Financial markets depend on increasingly sophisticated models to price complex financial instruments and manage risk. As those models become more computationally intensive, new approaches are needed to keep pace.

To explore this, OQC, Citi, and the NQCC partnered through the SparQ programme to investigate how quantum computing and AI can work together to improve derivative pricing, one of the most computationally demanding workloads in finance.

The project evaluated whether hybrid quantum–AI techniques could deliver more efficient financial modelling without compromising the accuracy expected by financial institutions and regulators. The findings mark another step towards bringing quantum computing into real-world financial workstreams.

Why derivative pricing matters

Derivative pricing underpins many of the decisions made by banks and financial institutions. Accurate pricing models are essential for managing risk, supporting trading activity, allocating capital and meeting regulatory obligations.

As portfolios grow larger and market dynamics become more complex, these models must process increasing volumes of data across high-dimensional scenarios. Hybrid quantum approaches offer a potential path to scaling these calculations more efficiently, helping financial institutions meet tomorrow’s computational demands.

A new approach: combining quantum and AI

The goal was not to build a production pricing engine immediately, but to explore whether this emerging combination of quantum and AI techniques could offer advantages in the long term.

The collaboration explored the use of physics-informed neural networks (PINNs), a machine learning technique designed to solve complex mathematical models more efficiently.

In financial markets, many pricing models are governed by differential equations – mathematical formulas that describe how asset prices evolve over time. PINNs embed these equations directly into the training process of a neural network, allowing the model to learn pricing behaviour while remaining consistent with financial theory.

The project then explored how quantum methods could enhance these models by compressing parts of the neural network architecture, potentially reducing the number of parameters required for training. This quantum compression approach, known as Quantum-Train, aims to represent large neural network layers using quantum states and circuits, potentially improving efficiency while maintaining performance.

What the research showed

The team first benchmarked a classical machine learning approach against analytical pricing models to establish a baseline. From there, quantum compression techniques were applied to parts of the neural network architecture. The results demonstrated that a significant reduction in model complexity could be achieved.

In one set of experiments, the approach substantially reduced the number of parameters in the neural network layer, while producing pricing results that remained broadly aligned with the original model in selected scenarios. While some increases in modelling error were observed depending on where compression was applied within the architecture, the results demonstrated a clear trade-off between model size and predictive performance: a key insight for designing future quantum-enhanced machine learning systems.

Just as importantly, the project highlighted current limitations, including that compression produced different results depending on which hidden layer of the neural network was compressed. Certain regions of the pricing problem proved more challenging for both classical and quantum approaches, particularly where pricing curves become mathematically sharp or highly sensitive to market conditions.

One of the most interesting outcomes of the project was the ability to significantly compress the size of a classical neural network using a quantum-based approach without dramatically affecting its predictive performance. By applying the Quantum-Train method to a shallow neural network architecture, we substantially reduced the number of parameters in a key layer. Despite this substantial reduction in model complexity, the pricing results remained broadly comparable to the classical model in many scenarios, with errors still within the same order of magnitude for several cases. 

This highlights a promising direction for quantum-enhanced machine learning: using quantum representations to make large models more efficient while retaining much of their predictive power, an important step toward scalable AI systems for computationally demanding applications such as financial modelling. These findings provide valuable guidance for future research into hybrid quantum–classical modelling.

Moving quantum from theory to financial applications

Projects like this are an important step in turning quantum computing from a theoretical promise into a practical tool for industry.

Financial services are widely seen as one of the earliest sectors where quantum computing could deliver value. Many of the industry’s core problems, from portfolio optimisation to risk modelling, are computationally intensive and mathematically complex.

By working directly with financial institutions such as Citi, OQC is helping bridge the gap between quantum research and real-world use cases. This collaboration also reflects OQC’s broader strategy: developing application-optimised quantum computing designed to address industry problems rather than focusing solely on hardware development.

This highlights a promising direction for quantum-enhanced machine learning: using quantum representations to make large models more efficient while retaining much of their predictive power, an important step toward scalable AI systems for computationally demanding applications such as financial modelling. These findings provide valuable guidance for future research into hybrid quantum–classical modelling.

Building the foundations of quantum-ready finance

While the work was exploratory, it opened several promising directions for future research. Quantum computing will not transform financial markets overnight, however progress happens through collaborations like this, bringing together quantum engineers, AI researchers and financial experts to explore what works, what doesn’t, and where the opportunities lie.

For OQC, partnerships with organisations like Citi and SparQ are an essential part of that journey. They allow us to test quantum approaches against real industry problems and ensure that the systems we build are aligned with the needs of the financial sector.

As quantum technology advances, the insights gained today will help shape the next generation of financial infrastructure.