Depth-Efficient Quantum Topological Data Analysis for Regime-Specific Detection of Financial Stress
Abstract
We present, to our knowledge, the first adaptation of Pauli Correlation Encoding (PCE) to quantum topological data analysis, reformulating Betti number estimation as a depth-efficient variational optimization over a compressed qubit register. From a Takens embedding and Vietoris-Rips filtration of S&P 500 returns, we extract combinatorial Laplacians and recast null-space counting as a continuous-PCE Rayleigh-quotient minimization with variational deflation, encoding nk simplex indices into O(nk1/κ) qubits with shallow, ancilla-free circuits. Because the resulting loss is rational rather than bilinear in the correlators, the barren-plateau bound of Sciorilli et al. does not transfer; empirically the gradient variance decays only polynomially, with no exponential barren plateau, over n=4-$12$ qubits. The classical stage matches ripser on all 190 sliding windows (2003-2010). On the real market Laplacians (β1=1-$22$), PCE-VQE recovers no null vector from a random start, but warm-starting from a classical null-space surrogate recovers β1 exactly on all seven windows tested (nk ≤ 259), placing the obstacle in the optimization landscape rather than the encoding. Chronologically split classification gives in-regime ROC AUC 0.818, but out-of-distribution evaluation on the 2020 COVID shock and 2022 rate cycle (AUC 0.009, 0.515) shows the calibration does not generalize across crisis regimes.
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BibTeX
@misc{mazumder2026depthefficient,
title = {{Depth-Efficient Quantum Topological Data Analysis for Regime-Specific Detection of Financial Stress}},
author = {Arul Rhik Mazumder and Shreyan Ronit Mazumder},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.09906},
eprint = {2607.09906},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.09906},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Depth-Efficient Quantum Topological Data Analysis for Regime-Specific Detection of Financial Stress
AU - Arul Rhik Mazumder
AU - Shreyan Ronit Mazumder
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2607.09906
UR - https://arxiv.org/abs/2607.09906
AB - We present, to our knowledge, the first adaptation of Pauli Correlation Encoding (PCE) to quantum topological data analysis, reformulating Betti number estimation as a depth-efficient variational optimization over a compressed qubit register. From a Takens embedding and Vietoris-Rips filtration of S&P 500 returns, we extract combinatorial Laplacians and recast null-space counting as a continuous-PCE Rayleigh-quotient minimization with variational deflation, encoding n_k simplex indices into O(n_k^1/κ) qubits with shallow, ancilla-free circuits. Because the resulting loss is rational rather than bilinear in the correlators, the barren-plateau bound of Sciorilli et al. does not transfer; empirically the gradient variance decays only polynomially, with no exponential barren plateau, over n=4-$12$ qubits. The classical stage matches ripser on all 190 sliding windows (2003-2010). On the real market Laplacians (β_1=1-$22$), PCE-VQE recovers no null vector from a random start, but warm-starting from a classical null-space surrogate recovers β_1 exactly on all seven windows tested (n_k ≤ 259), placing the obstacle in the optimization landscape rather than the encoding. Chronologically split classification gives in-regime ROC AUC 0.818, but out-of-distribution evaluation on the 2020 COVID shock and 2022 rate cycle (AUC 0.009, 0.515) shows the calibration does not generalize across crisis regimes.
ER -