Circuits containing up to 64 qubits have successfully reproduced key features of complex financial models, demonstrating the growing potential of quantum computing for real-world applications. Haiqu, a quantum middleware developer, and HSBC jointly published research in Physical Review Research detailing an efficient method for encoding probability distributions into quantum circuits, addressing a major bottleneck in quantum algorithm implementation. The approach utilizes matrix product state methods and a sampling-based workflow to construct shallower circuits, enabling the encoding of larger datasets without overwhelming classical memory. “Preparing complex probability distributions efficiently is a key step in many quantum algorithms,” said Dr. Philip Intallura, Group Head of Quantum Technologies at HSBC. “This work shows how they can be implemented with much shallower quantum circuits, bringing practical applications such as financial risk modelling closer.”
Matrix Product States Enable Shallow Quantum Circuits
Researchers have demonstrated the ability to encode complex, real-world probability distributions into quantum circuits containing up to 64 qubits, a significant leap toward practical quantum applications in fields like finance. This achievement, detailed in a recent Physical Review Research publication, bypasses a critical limitation in quantum computing: the difficulty of efficiently loading classical data onto quantum hardware. The team, a collaboration between Haiqu and HSBC, employed matrix product state methods to construct remarkably shallow quantum circuits, minimizing the computational demands and potential for errors. This approach allows for the direct encoding of smooth functions, including the intricate probability distributions essential for modeling financial markets. A key innovation lies in the development of a sampling-based workflow, which circumvents the need to store massive datasets in classical memory, enabling the generation of circuits capable of handling substantially larger and more complex data.
Validation focused on heavy-tailed Lévy distributions, a standard tool for modeling extreme market events such as financial crashes, confirming the method’s relevance to critical financial modeling needs. Experiments conducted on IBM quantum hardware successfully produced samples from circuits up to 25 qubits that passed rigorous statistical tests, proving the accuracy of the encoded distributions in a practical setting. The research extends beyond current hardware limitations, with simulations demonstrating scalability up to 156 qubits, suggesting the potential for even more sophisticated applications.
Mykola Maksymenko, Co-founder and CTO of Haiqu, emphasized the practical implications of this work, stating that “One of the biggest practical barriers is getting realistic financial data onto today’s quantum hardware,” and that this research “shows a scalable path around that barrier and helps move quantum finance workflows from theory toward execution.” The success of these shallow circuits, combined with the sampling workflow, represents a crucial step in bridging the gap between theoretical quantum algorithms and tangible, real-world solutions for financial risk modeling and beyond.
Qubit Validation Reproduces Lévy Distributions with Noise
The pursuit of practical quantum computation increasingly focuses on demonstrating utility beyond benchmark algorithms, with recent efforts targeting applications in financial modeling. Researchers successfully executed circuits containing up to 64 qubits, reproducing qualitative features of target distributions even while accounting for the inherent noise present in current quantum devices, a scale significantly exceeding previous demonstrations of similar techniques. The team employed matrix product state methods alongside a novel sampling-based workflow to construct shallow quantum circuits capable of directly encoding smooth functions, including the probability distributions vital for financial analysis. This sampling approach circumvents the limitations of storing large datasets in classical memory, enabling the generation of circuits for more extensive encoding.
This work shows a scalable path around that barrier and helps move quantum finance workflows from theory toward execution.
Mykola Maksymenko, Co-founder and CTO of Haiqu
