Industry · Early Pilots
Quantum Computing for Finance
Financial institutions are exploring quantum algorithms for optimization and Monte Carlo-style simulations — among the most actively piloted near-term applications.
Maturity
Early pilots, with post-quantum security migration already underway
Most credible quantum workload
Monte Carlo estimation for derivative pricing and risk (amplitude estimation)
Hardware needed for that workload
Fault-tolerant machine with thousands of logical qubits
Strongest classical competition
GPU Monte Carlo, quasi-Monte Carlo, and commercial optimization solvers
Only urgent action today
Migrating cryptography to post-quantum standards
Realistic horizon for production use
Early 2030s for estimation tasks; later and less certain for the rest
Overview
Finance is the most visible commercial testing ground for quantum computing. Banks, asset managers, and insurers run some of the most computation-hungry workloads in the economy: pricing derivatives, measuring risk across millions of scenarios, building portfolios under dozens of constraints, and screening transactions for fraud. They also employ large numbers of quantitative researchers, so the sector can evaluate new methods quickly, and a small edge in speed or accuracy can be worth a great deal of money.
That combination explains why nearly every major bank now has a quantum team or a research partnership. It does not mean quantum computers are running trading desks. Today's activity falls into three groups: pilots on small, noisy machines whose results are compared against classical baselines; resource estimates that ask how large a fault-tolerant machine would need to be for a given task; and preparation for the security effects of quantum computing, which is the one area where action is already required.
Why this industry is a candidate for quantum computing
Two kinds of problems dominate quantitative finance. The first is simulation: estimating an average over many random scenarios, which is what Monte Carlo methods do for pricing and risk. The second is optimization: choosing the best combination of assets, trades, or hedges from an astronomically large set of possibilities. Quantum algorithms offer a provable quadratic speedup for Monte Carlo estimation and heuristic approaches to optimization.
Finance also has an unusual tolerance for approximate answers. A price needs to be correct to a cent, not to the last digit, and a portfolio only needs to be good, not provably optimal. That tolerance suits near-term hybrid methods that give approximate answers, and it lowers the bar for a useful quantum contribution compared with fields that need exact results.
Key facts and numbers
| Item | Detail |
|---|---|
| Post-quantum standards | NIST FIPS 203 (ML-KEM), 204 (ML-DSA), and 205 (SLH-DSA), published in August 2024 |
| RSA-2048 break estimate | Fewer than one million noisy physical qubits, under a week (Gidney, 2025) |
| Derivative pricing advantage | On the order of 8,000 logical qubits (Goldman Sachs, IBM, and QC Ware, 2021) |
| HSBC and IBM bond study | Up to 34 percent better fill prediction, up to 109 qubits and about 4,200 gates (September 2025) |
| JPMorgan certified randomness | 56-qubit Quantinuum H2 with supercomputer verification, published in Nature in 2025 |
| Monte Carlo error scaling | Classical: 1 over the square root of N; quantum amplitude estimation: 1 over N |
| Key sizes | ML-KEM-768 public key is 1,184 bytes versus 32 bytes for X25519 |
Where quantum computing could help
Derivative pricing and risk measurement
The problem: Pricing a complex derivative or computing a risk measure such as value at risk usually means simulating many paths of market variables and averaging the payoff. Accuracy improves only as one over the square root of the number of paths, so a ten-fold gain in accuracy needs a hundred-fold increase in computation, and large banks run these calculations overnight on big clusters.
The quantum approach: Quantum amplitude estimation encodes the expected payoff as an amplitude and estimates it with error that shrinks as one over the number of circuit runs, a quadratic improvement. The 2021 study by Goldman Sachs, IBM, and QC Ware titled A Threshold for Quantum Advantage in Derivative Pricing estimated what hardware this needs.
Where things stand: That study found that a useful advantage for a representative derivative would need on the order of eight thousand logical qubits and a very fast, error-corrected machine, which is well beyond today's chips. Small price calculations have been run on IBM and other devices, but they use a handful of qubits and do not beat classical methods.
Related algorithms: Quantum Amplitude Estimation, Quantum Monte Carlo Integration, Quantum Mean Estimation
Portfolio optimization and trading
The problem: Building a portfolio that maximizes return for a given risk, while respecting limits on position size, sectors, turnover, and transaction costs, is a constrained optimization problem that grows hard as assets and constraints are added.
The quantum approach: The problem is written as a quadratic binary optimization and attacked with QAOA on gate-based machines or with quantum annealing. Hybrid solvers split large problems between classical and quantum parts. Banks such as BBVA and Santander have run studies with Multiverse Computing and others on exactly this task.
Where things stand: Benchmarks generally show strong classical heuristics and solvers matching or beating current quantum methods at realistic sizes. Quantum-inspired classical hardware, such as Fujitsu's Digital Annealer and Toshiba's simulated bifurcation machines, has found some commercial use for similar problems, which shows that part of the value comes from the formulation, not from quantum effects.
Related algorithms: Quantum Approximate Optimization Algorithm (QAOA), Quantum Annealing, Max-Cut with Quantum Algorithms (QAOA and Quantum Max-Cut)
Machine learning for prediction and fraud detection
The problem: Predicting whether a customer's trade request will be filled, flagging fraudulent transactions, and scoring credit risk are classification and regression tasks on noisy, high-dimensional data, where small accuracy gains translate into real revenue or avoided losses.
The quantum approach: Quantum feature maps and kernel methods embed data in a high-dimensional quantum state space, and a classical model is trained on top. The hope is that quantum features capture structure that classical features miss.
Where things stand: In September 2025, HSBC and IBM reported up to a 34 percent improvement in predicting whether a European corporate bond trade would be filled at the quoted price, using real production-scale data, a hybrid workflow, and up to 109 qubits of an IBM Heron processor with circuits of up to about 4,200 gates. The authors noted that the result lacks guarantees of generalization to other markets and datasets, and that device noise may have contributed to the effect, so it is an encouraging data point and not proof of advantage.
Related algorithms: Quantum Kernel Estimation, Quantum Support Vector Machine, Quantum Anomaly Detection
Cryptography, randomness, and security
The problem: Financial systems rely on public-key cryptography for payments, settlement, signatures, and customer data, and adversaries can record encrypted traffic today and decrypt it once a large quantum computer exists. That risk is called harvest now, decrypt later.
The quantum approach: The fix is to migrate to post-quantum cryptography, which runs on ordinary computers. Quantum devices also contribute directly: in 2025 JPMorgan Chase, working with Quantinuum and U.S. national laboratories, published in Nature a protocol that used a 56-qubit trapped-ion machine to generate randomness that can be certified, with classical supercomputers verifying the result.
Where things stand: Migration is the one quantum-related task in finance with a firm deadline. The U.S. National Institute of Standards and Technology published its first post-quantum standards in August 2024, and regulators and industry groups in the United States, Europe, and the United Kingdom have issued timelines running to the early and mid 2030s. Certified randomness is a proof of principle with niche commercial relevance.
Related algorithms: Shor's Algorithm, Random Circuit Sampling (Quantum Supremacy Experiments), BB84 Quantum Key Distribution
Who is working on it
- HSBC, with IBM, on algorithmic bond trading, and with a dedicated Group Head of Quantum Technologies who has described operational enhancement, financial simulation, and machine learning as the focus areas.
- JPMorgan Chase, which publishes extensively, including a 2023 survey of quantum computing for finance in Nature Reviews Physics, and the 2025 certified randomness work with Quantinuum.
- Goldman Sachs, whose researchers produced the widely cited derivative pricing resource estimate with IBM and QC Ware.
- BBVA, Santander, Wells Fargo, Citi, Barclays, and Vanguard, which have run pilots or partnerships on portfolio optimization, risk, and security, often with Multiverse Computing, IBM, IonQ, or Quantinuum.
- Regulators and standards bodies, including NIST and European and UK authorities, on the post-quantum migration timeline.
Realistic timeline
| Horizon | What to expect |
|---|---|
| Now to 2028 | Post-quantum migration is the main operational task. Pilots on noisy hardware continue, mostly hybrid workflows for prediction and optimization, benchmarked against strong classical baselines. |
| 2028 to 2032 | Early fault-tolerant machines with tens to hundreds of logical qubits arrive. Small amplitude estimation and optimization demonstrations become possible, but probably not yet cost-effective. |
| 2032 and later | If error-corrected machines reach thousands of logical qubits at fast clock rates, Monte Carlo estimation for pricing and risk becomes the first likely production use. Broader advantage in optimization and machine learning remains uncertain. |
How to judge quantum claims in this sector
Finance is a good place to learn how to read quantum claims, because the baselines are well defined. For a pricing or risk task, ask what the classical method is, what hardware it runs on, and what accuracy it reaches in the same time. Production banks use GPU-accelerated Monte Carlo, variance reduction, and quasi-Monte Carlo methods, and a fair test compares against those, not against a naive single-core simulation. For optimization, the right baseline is a commercial mixed-integer solver or a tuned heuristic, run for the same wall-clock time.
Several features of a claim deserve scrutiny. Was the problem small enough to solve exactly on a laptop? Did the quantum step carry the work, or did classical pre- and post-processing do most of it? Was the result tested on out-of-sample data, and does it hold at larger sizes? The HSBC study is useful because it used production-scale data, but its authors state clearly that generalization and the role of noise are open questions, which is the standard to hold other announcements to.
What stands in the way
- Hardware: the cleanest speedup, amplitude estimation, needs deep circuits and thousands of logical qubits.
- Data loading: encoding market distributions and models into quantum states can cost as much as the computation it replaces.
- Classical competition: GPUs, quasi-Monte Carlo methods, and specialized optimizers keep improving, which keeps raising the bar.
- Governance: model validation, regulation, and explainability requirements slow adoption of any new method in production.
What organizations in this sector should do now
- Inventory cryptography across systems and vendors, and plan the post-quantum migration now, because it has a deadline and a long lead time.
- Keep a small research group that benchmarks quantum methods against the best classical alternatives on real internal problems.
- Estimate which workloads, such as large Monte Carlo runs, would benefit from a quadratic speedup and how large the hardware would need to be.
- Develop talent through partnerships and training, so the firm can evaluate vendor claims independently.
Myths versus reality
- Myth: banks already trade with quantum computers. Reality: results so far come from trials, not live trading.
- Myth: a quantum computer will instantly price everything. Reality: the proven speedup for pricing is quadratic and needs large fault-tolerant machines.
- Myth: quantum computing only matters to finance in the future. Reality: the cryptographic risk requires action today.
The bottom line
For financial firms the quantum story has two timelines. Security is urgent, concrete, and already regulated, so it deserves budget now. Computational advantage is a probable but distant event that depends on fault-tolerant hardware, and is best handled by a small research team that benchmarks honestly and builds expertise. Treat headlines about speedups with care until they are reproduced against strong classical baselines.
Frequently asked questions
Is quantum computing used in banks today?
Banks run pilots and research projects on quantum hardware, but not in core trading or risk systems. The one area where action is already required is migrating cryptography to post-quantum standards.
What did the HSBC and IBM trial show?
Using a hybrid quantum-classical workflow on IBM Heron processors and real bond trading data, HSBC reported up to a 34 percent improvement in predicting whether a trade would be filled at a quoted price. It was not a live deployment, and the authors caution that results may not generalize.
How many qubits would derivative pricing need?
A 2021 study by Goldman Sachs, IBM, and QC Ware estimated roughly eight thousand logical qubits and extremely fast error-corrected operation for a useful advantage on a representative derivative.
Which financial problems benefit most from quantum computers?
Monte Carlo estimation for pricing and risk has the best-established theoretical speedup. Optimization and machine learning are promising but unproven.
What should a financial firm do first?
Start the post-quantum cryptography migration, since it is the one quantum-related task with a deadline, and keep a small team benchmarking quantum methods against classical baselines.
Keep exploring
- Algorithm: Quantum Amplitude Estimation
- Algorithm: Quantum Approximate Optimization Algorithm (QAOA)
- Algorithm: Quantum Monte Carlo Integration
- Algorithm: Shor's Algorithm
- Hardware: IBM Heron (r1, r2, and r3)
- Hardware: Quantinuum H2
- Company: IBM
- Company: Quantinuum
- Company: Multiverse Computing
- Research: Benchmarking QAOA Against Classical Heuristics for Portfolio Optimization
- Research: Quantum Kernel Methods Show Advantage on a Specific Synthetic Dataset
- Research: Case Study: Post-Quantum Cryptography Migration in a Large Financial Institution
- Industry: Quantum Computing for Cybersecurity
- Industry: Quantum Computing for Insurance
- Industry: Quantum Computing for Logistics
- Industry: Quantum Computing for Manufacturing
This page is written for educational purposes and summarizes public announcements, published research, and published resource estimates (last reviewed September 30, 2026). Vendor and customer claims have not all been independently verified, timelines are estimates, and nothing here is investment or business advice.