Quantum computing for multidimensional option pricing: End-to-end pipeline

The quantum-assisted methodology builds on Quantum Amplitude Estimation (QAE) to accelerate two central components of the multi-asset pricing pipeline: the recovery of marginal risk-neutral densities and the final multidimensional valuation integral. Classical Monte Carlo suffers from a well-known low convergence rate, while QAE improves it, offering a theoretical quadratic speedup. To remain compatible with current hardware, the framework employs hardware‑efficient QAE variants, avoiding deep circuits, controlled Grover iterations, and quantum Fourier transforms. The quantum routines are used to compute expectations required for both the cosine-series reconstruction of NIG-based marginal densities and the final expected payoff under the Gaussian copula joint distribution.

State preparation follows a structured encoding strategy in which the integrand of each expectation-either a cosine basis function or a payoff transformation-is embedded into the amplitude of a quantum register. For marginal reconstruction, the cosine coefficients that characterize the calibrated NIG density are estimated by mapping their integral representation into a quantum amplitude. For multidimensional pricing, asset dependence is first imposed classically through the Gaussian copula, producing correlated draws that are then encoded into the quantum circuit. The preparation unitary loads discretized values or function evaluations into amplitudes, ensuring the quantum state represents the value of the price of interest or reconstruction integral.

The correct functioning of the quantum‑assisted methodology is demonstrated through a combination of rigorous simulation‑based validation and fully specified quantum components, ensuring credibility even without execution on physical quantum hardware. Our study does not run the algorithm on real devices; instead, it justifies that current hardware limitations-primarily circuit depth and noise-make full QAE implementations impractical, motivating the use of hardware‑efficient variants compatible with near‑term machines though evaluated only in simulation. We implement and run the Quantum Accelerated Monte Carlo (QAMC) routines on a quantum simulator, applying QAE both to the reconstruction of marginal risk‑neutral densities via cosine‑series expectations and to the multidimensional option pricing integral under the Gaussian copula. These simulation results empirically confirm the theoretical quadratic speedup, showing that QAE requires 10–100 times fewer queries than classical Monte Carlo for comparable accuracy when calibrated to real market data from Credit Agricole, AXA, and Michelin. Finally, the methodology includes all elements needed to construct the full quantum circuits: amplitude‑encoding state‑preparation operators, oracle structures for QAE, and explicit mappings of pricing integrals to quantum amplitudes. The paper provides a complete algorithmic specification and theoretical error bounds for these components, thereby constituting a fully worked‑out quantum circuit blueprint that demonstrates the internal correctness of the approach even before hardware realization.

The proposed quantum‑assisted approach shows credible potential for scaling to realistic financial problem sizes through a hybrid workflow that strategically combines quantum and classical components. In the presented pipeline, all modeling, calibration, and dependence construction steps-such as NIG marginal calibration, arbitrage filtering, and Gaussian‑copula coupling-are performed classically, leveraging robust numerical optimization and statistical preprocessing. The quantum component is then used only at the stages where classical computation becomes the bottleneck, namely the high‑dimensional numerical integrations required for marginal density reconstruction and multi‑asset option pricing. This division of labor defines a natural and credible hybridization strategy: classical resources perform all data‑intensive and optimization‑heavy tasks, while quantum routines accelerate the expensive expectation computations through Quantum Amplitude Estimation (QAE). Because QAE is modular and operates on integrands already prepared by classical transformations, the pipeline is inherently scalable: adding more assets, maturities, or calibration points increases classical preprocessing cost but leaves quantum routines responsible only for evaluating expectations of similar structure.

Scalability is further supported by the complexity analysis in the article, which emphasizes the quadratic convergence advantage of QAE over classical Monte Carlo. Classical Monte Carlo requires quadratically more samples to achieve a given accuracy when compared against QAE, implying that beyond a moderate precision threshold the quantum‑assisted method becomes asymptotically superior. In high‑dimensional option pricing, where the payoff depends on multiple correlated assets, classical Monte Carlo scales poorly with dimension due to variance growth. In contrast, the quantum circuit complexity for QAE grows primarily with the cost of implementing the amplitude‑encoding oracle rather than with the dimensionality of the underlying asset space. The study's simulation benchmarks show reductions of 10–100× in query complexity for realistic market distributions, suggesting that as hardware improves, the full QAMC pipeline could outperform best‑in‑class classical methods for multi‑asset pricing tasks with demanding accuracy requirements.