Financial services has always been one of the clearest places to look for quantum value, with many financial applications achieving small scale commercial advantage using quantum computing today. The sector runs on complex models, fast decisions and an enormous volume of uncertainty from derivatives pricing and market risk to credit exposure and capital optimisation, the problems are mathematically rich and commercially material.

But the real question is not simply whether quantum algorithms are interesting in theory. It is where quantum methods can fit into real financial workflows, how they compare with strong classical baselines, and what needs to happen for them to become operationally useful.

In recent work with Trust Base, OQC explored exactly this question across Value-at-Risk, Credit Valuation Adjustment and derivative pricing workflows. The project brought together classical Monte Carlo baselines, quantum-enhanced Monte Carlo, Physics-Informed Neural Networks and hybrid Quantum Physics-Informed Neural Networks to understand not just the promise of quantum finance, but the practical route towards it.

The result is a more grounded picture of quantum readiness in finance: one where near-term value comes from disciplined benchmarking, hybrid architectures and hardware-aware research, while the longer-term opportunity remains significant.

Why Derivative Pricing Is a Useful Testbed

Derivative pricing is central to modern financial markets. A pricing model needs to produce a value today for a payoff that depends on uncertain market movements in the future. For simple products, established methods such as Black-Scholes, finite-difference solvers and Monte Carlo simulation are well understood.

The challenge increases quickly when products become path-dependent, when volatility changes across time and market levels, or when interest-rate models introduce more complex dynamics. Barrier options, local-volatility models and swaptions all create difficult numerical features: sharp payoff kinks, absorbing boundaries, noisy curvature, nonlinear terminal payoffs and sensitivity measures that can be harder to stabilise than the price itself.

That makes this a powerful application for quantum-relevant methods. It tests whether a model can do more than match a single price and asks whether the fully learned surface is reliable enough for Greeks, exposure profiles and CVA.

For financial institutions, that distinction matters as a model that gets the price right but produces unstable sensitivities is not yet ready to be used for real risk management.

The Methods We Explored

The project examined three complementary approaches.

• Physics-Informed Neural Networks, or PINNs, learn the solution to a pricing partial differential equation directly from the governing equation, boundary conditions and payoff conditions. Instead of solving on a fixed grid, the model learns a continuous pricing surface over time and state variables.
• Quantum Physics-Informed Neural Networks, or Quantum-compressed Physics-Informed Neural Networks (QPINNs), extend this architecture with a parameterised quantum circuit that acts as a trainable quantum feature map. The aim is not to replace the classical workflow wholesale, but to investigate whether quantum features can improve expressivity or parameter efficiency inside a hybrid model.
• Quantum Monte Carlo takes a different route. Rather than solving the pricing PDE directly, it explores amplitude-estimation-based methods for estimating payoff expectations. In theory, this can offer attractive asymptotic speedups, whilst in practice, the work has to confront circuit depth, transpilation, qubit layout, noise and calibration.

Together, these approaches cover the two main routes being explored in quantum finance: 1) quantum-enhanced learning for pricing surfaces, and 2) quantum-enhanced simulation for expectation estimation.

Key Findings

1. The most important finding is also the most practical: price accuracy alone is not enough.Across the Black-Scholes/Garman-Kohlhagen, Dupire local-volatility and Hull-White model families, several models were able to match a benchmark price at a reference point. But the full pricing surface and its derivatives told a more nuanced story. Delta could often be improved with targeted training. Gamma however, which depends on second derivatives, remained much more fragile because it amplifies even small amounts of surface roughness.This matters because financial workflows depend on more than headline pricing. Hedging, exposure, CVA and stress analysis require models that behave consistently across the surface, not only at one chosen market point.
2. The second finding is that sampling and constraints matter more than parameter count alone. Adaptive sampling near maturity, strikes, barriers, exercise boundaries and domain edges had a material impact because these are exactly the regions where the equations are hardest to satisfy. In other words, better financial structure in the training process was often more valuable than simply making the network bigger.
3. A third lesson is that, within the specific use cases, implementations and evaluation conditions considered in this project, classical PINNs currently emerge as a practical recommendation among the tested methods. They provide a useful balance between implementation simplicity, runtime and numerical quality on today’s hardware. In the reported experiments, the classical PINN workflow was fast, flexible across product types and well suited to repeated downstream calculations such as EPE and CVA.

QPINNs remain highly valuable as a research direction. They can be competitive in parameter count and, in some cases, improve scalar pricing or exposure-based quantities. However, the current cost of repeatedly evaluating and differentiating through the quantum feature map makes the hybrid model much slower in wall-clock terms. Today, QPINNs are best understood as a platform for studying hybrid expressivity and future quantum-classical interfaces, rather than as a production replacement for classical solvers.

Quantum Monte Carlo offered a complementary lesson. Amplitude estimation is attractive in theory, but near-term performance depends heavily on the realities of execution: reflector choice, compilation strategy, qubit placement and hardware noise. The results showed that lower-cost circuit choices could sometimes produce smoother empirical behaviour than more exact but deeper constructions. 

That is an important reminder that practical quantum advantage will be won across the full stack, not in algorithm design alone.

Why This Matters for Financial Institutions

For banks and financial institutions, the path to quantum value is not a single leap from classical systems to fault-tolerant quantum advantage. It is a staged process of building capability, identifying the right workloads and understanding where quantum methods can be integrated into existing risk and pricing pipelines.

The work with Trust Base points towards a pragmatic roadmap.

First, build strong classical baselines. Without reproducible benchmarks for Monte Carlo, finite-difference methods and neural PDE solvers, it is impossible to measure whether a quantum-enhanced method is genuinely adding value.

Second, focus on hybrid workflows. Near-term quantum systems are most likely to contribute as part of a broader classical stack, where quantum components are used selectively for the parts of the problem where they may offer better representation, sampling or optimisation behaviour.

Third, evaluate the full workflow. For finance, a useful model must support pricing, sensitivities, exposure and risk calculations. Runtime, calibration cost, stability and integration all matter.

Finally, prepare for the hardware curve. As quantum hardware improves in qubit quality, qubit count, latency and error correction, the balance between classical and hybrid methods will change. The research being done today helps define which workloads will be ready when that shift arrives.

The results

The results show that resource requirements scale broadly linearly with the number of qubits used to encode the probability distribution. They also highlight the importance of hardware assumptions: increasing the fault-tolerance error correction threshold from 1% to 5%, for example through approaches such as dual-rail or erasure qubits, could reduce the required physical qubit count for a 32-qubit setup from around 404,000 to around 130,000. However, practical target precisions of (10-3 to 10-4) require high numbers of Grover repetitions, which remain beyond current classical resource estimation limits. This means that simplified baseline models are still needed today. Future algorithmic improvements, including Quantum Signal Processing (QSP), could materially reduce costs, with potential reductions of up to 16× in T-gates and 4× in logical qubits.

This is what quantum readiness looks like in practice. It is not about claiming that every financial workload should move to quantum today. It is about building the evidence, infrastructure and partnerships that allow the industry to move quickly when the technology is ready.

At OQC, that means bringing quantum out of the lab and into the enterprise environment: testing real workloads, benchmarking honestly, and building the systems that will allow customers to explore quantum capability through practical, secure and scalable infrastructure.

For finance, the opportunity is substantial. The route to it starts with work like this: rigorous, collaborative and grounded in the realities of both markets and machines.