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arXiv:2607.12990

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

Guillem Borràs Espert, Francisco Gómez Casanova, Luis de Pedro Sánchez, Senaida Hernández Santana, Pablo Serrano Molinero

quant-phq-fin.CPSubmitted Jul 14, 2026• Announced Jul 15, 2026• 0 citations• Revised Sep 7, 2026 (v3)
v1 · Jul 14, 2026v2 · Aug 25, 2026v3 · Sep 7, 2026
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Abstract

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.

Comments
56 pages, 14 figures, 18 tables. Includes supplementary appendices with implementation details, extended results, calibration data, and quantum-resource analysis

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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.
Abstract Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases, credit valuation adjustment (CVA), and identify opportunities and challenges towards quantum advantage for practical instances. To build a NISQ-friendly quantum circuit able to solve such problem, we draw on various heuristics that indicate the potential for significant improvement over well-known techniques such as reversible logical circuit synthesis. In minimizing the resource requirements for amplitude amplification while maximizing the speedup gained from the quantum coherence of a noisy device, we adopt a recently developed Bayesian variant of quantum amplitude estimation using engineered likelihood functions. We perform numerical analyses to characterize the prospect of quantum speedup in concrete CVA instances over classical Monte Carlo simulations.
A critical problem in the financial world deals with the management of risk, from regulatory risk to portfolio risk. Many such problems involve the analysis of securities modelled by complex dynamics that cannot be captured analytically, and hence rely on numerical techniques that simulate the stochastic nature of the underlying variables. These techniques may be computationally difficult or demanding. Hence, improving these methods offers a variety of opportunities for quantum algorithms. In this work, we study the problem of Credit Valuation Adjustments (CVAs) which has significant importance in the valuation of derivative portfolios. As a variant, we also consider the problem of pricing a portfolio of many different financial options. We propose quantum algorithms that accelerate statistical sampling processes to approximate the price of the multi-option portfolio and the CVA under different measures of dispersion. Technically, our algorithms are based on enhancing the quantum Monte Carlo (QMC) algorithms by Montanaro with an unbiased version of quantum amplitude estimation. We analyse the conditions under which we may employ these techniques and demonstrate the application of QMC techniques on CVA approximation when particular bounds for the variance of CVA are known.
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.
Estimating potential future exposure (PFE) for path-dependent derivatives, such as FX Target Redemption Forwards (TARFs), represents a formidable computational challenge due to the demand of nested Monte Carlo simulations. We present a hybrid quantum-classical framework that leverages Iterative Quantum Amplitude Estimation (IQAE) to address this via a reduced-order counterparty credit risk model. Our methodology maps the non-linear TARF payoff -- including cumulative gains and knock-out features -- into a quantum circuit via a two-step formulation, whereby a first-step percentile is computed classically and then used to condition quantum evaluation of subsequent exposure. We employ discretisation of the FX process and a linearised additive approximation of dynamics to enable implementation on current quantum platforms. Developed via the Classiq platform and validated on NVIDIA CUDA-Q and Amazon Braket SV1, our approach achieves relative errors of 1%-8% against classical benchmarks at the 97.5% and 99% confidence levels. While discretisation constraints and approximate monotonicity assumption may introduce bias and limit recovery of the full exposure distribution, our framework offers a tractable testbed for quantum acceleration. Scaling analysis suggests that $\sim$300 logical qubits could enable full 52-week exposure estimation, reducing sample complexity for tail-risk estimation via amplitude estimation at the cost of increased circuit depth.
Noisy and Intermediate-Scale Quantum, or NISQ, processors are sensitive to noise, prone to quantum decoherence, and are not yet capable of continuous quantum error correction for fault-tolerant quantum computation. Hence, quantum algorithms designed in the pre-faulttolerant era cannot neglect the noisy nature of the hardware, and investigating the relationship between quantum hardware performance and the output of quantum algorithms is essential. In this work, we experimentally study how hardware-aware variational quantum circuits on a superconducting quantum processing unit can model distributions relevant to specific use-case applications for Credit Risk Analysis, e.g., standard Gaussian distributions for latent factor loading in the Gaussian Conditional- Independence model. We use a transpilation technique tailored to the specific quantum hardware topology, which minimizes gate depth and connectivity violations, and we calibrate the gate rotations of the circuit to achieve an optimized output from quantum algorithms. Our results demonstrate the viability of quantum adaptation on a small scale, proof-of-concept model inspired by financial applications and offer a good starting point for understanding the practical use of NISQ devices.
Financial modeling and risk analysis involve computationally intensive tasks -- Monte Carlo simulation for derivative pricing, portfolio optimisation over high-dimensional asset spaces, and Value-at-Risk estimation from complex multivariate distributions -- where quantum computing offers potential polynomial-to-quadratic speedups. This paper proposes the Quantum Financial Computation Framework (QFCF), a systematic evaluation of quantum algorithms for four core financial computing tasks: option pricing (quantum amplitude estimation for Monte Carlo), portfolio optimisation (QAOA and VQE on quadratic unconstrained binary optimisation formulations), credit risk assessment (quantum Bayesian inference), and Value-at-Risk estimation (quantum arithmetic circuits). QFCF is evaluated on 16 financial benchmark problems spanning European and Asian option pricing, 50-500 asset portfolio optimisation, and credit portfolio loss distributions on near-term (NISQ) and fault-tolerant quantum hardware models. Key results: quantum amplitude estimation achieves quadratic speedup over classical Monte Carlo for option pricing with circuit depth scaling as O(1/ε) versus classical O(1/ε2); QAOA achieves portfolio optimisation solution quality within 4.8% of classical branch-and-bound for 50-asset problems; quantum Bayesian credit scoring reduces inference time by 38x for 200-variable credit networks. The framework introduces the Quantum Financial Utility Index (QFUI) and quantitative quantum advantage thresholds for each financial task.