对比两种量子算法在金融组合优化中的表现,发现硬件限制导致无法兼顾精度与稳定性。
Benchmarking Quantum Algorithmic Resilience for CVaR Portfolio Optimization: The Expressibility-Coherence Trade-off

- 用新型混合矩阵绕过辅助量子比特瓶颈,实现16只股票的映射
- WS-QAOA因非局域门开销大,导致量子退相干严重,性能崩溃
- HE-VQNN虽保相干但表达能力弱,难捕捉资产尾部风险关联
量子组合优化在复杂金融建模中具理论优势,但在嘈杂中等规模量子(NISQ)设备上受硬件拓扑严重制约。本研究对硬件高效变分量子神经网络(HE-VQNN)与温启动量子近似优化算法(WS-QAOA)在混合均值-方差与条件风险价值(CVaR)组合目标下进行硬件基准测试。通过引入新型经典-量子混合代理矩阵,规避了CVaR的辅助量子比特瓶颈,成功将最多16只来自印度尼西亚50指数(NIFTY 50)的资产映射至IBM重六边形处理器。系统量化了算法在路由过程中产生的“SWAP税”影响。实证结果揭示关键权衡:WS-QAOA虽具理论精确映射,却因指数级非局域门开销导致灾难性硬件退相干;而HE-VQNN虽保持硬件相干性,但数学表达能力不足,无法捕捉密集尾部风险的资产相关性。该研究揭示当前架构下密集金融优化迫使算法在表达不可行与硬件退相干之间做出不可接受的抉择,暴露出缺乏全连接性的NISQ计算机在实际应用中的深层局限。
原文摘要 · Abstract (English)
Quantum combinatorial optimization offers theoretical advantages for complex financial modeling, but physical implementation on Noisy Intermediate Scale Quantum (NISQ) devices is severely constrained by hardware topology. This study presents a hardware benchmarking analysis between a Hardware Efficient Variational Quantum Neural Network (HE-VQNN) and the Warm Start Quantum Approximate Optimization Algorithm (WS-QAOA) for a hybrid Mean Variance and Conditional Value at Risk (CVaR) portfolio objective. By implementing a novel classical quantum hybrid proxy matrix to bypass the CVaR auxiliary qubit bottleneck, we map up to 16 assets from the NIFTY 50 index onto an IBM heavy hex processor. We systematically quantify algorithmic resilience to the "SWAP tax" incurred during routing. Empirical results reveal a critical operational trade-off: WS-QAOA provides exact theoretical mapping but suffers catastrophic hardware decoherence due to exponential nonlocal gate overhead. Conversely, HE-VQNN preserves hardware coherence but lacks the mathematical expressibility to capture dense tail risk asset correlations. This study exposes the limitations of dense financial optimization on current architectures forces an nonviable choice between algorithmic inexpressibility and hardware decoherence. This is indicative of a deeper limitation as to what can and cannot be done with NISQ computers lacking in all-to-all connectivity.
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