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Circuit and execution metrics_
| Platform | Avg. Depth | Fidelity |
|---|---|---|
| AerSimulator (ideal) | 98 | 1.000 |
| AerSimulator (noisy) | 98 | 0.991 |
| IBM Brisbane (real) | 112 | 0.967 |
Quantum approaches to financial risk estimation_
| Authors | Method | Circuit Depth | Hardware | Limitation / Gaps |
|---|---|---|---|---|
| Woerner & Egger [9] | QAE | 500–1000 | Theoretical | Deep circuits unsuitable for NISQ; no hardware results |
| Orús et al. [12] | Quantum annealing | 200–500 | D-Wave | Limited to small portfolios; lacks CVaR support |
| Herman et al. [13] | VQA | 50–100 | IBM Simulator | No scalability analysis on real datasets |
| Chakrabarti et al. [14] | QPE + QAA | 600–1200 | Theoretical | Deep circuits not NISQ compatible; synthetic dataset only |
| Fontana et al. [15] | VQA for VaR | 100–200 | IBM Quantum | Focused only on VaR; no CVaR extension |
| Li & Zhang [16] | Optimized QPE Oracle | 150–300 | Simulated | Assumes ideal distributions; lacks robustness test |
| Pérez-Salinas et al. [17] | VQE | 200–400 | Simulated | High classical cost; limited scalability |
| Miyamoto & Kubo [18] | Quantum walk | 300–600 | N/A | Lacks practical integration with CVaR pipelines |
| Gilles et al. [19] | QAE with EVaR/RVaR | 500–1000 | NISQ Simulator | No hardware runs; circuit depth remains a bottleneck |
| Matsakos & Nield [20] | Quantum-enhanced Monte Carlo | 400–800 | Simulated | Complex mapping for highdimensional risks |
| Wu et al. [21] | End-to-end QAE | 300–600 | Simulated | No extension to American options; limited derivatives covered |
| Ghosh et al. [22] | Dynamic Amplitude Estimation | 200–400 | Simulated | Domain-specific; lacks generalizability |
| Yohichi et al. [23] | Quantum PDE solver | 300–600 | None | No quantum hardware implementation yet |
| Cong & Thi [24] | VQA Survey | 100–500 | N/A | No empirical tests; theoretical-only |
| Thakkar et al. [25] | Quantum ML | 150–300 | Simulated | Not integrated into enterprise-grade risk systems |
Algorithmic and resource comparison_
| Metric | Classical MC | Canonical QAE | VQA+MLAE (Ours) |
|---|---|---|---|
| Sampling complexity | O(1/ϵ2) | O(1/ϵ) | O(1/ϵ) |
| Circuit depth (max k) | – | 20 | 6 (–70%) |
| Tail-probability MAE | – | 2.1 × 10−3 | 1.7 × 10−3 |
| CVaR error | 0.4% | 1.3% | <1.1% |
| Total shots (K = 6) | 106 | 20,480 | 6,144 |
| Runtime (ibm_brisbane) | 184 s | 42 s | 13 s |
Estimated energy per logical gate using spintronic analogues_
| Logical Gate | Physical Mechanism | Energy (fJ) |
|---|---|---|
| Hadamard | STO precession | 1.9 |
| Ry(θ) | Rashba SO coupling | 1.7 |
| CNOT | Exchange interaction | 2.3 |
| Measurement | MTJ readout | 2.0 |