Periodic Reporting for period 2 - SINGULARITY (SINGULARITY: The first quantum software toolbox for finance)
Okres sprawozdawczy: 2023-09-01 do 2024-12-31
SINGULARITY is the first quantum software toolkit for finance. The toolkit leverages the best of classical and quantum hardware to tackle financial problems in their full complexity. SINGULARITY contains several proprietary quantum and quantum-inspired algorithms based on quantum machine learning, tensor networks, and quantum annealing. These methods outperform state-of-the-art approaches in investment optimisation, capital allocation, and risk management. Their performance has been stringently tested in proof-of-concept trials with leading financial institutions using real quantum computers. While SINGULARITY owes its performance to advanced quantum techniques, its interface is intuitive and requires no specialised quantum computing knowledge. The toolbox does all the preprocessing needed to make financial data quantum-ready autonomously. Thus, SINGULARITY can be seamlessly integrated into standard financial software and used by quantitative staff without further training.
In this project we focus on developing the algorithms and tools to be integrated into the SINGULARITY financial toolkit. In particular, in this project we focus on developing tools that can be used to help improve the stability of the global financial markets by improving securities pricing and risk management, and global network analysis techniques .
In this project we focus on developing the algorithms and tools to be integrated into the SINGULARITY financial toolkit. In particular, in this project we focus on developing tools that can be used to help improve the stability of the global financial markets by improving securities pricing and risk management, and global network analysis techniques .
A major focus is on pricing complex derivatives. Our main achievement is the development of deep pricing methodology to improve speed and efficiency, up to 15,000x compared to traditional Monte Carlo, using quantum-inspired deep learning architectures. For other complex high-dimensional we introduce a tensor network-enhanced deep learning framework for Bermudan derivatives, achieving more accurate Swaption pricing than standard Monte Carlo methods. Alongside these deep learning approaches we designed quantum circuits for pricing Autocallables via quantum Monte Carlo showcasing the future potential.
We also applied quantum Monte Carlo to portfolio valuation under stochastic growth, resulting in the Singularity Quantum Monte Carlo SDK—an accessible toolkit for building advanced quantum circuits. Additionally, our tensor network integration framework outperformed classical Monte Carlo methods on high-dimensional financial problems.
On the macroeconomic front, we proposed a QUBO-based quantum approach for analyzing financial network stability using quantum annealing and quantum-inspired algorithms, enabling practical applications.
A core goal of the Singularity project is democratizing quantum computing. To support non-expert users, we developed intuitive middleware, including:
• A Python-accessible API;
• AWS-based backend for running solutions on quantum and GPU hardware;
• User-friendly interfaces such as Webapps and an Excel plugin for financial applications like derivatives pricing.
We also applied quantum Monte Carlo to portfolio valuation under stochastic growth, resulting in the Singularity Quantum Monte Carlo SDK—an accessible toolkit for building advanced quantum circuits. Additionally, our tensor network integration framework outperformed classical Monte Carlo methods on high-dimensional financial problems.
On the macroeconomic front, we proposed a QUBO-based quantum approach for analyzing financial network stability using quantum annealing and quantum-inspired algorithms, enabling practical applications.
A core goal of the Singularity project is democratizing quantum computing. To support non-expert users, we developed intuitive middleware, including:
• A Python-accessible API;
• AWS-based backend for running solutions on quantum and GPU hardware;
• User-friendly interfaces such as Webapps and an Excel plugin for financial applications like derivatives pricing.
Improving the speed and stability of derivatives pricing is crucial for the multi-trillion-dollar OTC market, where even small gains in accuracy can significantly enhance risk management and operational efficiency. We introduce two flagship quantum-inspired deep learning methods using tensor neural networks (TNNs) for derivatives pricing:
1. High-Dimensional Bermudan Pricing: This method improves deep learning solutions for forward-backward SDEs by incorporating TNNs. It delivers faster training, improved stability, and more accurate pricing than industry-standard Monte Carlo, which tends to underestimate Bermudan options and scale poorly with model complexity. TNNs also reduce variance in loss functions and model size while improving convergence. However, this approach requires retraining when market parameters shift.
2. Parameterized Deep Pricing Framework: To address retraining limitations, we developed a TNN-based model that encapsulates full market parameter ranges, eliminating the need for retraining. Applied to Heston models for European, Barrier, and Basket options, our method achieved 90–95% accuracy within a 5% error tolerance, and was 1,000–5,000× more efficient than Monte Carlo. Tensor compression further boosted efficiency, reaching up to 15,000× gains with minimal accuracy loss. These results demonstrate the method's potential to disrupt traditional pricing workflows.
For macroeconomic stability, we extended quantum algorithms for financial network analysis by scaling QUBO-based crash propagation models to realistic scenarios. Our method avoids exponential scaling by exactly encoding crash dynamics with only quadratic overhead. Benchmarking across static, dynamic, and uncertain models showed robust performance for complex networks, enabling analyses previously intractable on quantum hardware.
In transaction networks, our quantum-inspired optimization outperformed the Guntzner Liquidity Saving Mechanism (GLSM) in large, interconnected systems where GLSM's cycle detection faltered. We introduced a netted maximization method to improve settlement quality and reduce systemic risk. Tensor network optimization was also more cost-effective and scalable than quantum solvers in specific scenarios.
The Singularity QMC framework advanced probabilistic methods for financial risk analysis. We benchmarked MPS-based state preparation and quantum Monte Carlo on IBM QPUs, finding MPS methods to be the most scalable and accurate, though noisy hardware remains a challenge. Compared to qGANs and deep direct encoding, MPS offered superior performance in simulation.
Finally, tensor network integration emerged as a powerful classical alternative to quantum Monte Carlo. By leveraging Tensor Cross Approximation, we achieved near-linear scaling in high-dimensional settings, outperforming classical Monte Carlo and QMC in efficiency and precision.
Our results highlight the potential of combining quantum and quantum-inspired technologies for real-world finance. While pure quantum methods await further hardware advances, quantum-inspired approaches offer immediate, high-impact benefits today.
1. High-Dimensional Bermudan Pricing: This method improves deep learning solutions for forward-backward SDEs by incorporating TNNs. It delivers faster training, improved stability, and more accurate pricing than industry-standard Monte Carlo, which tends to underestimate Bermudan options and scale poorly with model complexity. TNNs also reduce variance in loss functions and model size while improving convergence. However, this approach requires retraining when market parameters shift.
2. Parameterized Deep Pricing Framework: To address retraining limitations, we developed a TNN-based model that encapsulates full market parameter ranges, eliminating the need for retraining. Applied to Heston models for European, Barrier, and Basket options, our method achieved 90–95% accuracy within a 5% error tolerance, and was 1,000–5,000× more efficient than Monte Carlo. Tensor compression further boosted efficiency, reaching up to 15,000× gains with minimal accuracy loss. These results demonstrate the method's potential to disrupt traditional pricing workflows.
For macroeconomic stability, we extended quantum algorithms for financial network analysis by scaling QUBO-based crash propagation models to realistic scenarios. Our method avoids exponential scaling by exactly encoding crash dynamics with only quadratic overhead. Benchmarking across static, dynamic, and uncertain models showed robust performance for complex networks, enabling analyses previously intractable on quantum hardware.
In transaction networks, our quantum-inspired optimization outperformed the Guntzner Liquidity Saving Mechanism (GLSM) in large, interconnected systems where GLSM's cycle detection faltered. We introduced a netted maximization method to improve settlement quality and reduce systemic risk. Tensor network optimization was also more cost-effective and scalable than quantum solvers in specific scenarios.
The Singularity QMC framework advanced probabilistic methods for financial risk analysis. We benchmarked MPS-based state preparation and quantum Monte Carlo on IBM QPUs, finding MPS methods to be the most scalable and accurate, though noisy hardware remains a challenge. Compared to qGANs and deep direct encoding, MPS offered superior performance in simulation.
Finally, tensor network integration emerged as a powerful classical alternative to quantum Monte Carlo. By leveraging Tensor Cross Approximation, we achieved near-linear scaling in high-dimensional settings, outperforming classical Monte Carlo and QMC in efficiency and precision.
Our results highlight the potential of combining quantum and quantum-inspired technologies for real-world finance. While pure quantum methods await further hardware advances, quantum-inspired approaches offer immediate, high-impact benefits today.