This note separates two things often labelled “quantum finance”: the quantum formalism, which applies quantum-mechanical mathematics on classical computers and is judged by empirical fit, and quantum computers, which are judged by whether they complete tasks classical machines cannot. Classifying the evidence into four types (unconditional; beyond-classical under complexity assumptions; empirical claims on specific problems; asymptotic speedups requiring fault tolerance), it finds that, among the public evidence identified and verified here (cut-off 17 October 2026), no economic or financial task has demonstrated broadly accepted practical quantum advantage against strong classical baselines and end-to-end costs. The strongest unconditional results concern information resources rather than computational speed; the formalism has already produced methods usable on classical hardware and testable empirical results; the most mature provable speedup directly relevant to finance is the quadratic speedup of amplitude estimation, which requires fault-tolerant hardware; and because published estimates place the logical-qubit threshold for elliptic-curve discrete logarithms below that for derivative-pricing advantage, cryptographic infrastructure is a channel through which material impact may arrive earlier — a scenario, not a timing prediction, since the two workloads differ in gate counts, runtimes and fault-tolerance assumptions. The note is a structured synthesis of published evidence and reports no new experiments or measurements.
This note separates two things often labelled “quantum finance”: the quantum formalism, which applies quantum-mechanical mathematics on classical computers and is judged by empirical fit, and quantum computers, which are judged by whether they complete tasks classical machines cannot. Classifying the evidence into four types (unconditional; beyond-classical under complexity assumptions; empirical claims on specific problems; asymptotic speedups requiring fault tolerance), it finds that, among the public evidence identified and verified here (cut-off 17 October 2026), no economic or financial task has demonstrated broadly accepted practical quantum advantage against strong classical baselines and end-to-end costs. The strongest unconditional results concern information resources rather than computational speed; the formalism has already produced methods usable on classical hardware and testable empirical results; the most mature provable speedup directly relevant to finance is the quadratic speedup of amplitude estimation, which requires fault-tolerant hardware; and because published estimates place the logical-qubit threshold for elliptic-curve discrete logarithms below that for derivative-pricing advantage, cryptographic infrastructure is a channel through which material impact may arrive earlier — a scenario, not a timing prediction, since the two workloads differ in gate counts, runtimes and fault-tolerance assumptions. The note is a structured synthesis of published evidence and reports no new experiments or measurements.
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.
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 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.
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 physics and finance are often connected through mathematical analogy or promises of computational acceleration. This article develops an alternative account of asymmetric co-evolution. A selective conceptual synthesis distinguishes shared mathematical ancestry, explicit transfer, and reciprocal innovation across uncertainty, valuation, measurement, computation, and monetary security. Quantum theory supplies representational and computational possibilities; financial problems impose constraints that can redirect quantum information research. Documented feedback is strongest in algorithm design and cryptographic tasks. This article proposes testable research directions concerning investor judgment, financial validation, decision-relevant computational advantage, market adoption, and quantum money. Progress requires reciprocal discipline: quantum methods must satisfy financial restrictions, while finance must incorporate the physical and computational conditions governing information.
The world of finance is in flux again, and one of the reasons for this is due to quantum computers. This chapter, investigates the ways that financial thinking has grown over the years, and the role computers have played in that growth. Development of models such as Markowitz’s portfolio theory, Monte Carlo simulation and the Black-Scholes model, impacted the way modern finance operates. This was later pushed even further by high frequency trading. Now a new change is taking place as quantum approaches begin to enter the game. Quantum computing started as a collection of theoretical concepts. People like Feynman, Benioff ,Deutsch, Grover and Shor played major role in the development of the founding ideas. these founding ideas eventually led to the real machines, like International Business Machines’ (IBM’s) Q System One and Google’s Sycamore. Even though these devices are limited at this time, they have paved the way for new types of financial applications. For example, Monte Carlo for quantum, can bring forward the risk calculations quicker. Portfolio optimisation can be tried out by Quantum Approximate Optimization Algorithm (QAOA) or quantum annealing. Some researchers are using the quantum machine learning tools to detect fraud as well. Others are trying out pricing models for complex derivatives. Many large financial companies are already active in this field. John Pierpont Morgan (JPMorgan), Goldman Sachs, Wells Fargo, Hongkong and Shanghai Banking Corporation (HSBC), Mastercard and Banco Bilbao Vizcaya Argentaria (BBVA) have all been conducting experiments or partnerships. Small companies are also active, such as fintech firms such as Multiverse Computing. The governments are taking notice as well. The United States of America, the European Union, China and India have commenced major programs (like the US National Quantum Initiative and India’s National Quantum Mission), given that they recognize quantum technology as a major economical opportunity, as well as a strategic necessity. A lot of current work mixes classical and quantum methods. Most companies run small pilot tests, build hybrid algorithms, or work inside simulation platforms because fully reliable quantum computers do not exist yet. There are also many issues to deal with. Noise in the hardware, difficulty scaling up, challenges in translating financial problems into quantum formats, and questions about regulation all remain. There are ethical worries as well. Quantum tools could give some players an unfair advantage, weaken existing cryptographic systems, or increase the gap between countries and institutions. In the end, the message is simple. Large, fault-tolerant quantum computers may take time to arrive, but waiting too long is risky. Firms that start learning, testing, and training now will be in a much stronger position later. Quantum computing is no longer a far-off dream.