Introduction
Haiqu and HSBC published breakthrough research in December 2024 demonstrating the successful encoding of the largest financial distributions to date on quantum computers. The collaboration, documented in a peer-reviewed paper on arXiv, developed novel methods for encoding complex financial data into quantum circuits using shallow and efficient designs that push the limits of IBM’s quantum processors. HSBC, one of the world’s largest banking and financial services organizations, partnered with Haiqu, a San Francisco-based quantum software company specializing in quantum middleware solutions for near-term hardware. The research team included Vladyslav Bohun, Illia Lukin, Mykola Luhanko, Mykola Maksymenko, and Maciej Koch-Janusz from Haiqu, alongside Georgios Korpas from HSBC Lab Singapore, the Czech Technical University in Prague, and the Athena Research Center in Greece. The study focused on encoding large-scale financial distributions, particularly Lévy distributions that model heavy-tailed and skewed data common in financial markets including extreme events such as market crashes and sudden price movements. The collaboration represents a significant advancement toward practical quantum computing applications in financial services, addressing fundamental challenges in quantum data loading that have limited near-term quantum utility.
Problem Statement
Financial institutions face computational challenges when modeling complex market behaviors involving heavy-tailed distributions and extreme events that occur more frequently than normal distributions predict. Traditional financial models struggle with Lévy distributions and similar heavy-tailed phenomena that characterize real market data, including sudden market crashes, volatility spikes, and asymmetric price movements. Classical computational approaches for encoding large-scale financial data require exponential memory scaling, creating bottlenecks for portfolio optimization, risk management, and derivative pricing applications. HSBC and other major financial institutions manage portfolios worth hundreds of billions of dollars, requiring sophisticated mathematical models to assess risk and optimize returns across thousands of financial instruments. Current classical methods for handling complex financial distributions become computationally intractable when scaling to enterprise-level portfolio sizes with high-dimensional parameter spaces. The challenge intensifies when modeling correlations between multiple assets, currencies, and market factors, as the computational complexity grows exponentially with the number of variables. Financial risk management requires real-time or near-real-time calculations for value-at-risk assessments, stress testing, and regulatory compliance reporting, placing severe constraints on computational time budgets. Monte Carlo simulations, widely used in financial modeling, face convergence challenges when dealing with heavy-tailed distributions, often requiring millions of samples to achieve acceptable accuracy levels. The quantum computing field has long recognized data loading as a fundamental bottleneck, with researchers noting that efficient quantum data encoding remains essential for achieving quantum advantage in practical applications. Industry analysts estimate that financial services could realize significant competitive advantages from quantum computing, but only if fundamental challenges in quantum data representation are resolved.
Quantum Approach
The collaboration developed a novel approach using Matrix Product States (MPS) techniques to encode complex financial distributions into shallow quantum circuits optimized for near-term quantum hardware. The research team utilized MPS methods that approximate input functions with quantum circuits of reduced depth, organizing financial data into smaller, manageable components to reduce computational load and circuit complexity. Haiqu’s quantum middleware expertise enabled the development of circuits that could execute reliably on IBM’s quantum processors, including the ibm_torino and ibm_marrakesh systems, despite hardware noise limitations. The team implemented Tensor Cross Interpolation (TCI) methodology, which avoids storing large financial datasets in classical memory by sampling data locally, making the process memory-efficient and scalable for enterprise financial applications. The quantum approach specifically targeted Lévy distributions and other heavy-tailed probability distributions commonly encountered in financial markets, including modeling of extreme price movements and volatility clustering phenomena. Circuit design focused on shallow implementations to minimize the impact of quantum decoherence and gate errors that plague current noisy intermediate-scale quantum devices. The research incorporated statistical validation through Kolmogorov-Smirnov tests and other rigorous statistical measures to ensure quantum-generated distributions matched theoretical expectations. IBM quantum hardware provided the experimental testbed for validating circuit performance under real-world quantum computing conditions, with particular attention to noise characterization and error mitigation strategies. The team analyzed how the smoothness and localization properties of financial functions affect the complexity of MPS representations, enabling optimization of circuit designs for specific types of financial data. The quantum encoding approach demonstrated the ability to represent complex multi-dimensional financial distributions with exponentially fewer quantum resources compared to classical approaches, potentially enabling quantum advantage for certain classes of financial modeling problems.
Results and Business Impact
The research achieved successful encoding of the largest financial distributions demonstrated to date on quantum computers, specifically implementing complex Lévy distributions and heavy-tailed financial data on IBM quantum processors. Experimental validation on the ibm_torino and ibm_marrakesh quantum systems confirmed that quantum circuits could accurately represent financial distributions while maintaining computational efficiency through shallow circuit designs. Statistical testing using Kolmogorov-Smirnov and other validation measures verified that quantum-generated distributions matched theoretical financial models with high fidelity, demonstrating practical applicability for financial services. The collaboration’s results were published on arXiv, a prestigious preprint server widely used by the financial technology and quantum computing research communities, establishing the work’s credibility and enabling peer review by global experts. HSBC’s participation through their Singapore research lab demonstrates the bank’s commitment to quantum technology development and positions the institution as a leader in quantum finance applications. The research established a framework for encoding multivariate financial functions, which are essential for modeling complex financial instruments such as derivatives, structured products, and portfolio optimization problems involving multiple assets. Benchmarking results showed quantum circuits performed effectively under real-world hardware conditions, indicating near-term commercial viability for specific financial modeling applications. The study’s emphasis on shallow circuit designs addresses the fundamental challenge of quantum decoherence, making the approach practical for implementation on current and near-future quantum hardware generations. Industry recognition of the work positions both Haiqu and HSBC as thought leaders in quantum finance, potentially attracting partnerships with other financial institutions seeking quantum computing capabilities. The research methodology provides a template for other financial institutions to develop quantum computing applications, potentially accelerating adoption across the financial services sector. Commercial implications include potential applications in risk management, portfolio optimization, derivative pricing, and regulatory stress testing, where quantum computing could provide computational advantages over classical approaches.
Future Directions
The partnership plans to extend quantum encoding capabilities to multivariate financial functions, enabling modeling of complex financial instruments involving multiple underlying assets and risk factors. Development roadmap includes implementing the methodology for real-time trading applications, where quantum computing could provide speed advantages for high-frequency trading and algorithmic execution strategies. Algorithm optimization efforts will focus on fault-tolerant quantum computing implementations as error correction technologies mature, potentially enabling quantum advantage for enterprise-scale financial modeling within the next decade. Integration with existing financial infrastructure represents a priority development area, with plans to create interfaces between quantum financial algorithms and standard trading platforms, risk management systems, and regulatory reporting tools used throughout the financial services industry. The collaboration will investigate quantum applications for climate risk modeling, cryptocurrency analysis, and ESG (Environmental, Social, Governance) investment strategies, areas where complex data modeling could benefit from quantum computational advantages. Hardware scaling strategies include evaluation of different quantum computing modalities, with particular interest in photonic and trapped-ion systems that may offer advantages for financial modeling applications requiring high precision and low error rates. Commercial deployment plans focus on quantum cloud services integration, allowing financial institutions to access quantum modeling capabilities without requiring on-premises quantum hardware investments. Partnership expansion with financial technology vendors aims to incorporate quantum algorithms into existing financial software suites, providing seamless adoption pathways for banks, asset managers, and insurance companies. Research expansion includes investigating quantum machine learning applications for financial forecasting, fraud detection, and customer behavior modeling, leveraging quantum computing’s potential advantages in pattern recognition and optimization. Long-term vision encompasses quantum-enhanced automated trading systems, real-time risk assessment platforms, and quantum-secured financial transactions, positioning quantum computing as a transformative technology for next-generation financial services.
Conclusion
The Haiqu-HSBC collaboration represents a crucial advancement in practical quantum computing applications for financial services, demonstrating that complex financial distributions can be successfully encoded and manipulated using near-term quantum hardware. The successful publication of research showing the largest financial distributions encoded to date on quantum computers establishes a new benchmark for quantum finance applications. The partnership’s focus on shallow circuit designs and real-world hardware validation addresses fundamental challenges that have limited quantum computing adoption in financial services. Industry implications extend beyond data encoding to broader quantum finance applications including portfolio optimization, risk management, and derivative pricing where quantum computing could provide significant computational advantages. The collaboration demonstrates the importance of combining domain expertise in financial modeling with quantum middleware optimization and hardware validation for achieving practical quantum applications. Competitive dynamics in quantum finance suggest early adopters will establish significant advantages in next-generation financial technology capabilities, particularly as quantum hardware continues to improve. The research establishes HSBC as a pioneer in quantum finance while positioning Haiqu as a leader in quantum software solutions for financial services applications. Transformative potential for financial modeling, particularly in complex risk assessment and portfolio optimization scenarios, positions quantum finance as a key driver for quantum computing commercialization in the financial services sector.