Hybrid Circuit–Spintronic Quantum Framework for Financial Risk Analysis with QCVaR Estimation Using Variational Quantum Algorithms and Maximum-Likelihood Amplitude Estimation

Gayathri S. S.; Muthulakshmi P.; R. Palanivel

doi:10.2478/qic-2026-0002

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Hybrid Circuit–Spintronic Quantum Framework for Financial Risk Analysis with QCVaR Estimation Using Variational Quantum Algorithms and Maximum-Likelihood Amplitude Estimation

Quantum Information & Computation

Volume 26 (2026): Issue 1 (March 2026)

By: Gayathri S. S., Muthulakshmi P. and R. Palanivel

Open Access

|Jun 2026

Abstract

Problem Statement

Accurate estimation of extreme financial risks, such as Conditional Value-at-Risk (CVaR) at high confidence levels (α ≥ 0.95), poses significant computational challenges for classical Monte Carlo methods, which require O(1/ϵ²) samples and struggle to scale under rare-event scenarios.

Methodology

To address this, we propose a hybrid variational quantum–spintronic framework integrating Variational Quantum State Preparation (VQA), a threshold comparator oracle, and Maximum-Likelihood Amplitude Estimation (MLAE) to enable quantum-accelerated CVaR estimation suitable for NISQ devices.

Results

Using only 6 qubits and K = 6 amplification levels, our approach achieves ${\hat{CVaR}}_{0.95} = 0.281 \pm 0.012$ {\widehat {{\rm{CVaR}}}_{0.95}} = 0.281 \pm 0.012(error < 1.1% compared to classical benchmarks), with tail probability $\hat{p} = 0.0478 \pm 0.0009$ \hat p = 0.0478 \pm 0.0009 and state fidelity 0.967 on the ibm_brisbane backend. MLAE reduces circuit depth by 3.3 × relative to canonical QAE, and a conceptual spintronic implementation achieves ∼2.0 fJ/gate, corresponding to an 80% energy reduction versus CMOS.

Contributions

This work introduces the first NISQ-compatible, energy-efficient quantum–spintronic pipeline for regulatory-compliant financial risk analytics, providing a quadratic sampling speedup, accurate tail-risk estimation, and a pathway toward sustainable quantum finance.

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Articles in this issue

DOI: https://doi.org/10.2478/qic-2026-0002 | Journal eISSN: 3106-0544 | Journal ISSN: 1533-7146

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Language: English

Page range: 20 - 37

Submitted on: Sep 1, 2025

Accepted on: Nov 20, 2025

Published on: Jun 4, 2026

Published by: Cerebration Science Publishing Co., Limited

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

quantum finance,

Conditional Value-at-Risk (CVaR),

Maximum-Likelihood Amplitude Estimation (MLAE),

spintronic quantum computing,

NISQ algorithms

Related subjects:

Physics,

Computer sciences in the humanities,

Computer sciences,

Computer sciences in natural sciences

© 2026 Gayathri S. S., Muthulakshmi P., R. Palanivel, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 26 (2026): Issue 1 (March 2026)