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Scaling Analysis of Quantum Amplitude Estimation for Tokenized Asset Option Pricing: Validation and Barriers to Practical Advantage

Abraham Itzhak Weinberg

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.2139/ssrn.6186258

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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.

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Accurate and efficient pricing of multi-asset basket options poses a significant challenge, especially when dealing with complex realworld data. In this work, we investigate the role of quantum-enhanced uncertainty modeling in financial pricing options on real-world data. Specifically, we use quantum amplitude estimation and analyze the impact of varying the number of uncertainty qubits while keeping the number of assets fixed, as well as the impact of varying the number of assets while keeping the number of uncertainty qubits fixed. To provide a comprehensive evaluation, we establish and validate a hybrid quantumclassical comparison framework, benchmarking quantum approaches against classical Monte Carlo simulations and Black-Scholes methods. Beyond simply computing option prices, we emphasize the trade-off between accuracy and computational resources, offering insights into the potential advantages and limitations of quantum approaches for different problem scales. Our results contribute to understanding the feasibility of quantum methods in finance and guide the optimal allocation of quantum resources in hybrid quantum-classical workflows.
We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.
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.