41
Abstract Quantum computing is increasingly discussed as a possible source of new computational methods for economics, but its relevance depends on whether economic bottlenecks match quantum algorithmic primitives. This critical review evaluates that match for computational economics. It synthesizes work on quantum amplitude estimation and quantum Monte Carlo for simulation and risk measurement; quadratic unconstrained binary optimization (QUBO), Ising formulations, quantum annealing, and the quantum approximate optimization algorithm for discrete optimization; and quantum linear-algebra and machine-learning primitives for econometrics and model solution. The review argues that there is no general-purpose quantum algorithm for economics analogous to Shor's algorithm for factoring. Credible claims are problem-class specific and depend on state preparation, output requirements, conditioning, hardware noise, embedding overhead, and comparison with strong classical and quantum-inspired baselines. The most mature economic applications are derivative pricing and financial risk, payment-system liquidity optimization, quantum Monte Carlo for stress testing, and early quantum-annealing formulations of dynamic programming. Transportation and infrastructure applications are relevant mainly as networked economic optimization problems. The article proposes an evidence ladder for quantum computational economics and a research agenda centered on reproducible benchmarks, economically meaningful objective functions, end-to-end resource accounting, and evaluation by economic value rather than hardware novelty. JEL Classification: C02; C15; C61; C63; C88; E37; G11; G17; R41
Quantum computing has emerged as a transformative computational paradigm, offering novel capabilities to tackle complex problems in finance—most notably in derivative pricing, risk management, and portfolio optimization. This review synthesizes recent advances in quantum algorithms and hybrid quantum–classical frameworks as applied to financial services, examining how technologies such as quantum-annealing, quantum amplitude estimation, and variational quantum circuits can improve efficiency, accuracy, and scalability over classical methods. The study provides a systematic assessment of key use-cases: (1) derivative pricing and greeks computation via quantum Monte Carlo and amplitude estimation; (2) risk management enhancements, including Value-at-Risk (VaR) and conditional VaR through quantum gradient estimation; and (3) portfolio optimization via QUBO (quadratic unconstrained binary optimization) mapping, the Quantum Approximate Optimization Algorithm (QAOA) and quantum annealing approaches. In addition to reviewing technological potential, the paper addresses critical barriers—hardware noise, coherence limitations, data integration, regulatory considerations—and outlines future research directions, including quantum-resilient cryptography in finance and industry coupling. By bringing together algorithmic, financial and regulatory perspectives, this review seeks to guide academics and practitioners toward the next frontier in financial computing.
Quantum computing represents one of the most disruptive technological paradigms of the 21st century, with profound implications for economic modelling, financial optimization, and computational decision-making. Unlike classical computing, quantum systems leverage superposition, entanglement, and interference to solve problems of exponentially higher complexity, a capability with transformative potential for economics and finance. This study examines the intersection of quantum computing and economics, systematically evaluating both the promises and the barriers defining this emerging field. Regarding opportunities, quantum algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA) and Grover's algorithm, demonstrate significant theoretical advantages in portfolio optimization, risk assessment, option pricing, and the resolution of large-scale combinatorial problems that are intractable for classical machines. Quantum machine learning extends these prospects, offering accelerated capabilities for pattern recognition and predictive modelling relevant to financial markets. However, substantial barriers temper these expectations. Current quantum hardware operates in the NISQ (Noisy Intermediate-Scale Quantum) era, where decoherence, gate errors, and a limited number of qubits constrain practical applicability. The gap between theoretical quantum advantage and real-world economic implementation remains significant, compounded by a shortage of specialists, high infrastructure costs, and the absence of standardized programming frameworks tailored to economic applications. Through a bibliometric analysis of existing literature and a critical review of recent experimental results, the study maps the current state of quantum computing adoption in economics, identifies the most active research frontiers—quantum game theory and quantum portfolio optimization—and outlines the conditions under which quantum advantage could become economically relevant. The findings suggest that, although quantum computing will not transform economic practice in the short term, its long-term disruptive potential warrants proactive engagement from economists, financial institutions, and policymakers.
Quantum computing is becoming strategically relevant to finance because several core financial bottlenecks are already defined by combinatorial search, expectation estimation, rare-event analysis, representation learning, and long-horizon cryptographic resilience. This review examines that landscape across five connected domains: constrained portfolio optimisation, derivative pricing, tail-risk and scenario estimation, quantum machine learning, and post-quantum security. Rather than treating these topics as isolated demonstrations, the article studies them as linked layers of a financial-computation stack. Across all five domains, the review applies a common evaluative logic: identify the financial bottleneck, specify the relevant quantum primitive, compare it with an explicit classical benchmark, and assess the result under realistic implementation and governance constraints. The main conclusion is measured but consequential. The strongest near-term case for quantum finance lies in carefully designed hybrid workflows rather than blanket claims of universal advantage. Quantum optimisation is most credible when constrained search dominates; amplitude-estimation methods matter most when repeated expectation evaluation is the binding cost; quantum machine learning remains task dependent; and post-quantum cryptography is already strategically necessary because financial infrastructures must migrate before fault-tolerant attacks arrive. By combining system-level synthesis with locally reproducible small-scale case studies on simulated qubit registers, the article is intended both as a review of the field and as a handbook-style entry point for future work.
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.
Quantum computing is revolutionizing computational methods in finance by enhancing efficiency and accuracy in financial modeling and risk management. This review explores the impact of quantum computing in finance, focusing on derivative pricing, risk management, and portfolio optimization. It analyzes the benefits, limitations, and future implications of integrating quantum technologies with classical financial systems. A comprehensive review of quantum Monte Carlo methods, quantum algorithms, and their financial applications was conducted. Theoretical foundations, including Chebyshev’s inequality and Grover’s search method, were evaluated for their role in enhancing sampling efficiency and predictive accuracy. Empirical studies and use cases demonstrate the practical implications of quantum computing in pricing financial derivatives and managing risk through Value at Risk and Conditional Value at Risk assessments. The critical findings reveal that Quantum Monte Carlo algorithms provide substantial efficiency gains, reducing sample size requirements by up to fourfold compared to classical methods. Techniques employed in prior studies highlight the effectiveness of Quantum Amplitude Estimation for derivative pricing and risk analysis. However, challenges persist in scalability, data quality, integration with classical systems, and compliance with regulatory standards. This research contributes to the current body of knowledge by providing a comprehensive analysis of quantum algorithms’ practical applications in derivative pricing, risk management, and portfolio optimization, demonstrating the efficiency gains and limitations of quantum approaches. Future research should explore hybrid quantum–classical frameworks, quantum applications in blockchain, and enhanced quantum cryptography to ensure secure and efficient financial transactions.
Quantum algorithms have been proposed for most computational tasks in trading, but the resulting literature is not a single body of work with a single standard of evidence. This survey partitions it into strands with distinct foundations and assesses each against the strongest available evidence. Pricing and market-risk computation rest on quantum amplitude estimation and carry a proven quadratic advantage in inverse precision; circuit-level resource estimates place the requirement at roughly 8000 logical qubits and a logical clock rate of tens of megahertz, several orders of magnitude beyond demonstrated hardware, with joint estimation of prices and sensitivities the main lever that lowers it. Combinatorial formulations of portfolio selection, multi-period trading trajectories and arbitrage detection map onto quadratic unconstrained binary optimization and have the field’s most mature hardware demonstrations, but an extensive benchmark on 250 real-stock instances finds classical mixed-integer programming and tailored heuristics dominant. Quantum machine learning for return prediction has been substantially dequantized, and a controlled evaluation on cross-sectional equity returns attributes reported advantages to evaluation protocol rather than to the model. A fourth strand exploits entanglement for decision coordination under latency constraints, where the advantage follows from Bell’s theorem rather than a complexity assumption. We identify the classical-quantum interface, superquadratic structure, resource-estimate methodology, nonlocal-game design and adversarial benchmarking as the productive open directions.