Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2603.15664

Quantum Amplitude Estimation for Catastrophe Insurance Tail-Risk Pricing: Empirical Convergence and NISQ Noise Analysis

Alexis Kirke

Published Mar 10, 2026• 0 citations
arXivHTMLPDF

Abstract

Classical Monte Carlo methods for pricing catastrophe insurance tail risk converge at order reciprocal root N, requiring large simulation budgets to resolve upper-tail percentiles of the loss distribution. This sample-sparsity problem can lead to AI models trained on impoverished tail data, producing poorly calibrated risk estimates where insolvency risk is greatest. Quantum Amplitude Estimation (QAE), following Montanaro, achieves convergence approaching order reciprocal N in oracle queries - a quadratic speedup that, at scale, would enable high-resolution tail estimation within practical budgets. We validate this advantage empirically using a Qiskit Aer simulator with genuine Grover amplification. A complete pipeline encodes fitted lognormal catastrophe distributions into quantum oracles via amplitude encoding, producing small readout probabilities that enable safe Grover amplification with up to k=16 iterations. Seven experiments on synthetic and real (NOAA Storm Events, 58,028 records) data yield three main findings: an oracle-model advantage, that strong classical baselines win when analytical access is available, and that discretisation, not estimation, is the current bottleneck.

DOI
10.48550/arxiv.2603.15664

Related papers

Quantum Monte Carlo Integration for Credit-Portfolio Tail Risk

Kavy Upadhyay

Monte Carlo simulations underpin computational quantitative finance, where they are used for derivative pricing, risk quantification and scenario analysis whenever closed-form solutions are unavailable. Their main limitation is the slow O(N^-1/2) convergence of classical sampling. Quantum amplitude estimation promises a quadratic improvement in query complexity over classical Monte Carlo, reducing the sample requirement from O(eps^-2) to O(eps^-1) under idealised conditions. This thesis measures the extent to which the quadratic improvement in query complexity survives a concrete risk task under gate noise when compared to classical Monte Carlo. A four-obligor correlated portfolio, whose loss distribution can be computed exactly, is encoded into quantum circuits, and its value at risk and expected shortfall are estimated by iterative amplitude estimation under exactly simulated depolarising noise on every two-qubit gate. Six configurations of 11 to 15 qubits vary the portfolio, the factor grid and the arithmetic construction. At matched loss-model evaluation budgets and without noise, amplitude estimation reduces the RMSE of the tail probability against classical Monte Carlo by a factor of 13.6 at the largest budget tested. The error budget is dominated by the circuit encoding, not the estimator. As a result, the value at risk at the 95% level picks the wrong loss level in none of the noiseless repetitions, while the encoding understates expected shortfall by 0.177 loss units. Under noise, the signal decays with every amplification round. The number of rounds that still help falls from 64 at an error rate of 3x10^-6 to none at 3x10^-2. This work concludes that amplification benefits only while the product of gate count and error rate stays small against one. Because every obligor added enlarges the circuit, the error rate at which amplification remains useful falls as the portfolio grows, and advantage starts depending on circuit compression instead of estimator design.

•Sep 4, 2026•0 citations

Call Option Pricing Using Quantum Amplitude Estimation: A Comparative Study with Monte Carlo Simulation

Kasidit Asavakittikawin, Somporn Punpocha

Option pricing is a fundamental problem in quantitative finance, where the accuracy and efficiency of valuation methods directly affect investment and risk management decisions. While the Black-Scholes model provides a closed-form solution for European options, numerical approaches such as Monte Carlo simulation are widely used when analytical methods are intractable. However, Monte Carlo suffers from slow convergence with complexity O(1/ε2).Quantum Amplitude Estimation (QAE), an algorithm in quantum computing, promises a quadratic speedup with complexity O(1/ε). This paper implements QAE, specifically Iterative Amplitude Estimation (IAE), for European call option pricing and compares its performance against Monte Carlo simulation and the Black-Scholes model. Experiments are conducted on both Qiskit simulators and IBM Quantum hardware (ibm_brisbane).Results show that QAE achieves estimates close to Monte Carlo and analytical benchmarks, with mean payoff deviations of less than 0.01. While QAE produces wider confidence intervals due to noise and discretization, the findings demonstrate its potential scalability advantage for future quantum finance applications.

International Computer Science and Engineering Conference•Nov 2, 2025•0 citations

A Quantum Risk Management Framework (QRMF): Quantum Amplitude Estimation for VaR/CVaR, Entanglement-Based Systemic Risk Analytics, and Variational Risk Optimization

Yalla Jnan Devi Satya Prasad

We present a rigorously derived Quantum Risk Management Framework (QRMF) integrating quantum amplitude estimation for tail risk metrics, entanglement-based systemic risk analytics, and variational quantum risk optimization. Our comprehensive approach encompasses three novel modules: (i) Quantum Risk Amplitude Estimation (QRAE) achieving quadratic sample complexity improvements over classical Monte Carlo for Value-at-Risk (VaR) and Conditional VaR (CVaR) computation through binary search with amplitude estimation subroutines; (ii) Quantum Systemic Risk Analysis (QSRA) encoding financial exposure networks into entangled bipartite states with purity-based early warning observables and QAOA partitioning for cascade mitigation; and (iii) Variational Quantum Risk Optimizer (VQRO) implementing constraint-aware portfolio optimization using risk-adjusted Hamiltonians with feasible-state ansätze and penalty-based formulations. We establish formal complexity theorems under explicit QRAM/QROM cost models, prove convergence guarantees for variational components under convex surrogate conditions, and demonstrate theoretical correspondence between entanglement purity responses and classical contagion path-sum sensitivities in linearized network models. The hybrid framework combines gate-model quantum circuits for amplitude estimation and entanglement encoding with variational quantum eigensolvers for optimization, validated through comprehensive simulations on synthetic financial networks and real market data. Extensive ablation studies on circuit depth versus accuracy trade-offs, noise resilience analysis, and resource scaling complement theoretical results, with all quantum amplitude estimation and entanglement simulations performed using Qiskit on classical hardware while baseline classical Monte Carlo and network centrality methods provide benchmarking baselines. This distinction ensures accurate interpretation of quantum advantages across the integrated risk management pipeline.

•Oct 7, 2025•0 citations

A Noise-Aware Quantum Algorithm for Credit Valuation Adjustments on Real Quantum Hardware

Guillem Borràs Espert, Francisco Gómez Casanova, Luis de Pedro Sánchez +2 more

Credit Valuation Adjustment (CVA) requires repeated risk-neutral expectation estimation, making it a natural test bed for quantum amplitude estimation, whose coherent amplification can in principle reduce Monte Carlo sampling cost. Whether this advantage survives realistic financial encoding and noisy hardware remains open. We develop an end-to-end, noise-aware quantum workflow for CVA, covering market calibration, discretisation, oracle construction, hardware execution and error-budget analysis. The model combines a correlated two-asset exposure with discount and default factors, encoded through a QCBM-based joint time-market distribution and controlled payoff rotations. We introduce contrast-aware Bayesian iterative quantum amplitude estimation (CABIQAE), which incorporates experimentally calibrated Grover-contrast loss into Bayesian inference and circuit-depth selection. Hardware-calibrated experiments show that CABIQAE exploits the limited amplification available on current devices more effectively than noise-agnostic alternatives and achieves a much lower classical post-processing runtime than the noise-aware BAE baseline. The analysis further decomposes the total CVA error into statistical, encoding, discretisation and hardware contributions. The full CVA oracle remains limited by circuit depth and discretisation resolution.

quant-pharXiv:2607.12990•Jul 15, 2026•0 citations

Bayesian Sequential Quantum Amplitude Estimation for Rare-Event Structural Failure Probability

Alireza Tabarraei

Structural reliability analysis often requires estimating small failure probabilities under uncertainty, a task for which direct Monte Carlo simulation becomes inefficient because failure observations are scarce. Quantum amplitude estimation offers a potential quadratic improvement in query complexity for bounded expectation estimation, but practical iterative formulations require reliable inference from finite, amplified measurement data. This paper develops a Bayesian sequential formulation of iterative quantum amplitude estimation for rare-event structural failure probability estimation. Structural failure is represented as a binary indicator over a finite stochastic ensemble and encoded through a lookup-table oracle, allowing the failure probability to be treated as a quantum amplitude. Measurement outcomes collected at different Grover depths are assimilated through Bayesian updating over the amplitude angle, yielding posterior estimates, credible intervals, and uncertainty-aware convergence diagnostics. The framework is evaluated on stochastic finite-element benchmark problems, including a one-dimensional bar and an L-bracket with stress concentration. The results show that amplitude amplification converts rare failure events into measurable success probabilities, enabling substantially lower estimation errors than direct Monte Carlo simulation under the same idealized oracle-query budget. The Bayesian formulation achieves point-estimation accuracy comparable to maximum-likelihood IQAE while additionally providing posterior uncertainty quantification, credible intervals, and transparent convergence assessment. The study demonstrates Bayesian IQAE as a statistically interpretable proof-of-concept for quantum-assisted rare-event reliability analysis, while relying on idealized oracle access.

arXiv:2607.18996•Jul 21, 2026•0 citations

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

Julien Hok, Álvaro Leitao

This work introduces an end-to-end framework for multi-asset option pricing that combines market-consistent risk-neutral density recovery with quantum-accelerated numerical integration. We first calibrate arbitrage-free marginal distributions from European option quotes using the Normal Inverse Gaussian (NIG) model, leveraging its analytical tractability and ability to capture skewness and fat tails. Marginals are coupled via a Gaussian copula to construct joint distributions. To address the computational bottleneck of the high-dimensional integration required to solve the option pricing formula, we employ Quantum Accelerated Monte Carlo (QAMC) techniques based on Quantum Amplitude Estimation (QAE), achieving quadratic convergence improvements over classical Monte Carlo (CMC) methods. Theoretical results establish accuracy bounds and query complexity for both marginal density estimation (via cosine-series expansions) and multidimensional pricing. Empirical tests on liquid equity entities (Credit Agricole, AXA, Michelin) confirm high calibration accuracy and demonstrate that QAMC requires 10-100 times fewer queries than classical methods for comparable precision. This study provides a practical route to integrate arbitrage-aware modelling with quantum computing, highlighting implications for scalability and future extensions to complex derivatives.

q-fin.CPCross-listedarXiv:2601.04049•Jan 8, 2026•0 citations
Classical Monte Carlo methods for pricing catastrophe insurance tail risk converge at order reciprocal root N, requiring large simulation budgets to resolve upper-tail percentiles of the loss distribution. This sample-sparsity problem can lead to AI models trained on impoverished tail data, producing poorly calibrated risk estimates where insolvency risk is greatest. Quantum Amplitude Estimation (QAE), following Montanaro, achieves convergence approaching order reciprocal N in oracle queries - a quadratic speedup that, at scale, would enable high-resolution tail estimation within practical budgets. We validate this advantage empirically using a Qiskit Aer simulator with genuine Grover amplification. A complete pipeline encodes fitted lognormal catastrophe distributions into quantum oracles via amplitude encoding, producing small readout probabilities that enable safe Grover amplification with up to k=16 iterations. Seven experiments on synthetic and real (NOAA Storm Events, 58,028 records) data yield three main findings: an oracle-model advantage, that strong classical baselines win when analytical access is available, and that discretisation, not estimation, is the current bottleneck.
Monte Carlo simulations underpin computational quantitative finance, where they are used for derivative pricing, risk quantification and scenario analysis whenever closed-form solutions are unavailable. Their main limitation is the slow O(N^-1/2) convergence of classical sampling. Quantum amplitude estimation promises a quadratic improvement in query complexity over classical Monte Carlo, reducing the sample requirement from O(eps^-2) to O(eps^-1) under idealised conditions. This thesis measures the extent to which the quadratic improvement in query complexity survives a concrete risk task under gate noise when compared to classical Monte Carlo. A four-obligor correlated portfolio, whose loss distribution can be computed exactly, is encoded into quantum circuits, and its value at risk and expected shortfall are estimated by iterative amplitude estimation under exactly simulated depolarising noise on every two-qubit gate. Six configurations of 11 to 15 qubits vary the portfolio, the factor grid and the arithmetic construction. At matched loss-model evaluation budgets and without noise, amplitude estimation reduces the RMSE of the tail probability against classical Monte Carlo by a factor of 13.6 at the largest budget tested. The error budget is dominated by the circuit encoding, not the estimator. As a result, the value at risk at the 95% level picks the wrong loss level in none of the noiseless repetitions, while the encoding understates expected shortfall by 0.177 loss units. Under noise, the signal decays with every amplification round. The number of rounds that still help falls from 64 at an error rate of 3x10^-6 to none at 3x10^-2. This work concludes that amplification benefits only while the product of gate count and error rate stays small against one. Because every obligor added enlarges the circuit, the error rate at which amplification remains useful falls as the portfolio grows, and advantage starts depending on circuit compression instead of estimator design.
Option pricing is a fundamental problem in quantitative finance, where the accuracy and efficiency of valuation methods directly affect investment and risk management decisions. While the Black-Scholes model provides a closed-form solution for European options, numerical approaches such as Monte Carlo simulation are widely used when analytical methods are intractable. However, Monte Carlo suffers from slow convergence with complexity O(1/ε2).Quantum Amplitude Estimation (QAE), an algorithm in quantum computing, promises a quadratic speedup with complexity O(1/ε). This paper implements QAE, specifically Iterative Amplitude Estimation (IAE), for European call option pricing and compares its performance against Monte Carlo simulation and the Black-Scholes model. Experiments are conducted on both Qiskit simulators and IBM Quantum hardware (ibm_brisbane).Results show that QAE achieves estimates close to Monte Carlo and analytical benchmarks, with mean payoff deviations of less than 0.01. While QAE produces wider confidence intervals due to noise and discretization, the findings demonstrate its potential scalability advantage for future quantum finance applications.
We present a rigorously derived Quantum Risk Management Framework (QRMF) integrating quantum amplitude estimation for tail risk metrics, entanglement-based systemic risk analytics, and variational quantum risk optimization. Our comprehensive approach encompasses three novel modules: (i) Quantum Risk Amplitude Estimation (QRAE) achieving quadratic sample complexity improvements over classical Monte Carlo for Value-at-Risk (VaR) and Conditional VaR (CVaR) computation through binary search with amplitude estimation subroutines; (ii) Quantum Systemic Risk Analysis (QSRA) encoding financial exposure networks into entangled bipartite states with purity-based early warning observables and QAOA partitioning for cascade mitigation; and (iii) Variational Quantum Risk Optimizer (VQRO) implementing constraint-aware portfolio optimization using risk-adjusted Hamiltonians with feasible-state ansätze and penalty-based formulations. We establish formal complexity theorems under explicit QRAM/QROM cost models, prove convergence guarantees for variational components under convex surrogate conditions, and demonstrate theoretical correspondence between entanglement purity responses and classical contagion path-sum sensitivities in linearized network models. The hybrid framework combines gate-model quantum circuits for amplitude estimation and entanglement encoding with variational quantum eigensolvers for optimization, validated through comprehensive simulations on synthetic financial networks and real market data. Extensive ablation studies on circuit depth versus accuracy trade-offs, noise resilience analysis, and resource scaling complement theoretical results, with all quantum amplitude estimation and entanglement simulations performed using Qiskit on classical hardware while baseline classical Monte Carlo and network centrality methods provide benchmarking baselines. This distinction ensures accurate interpretation of quantum advantages across the integrated risk management pipeline.
Credit Valuation Adjustment (CVA) requires repeated risk-neutral expectation estimation, making it a natural test bed for quantum amplitude estimation, whose coherent amplification can in principle reduce Monte Carlo sampling cost. Whether this advantage survives realistic financial encoding and noisy hardware remains open. We develop an end-to-end, noise-aware quantum workflow for CVA, covering market calibration, discretisation, oracle construction, hardware execution and error-budget analysis. The model combines a correlated two-asset exposure with discount and default factors, encoded through a QCBM-based joint time-market distribution and controlled payoff rotations. We introduce contrast-aware Bayesian iterative quantum amplitude estimation (CABIQAE), which incorporates experimentally calibrated Grover-contrast loss into Bayesian inference and circuit-depth selection. Hardware-calibrated experiments show that CABIQAE exploits the limited amplification available on current devices more effectively than noise-agnostic alternatives and achieves a much lower classical post-processing runtime than the noise-aware BAE baseline. The analysis further decomposes the total CVA error into statistical, encoding, discretisation and hardware contributions. The full CVA oracle remains limited by circuit depth and discretisation resolution.
Structural reliability analysis often requires estimating small failure probabilities under uncertainty, a task for which direct Monte Carlo simulation becomes inefficient because failure observations are scarce. Quantum amplitude estimation offers a potential quadratic improvement in query complexity for bounded expectation estimation, but practical iterative formulations require reliable inference from finite, amplified measurement data. This paper develops a Bayesian sequential formulation of iterative quantum amplitude estimation for rare-event structural failure probability estimation. Structural failure is represented as a binary indicator over a finite stochastic ensemble and encoded through a lookup-table oracle, allowing the failure probability to be treated as a quantum amplitude. Measurement outcomes collected at different Grover depths are assimilated through Bayesian updating over the amplitude angle, yielding posterior estimates, credible intervals, and uncertainty-aware convergence diagnostics. The framework is evaluated on stochastic finite-element benchmark problems, including a one-dimensional bar and an L-bracket with stress concentration. The results show that amplitude amplification converts rare failure events into measurable success probabilities, enabling substantially lower estimation errors than direct Monte Carlo simulation under the same idealized oracle-query budget. The Bayesian formulation achieves point-estimation accuracy comparable to maximum-likelihood IQAE while additionally providing posterior uncertainty quantification, credible intervals, and transparent convergence assessment. The study demonstrates Bayesian IQAE as a statistically interpretable proof-of-concept for quantum-assisted rare-event reliability analysis, while relying on idealized oracle access.
This work introduces an end-to-end framework for multi-asset option pricing that combines market-consistent risk-neutral density recovery with quantum-accelerated numerical integration. We first calibrate arbitrage-free marginal distributions from European option quotes using the Normal Inverse Gaussian (NIG) model, leveraging its analytical tractability and ability to capture skewness and fat tails. Marginals are coupled via a Gaussian copula to construct joint distributions. To address the computational bottleneck of the high-dimensional integration required to solve the option pricing formula, we employ Quantum Accelerated Monte Carlo (QAMC) techniques based on Quantum Amplitude Estimation (QAE), achieving quadratic convergence improvements over classical Monte Carlo (CMC) methods. Theoretical results establish accuracy bounds and query complexity for both marginal density estimation (via cosine-series expansions) and multidimensional pricing. Empirical tests on liquid equity entities (Credit Agricole, AXA, Michelin) confirm high calibration accuracy and demonstrate that QAMC requires 10-100 times fewer queries than classical methods for comparable precision. This study provides a practical route to integrate arbitrage-aware modelling with quantum computing, highlighting implications for scalability and future extensions to complex derivatives.