Quantum Computing Applications in Finance: Optimization, Simulation, and Risk
Summary
The document surveys learning resources and possible uses of quantum computing in quantitative finance. It highlights optimization and simulation as areas of interest, including quantum annealing for constrained graph problems that may help represent arbitrage searches involving multi-legged instruments. The responses also point to educational material on quantum mechanics and quantum computation, along with collections of finance-related work involving Monte Carlo methods, derivatives pricing, and optimization problems.
Other cited applications include financial risk management on quantum hardware and quantum machine learning, though some examples are general-purpose methods rather than finance-specific algorithms. The discussion is exploratory: it offers sources and examples, not a systematic performance comparison or evidence that quantum approaches outperform classical ones in practical trading. It also notes uncertainty about the maturity, novelty, and acceptance of some resources and approaches. Readers should distinguish demonstrations on simulators or specialized devices from scalable, production-ready quantum computing applications.
Key ideas
- Quantum optimization and simulation are proposed as potential applications in quantitative finance.
- Quantum annealing may address certain constrained graph problems, including representations of multi-instrument arbitrage searches.
- Suggested learning resources span quantum foundations, computation, derivatives pricing, Monte Carlo methods, and optimization.
- Quantum machine learning and risk-management examples are discussed, including work that is not finance-specific.
- The document is an exploratory resource survey and does not establish practical superiority over classical methods.
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Full text
# Quantum Computing for Quantitative Finance # Quantum Computing for Quantitative Finance It's been a while that quantum computing is looked as the next step in computational science. I somewhat always tought we were decade aways from it's happening but it appears I was wrong: ibm-quantum-computing-cloud (well, I am still not sure this is a large scale quantum computer or an efficient quantum computer replication; edit: changed the link; it is a simulator) Quantum mechanics and quantitative finance were already linked by some powerfull tools (ex. Random matrix theory (RMT) in finance) or shady reasonments (Quantum Mechanics and Economics... What) but I did not really considered quantum mechanics as the next step of QF. For a long time papers I could find on the topic were either quantum mechanics oriented (see Path_integral_formulation and links) or 'poor' in term of quantitative finance (see Quantum_finance and links). Now, I can find more interesting papers (currently at work, will post the relevant paper later) and I am somewhat convinced that quantum computing could be a huge step ahead in both optimization and simulation and so in quantitative finance. I am now looking for some good sources (keep in mind the aim is 3, I don't necessarly need to go trough all quantum mechanics again) on - quantum mechanics - quantum computing - quantum computing applied to quantitative finance ## Answer by user28802 (score 6) https://quant.stackexchange.com/a/35183 Try Quantum for Quants, which has contributions from people working actively in quantum computing, and some small scale examples solved on the D-Wave Systems Quantum Annealer. The picture below is from an article on Finding Arbitrage Opportunities using a Quantum Annealer (the link is on the Q4Q main page). The annealer can solve certain graph theory problems very quickly, including those with multiple constraints on traversing the edges, so that calculations with multi-legged instruments are easier to manage. ## Answer by KarolisR (score 2) https://quant.stackexchange.com/a/25829 For #1 and #2 I really enjoyed this Edx course from UC Berkeley: Quantum Mechanics and Quantum Computation And for #3 you seem to have the sources already :) ## Answer by Martin Vesely (score 2) https://quant.stackexchange.com/a/51640 See here list of articles and sources I have been interested in. They concern Monte Carlo method, derivative pricing and TSP. And here is a link to on-line course on basics of a quantum computing. I took the course and I could only recommend it. ## Answer by Lucas Morin (score 2) https://quant.stackexchange.com/a/74724 I have found one application of quantum computing in financial risk management: Financial Risk Management on a Neutral Atom Quantum Processor It was run on a real machine and seems it will outperform standard approach by 2026. It is not specificly a quant finance algo but mostly a general purpose ML algo. Still, it seems interesting in the context of the question. ## Answer by Lucas Morin (score 1) https://quant.stackexchange.com/a/77840 There seems to be a general advancement on the use of quantum computing for ML, that then can be applied in finance. See: Financial Risk Management on a Neutral Atom Quantum Processor. While it is not strictly quantitative finance, it can impact all ML applications in the financial domain. ## Answer by ZKMathquant (score 1) https://quant.stackexchange.com/a/85667 Can think of two books on top of my head. Not aware of the quality or acceptance of the same in quant world, however. Not that acquianted to quantum world either, to guarantee the novelty of the quantum methods being used including QFT,QML etc Here are the resources: - "Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates", Belal E. Baaquie (2010): Book on QFT applied to interest models. - "Quantum Machine Learning and Optimisation in Finance: Drive financial innovation with quantum-powered algorithms and optimisation strategies, Second Edition", Jacquier Antoine and Alexei Kondratyev (2024): QNNs applied to credit approvals, etc. - Recently concluded workshop by Fields institutes with lectures on quantum algorithms relevant and potentially useful to finance
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