Haiqu, a New York-based quantum middleware developer, and HSBC have published peer-reviewed research in Physical Review Research demonstrating a method to overcome one of quantum computing’s most significant hurdles: quantum state preparation. This process involves encoding classical data (such as financial probability distributions) into quantum states so that quantum algorithms can process them.

The research focuses on creating shallow quantum circuits—meaning circuits with fewer operations and lower depth—which are less susceptible to the noise and errors prevalent in today’s Near-Intermediate Scale Quantum (NISQ) devices.

Technical Breakthrough: MPS-Based Encoding

The joint team utilized Matrix Product States (MPS), a tensor network method, to approximate smooth functions like probability distributions. This allows for the construction of quantum circuits that scale linearly (O(N)) with the number of qubits, rather than exponentially.

Key technical highlights include:

  • Dimensionality Reduction: The method uses Tensor Cross Interpolation (TCI) to build circuits without needing to store exponentially large datasets in classical memory.
  • Hardware Validation: The approach was tested on IBM Quantum hardware (including the ibm_torino, ibm_marrakesh, and ibm_kingston processors).
  • Scaling Success: Researchers successfully executed circuits on up to 156 qubits. For smaller scales (up to 25 qubits), the sampled data passed standard statistical tests (like the Kolmogorov-Smirnov test), proving the high fidelity of the encoded distributions.

Applications in Quantitative Finance

The collaboration specifically targeted Lévy distributions, which are “heavy-tailed” models used by financial institutions to predict extreme market events (often called “Black Swan” events). Standard classical models often struggle with these distributions due to their complexity, but quantum systems are naturally suited for high-dimensional probability modeling.

“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

By reducing the circuit depth required to load these distributions, the research moves quantum finance from theoretical proofs of concept toward real-world execution in risk assessment, portfolio management, and derivative pricing.

You can find the official press release from Haiqu here and access the full peer-reviewed study in Physical Review Research here.

April 28, 2026

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