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

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/ ϵ 2 ) 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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mover accent="true"> <m:mrow> <m:mtext>CVaR</m:mtext> </m:mrow> <m:mo stretchy="true">^</m:mo> </m:mover> <m:mrow> <m:mn>0.95</m:mn> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:mn>0.281</m:mn> <m:mo>±</m:mo> <m:mn>0.012</m:mn> </m:math> { {{CVaR}}0.95} = 0.281 ± 0.012 (error < 1.1% compared to classical benchmarks), with tail probability <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mover accent="true"> <m:mi>p</m:mi> <m:mo>^</m:mo> </m:mover> <m:mo>=</m:mo> <m:mn>0.0478</m:mn> <m:mo>±</m:mo> <m:mn>0.0009</m:mn> </m:math> p = 0.0478 ± 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.