Depth-Efficient Quantum Topological Data Analysis for Regime-Specific Detection of Financial Stress
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摘要
This work adapting Pauli Correlation Encoding (PCE) to quantum topological data analysis reframes Betti-number estimation as a depth-efficient, variational Rayleigh-quotient minimization over a compressed qubit register, enabling Betti counting on realistic market datasets [page::1]. It demonstrates classical validation against ripser across 190 sliding windows (2007–2009) and shows that, with warm-start from a classical null-space surrogate, PCE-VQE can recover β1 exactly for real-market Laplacians (β1 = 1–22) at every scale, highlighting the obstacle as the optimization landscape rather than the encoding itself [page::1][page::6]. Chronologically split classification delivers in-regime ROC AUC of 0.818, while out-of-distribution crises (COVID shock, rate cycle) show calibration failure, indicating regime-aware deployment is necessary [page::9]. The paper provides resource models and end-to-end workflow for near-term quantum TDA on financial stress, concluding with a call for quantum-native warm starts and subspace strategies to extend beyond β1<‑=22 and to real-market scales [page::9].
