Structure-Aware Variational State Preparation for Quantum Basket Option Pricing

2026-07-15

AI Summary

This work addresses the challenge that quantum amplitude estimation (QAE) faces in basket option pricing due to excessively deep state preparation circuits, which hinder practical quantum speedup. The authors propose a structure-aware variational state preparation framework that, for the first time, incorporates tensor train (TT) rank information into circuit design. By tailoring entanglement structures for independent assets or optimizing local marginal distributions for correlated assets, and by directly targeting the basket cumulative distribution function (Basket-CDF) as the training objective—thereby avoiding full joint state reconstruction—the method reduces circuit depth from exponential to linear scaling. This approach maintains low percentage pricing errors while significantly enhancing hardware feasibility and remains compatible with standard QAE workflows.

Abstract

Basket option pricing often relies on Monte Carlo estimation, for which quantum amplitude estimation (QAE) provides a quadratic speed-up. However, the practical benefit of QAE can be limited by the depth of the state-preparation circuit. We propose a structure-aware quantum state-preparation framework for QAE-based basket option pricing. The framework uses tensor-train (TT) rank information to design shallow variational state-preparation circuits. In the independent regime, TT ranks remove unnecessary entangling links from a hardware-efficient ansatz. In correlated basket settings, we instead prepare asset-wise marginals locally and train a compact latent block to match the basket cumulative distribution function. The Basket-CDF objective targets the basket pushforward distribution rather than the full joint state, directly aligning state preparation with basket-dependent payoffs. Numerical experiments show that the proposed circuits replace the exponential state-preparation depth scaling of exact amplitude loading with linear scaling, while maintaining low-percent basket-pricing errors. Additional sampling-based training experiments and an end-to-end QAE integration study support compatibility with sample-estimated training and standard QAE-based pricing workflows.

Problem

• quantum amplitude estimation
• basket option pricing
• state preparation
• circuit depth
• tensor-train decomposition

Innovation

• structure-aware
• tensor-train decomposition
• variational quantum circuit
• basket option pricing
• quantum amplitude estimation