Quantum computing has long promised to transform financial risk modelling — calculating complex probability distributions at speeds classical computers cannot approach. But the promise has been blocked by a stubborn, fundamental problem: getting real-world financial data into a quantum computer is extraordinarily difficult. Now, a landmark collaboration between HSBC, quantum middleware startup Haiqu, and IBM Quantum has produced a peer-reviewed breakthrough — published in Physical Review Research — that directly solves this data bottleneck and brings practical quantum finance measurably closer to reality.
The Data Bottleneck: Why Getting Financial Data into a Quantum Computer Is So Hard
Quantum computers process information using quantum states — superpositions of 0 and 1 that can represent vast computational spaces simultaneously. But before any quantum algorithm can run, the input data must first be encoded into these quantum states — a process called Quantum State Preparation (QSP). For simple, idealised data, this is straightforward. For the kind of complex, high-dimensional probability distributions that financial institutions actually use — capturing everything from market volatility to extreme "Black Swan" events — it has historically been computationally prohibitive.
Traditional QSP methods require quantum circuits that grow exponentially in depth as the complexity of the data increases. This exponential scaling quickly places real-world financial distributions far beyond the reach of today's Near-term Intermediate Scale Quantum (NISQ) devices — machines that are highly sensitive to noise and error accumulation in deep circuits. The data bottleneck has been one of the most concrete barriers preventing quantum finance from moving from theoretical promise to practical deployment.
The Breakthrough: Matrix Product States & Shallow Quantum Circuits
The joint research team from Haiqu and HSBC has solved this problem using Matrix Product States (MPS) — a tensor network method drawn from quantum physics that approximates complex smooth functions, including financial probability distributions, with remarkable efficiency. By representing distributions in the MPS framework, the team was able to construct quantum circuits that are shallow — containing far fewer operations and significantly lower depth than conventional approaches — making them dramatically less susceptible to the noise and errors endemic to today's quantum hardware.
The critical innovation is that circuits built using MPS scale linearly — O(N) — with the number of qubits, rather than exponentially. This is the difference between a problem that becomes tractable as hardware improves and one that remains forever out of reach. The team also introduced a sampling-based workflow that avoids storing the full discretised dataset in classical memory — enabling larger encoding circuits to be generated without the classical computational overhead that would otherwise bottleneck the process upstream of the quantum device.
The collaboration specifically targeted Lévy distributions — the "heavy-tailed" probability models that financial institutions use to predict extreme market events. These distributions are precisely the ones where conventional quantum encoding has historically failed, making them the most demanding and commercially relevant test of the new methodology.
"Preparing complex probability distributions efficiently is a key step in many quantum algorithms. This work shows how they can be implemented with much shallower quantum circuits, bringing practical applications such as financial risk modelling closer."— Philip Intallura, Group Head of Quantum Technologies, HSBC
Validated on IBM Hardware: From 25 to 156 Qubits
The methodology was rigorously validated on real IBM Quantum processors — including the ibm_torino, ibm_marrakesh, and ibm_kingston devices — under real-world operational conditions. The results demonstrate scaling across three distinct levels of hardware complexity:
25 Qubits — Statistical Benchmarks Passed
At the 25-qubit level — a threshold where physical quantum processors begin to handle meaningful complexity — the team successfully reproduced probability distributions that satisfied all standard statistical benchmarks, including the rigorous Kolmogorov-Smirnov test. This confirmed the method's fundamental accuracy on real hardware.
64 Qubits — Noise Resilience Confirmed
To test resilience against the errors common in larger quantum processors, the team moved to 64 qubits — the largest financial data encoding ever performed on IBM quantum processors. They implemented a specialised workflow to run circuits under realistic noise conditions, confirming that the methodology remains robust even when the underlying hardware is imperfect. Qualitative agreement with theoretical expectations was demonstrated despite the known limitations of current NISQ devices.
156 Qubits — Simulation Demonstrates Future Scalability
In classical simulation, the approach was extended to 156 qubits — indicating that the method can scale to substantially larger problem sizes as quantum hardware continues to mature. This simulation result is a powerful signal of where the technology is headed: towards the quantum advantage at scale that the financial industry has been anticipating.
What This Means for Financial Risk Modelling, Trading & Derivatives Pricing
The ability to efficiently encode financial probability distributions into quantum circuits opens the door to a new generation of quantum-enabled financial applications. The most immediate use cases are in financial risk modelling and Monte Carlo simulation — the computational workhorses of modern risk management, used to price derivatives, stress-test portfolios, and calculate Value at Risk (VaR). These applications require sampling from complex probability distributions repeatedly and at scale, making them precisely the workloads where quantum state preparation has been the binding constraint.
Beyond risk modelling, the research has direct implications for high-frequency trading, derivatives pricing, and the modelling of Black Swan events — the rare but catastrophic tail-risk scenarios that financial regulators and risk managers must plan for but that are computationally expensive to model with classical methods. By unlocking efficient quantum encoding for Lévy distributions — the standard tool for heavy-tail modelling — the collaboration has addressed the most practically demanding class of financial distributions first.
The peer-reviewed publication in Physical Review Research — one of the most rigorous journals in the physical sciences — ensures that this is not a press release milestone but a scientifically validated result that the global research community can build upon. It represents a foundational contribution to the emerging field of quantum finance, not a proprietary capability held behind a single firm's walls.