Structure-Aware Variational State Preparation for Quantum Basket Option Pricing

Quantum Amplitude Estimation (QAE) offers a quadratic speed-up for pricing financial derivatives, but its practical utility is often bottlenecked by the depth of the quantum circuit required to load the probability distribution of asset prices. This paper addresses the challenge of preparing high-dimensional, correlated multi-asset distributions in a way that is shallow enough for near-term quantum hardware while remaining accurate for basket-dependent financial functionals.

The authors propose a two-part state-preparation framework. First, they use Tensor-Train (TT) rank information to identify the necessary entangling structure for asset-wise marginal distributions, allowing for the removal of redundant gates in the variational ansatz. Second, for correlated baskets, they introduce a 'marginal-latent' architecture. This involves preparing each asset's marginal distribution locally using TT-informed circuits and then training a compact latent dependence block to capture the cross-asset correlations. Instead of attempting to perfectly replicate the full joint distribution, the training objective is specifically aligned with the cumulative distribution function (CDF) of the basket projection, which is the quantity that directly determines the option payoff.

The proposed framework significantly reduces circuit depth compared to exact amplitude loading, achieving linear scaling in the number of qubits. Numerical experiments demonstrate that this structure-aware approach maintains low-percent pricing errors for basket options. By focusing on the basket-pushforward distribution rather than the full joint state, the method avoids the overhead of representing unnecessary correlations and provides a circuit that is more robust and reusable across different strike prices.

Input-state preparation is a primary resource bottleneck in quantum finance. By leveraging the inherent structure of financial data—specifically the low-rank nature of asset correlations and the fact that basket payoffs depend only on the aggregate portfolio value—this research provides a scalable path toward practical quantum-accelerated Monte Carlo methods. The framework is compatible with standard QAE workflows and offers a more efficient alternative to generic generative models, which often suffer from training instabilities.