Depth-Efficient Quantum Topological Data Analysis for Regime-Specific Detection of Financial Stress

• URL: http://arxiv.org/abs/2607.09906v1
• Date: Fri, 10 Jul 2026 18:56:45 GMT
• Title: Depth-Efficient Quantum Topological Data Analysis for Regime-Specific Detection of Financial Stress
• Abstract summary: We present the first adaptation of Pauli Correlation optimisation (PCE) to quantum topological data analysis.<n>From a Takens embedding and Vietoris--Rips filtration of S&P500 returns, we extract $0.8 Laplacians and recast null-space counting as a continuous-PCE-quotient with variational deflation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $n_k$ 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~\cite{Sciorilli25} 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~\cite{bauer2021ripser} on all 190 sliding windows (2007-2009). On the real market Laplacians ($β_1=1$--$22$), warm-starting from a classical null-space surrogate allows PCE-VQE to recover $β_1$ exactly at every scale, placing the obstacle in the optimisation 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.

Related papers

• Demixing Sparse Signals from Nonlinear Observations using Generalized Non-convex Regularization [0.0]
  We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition.<n>We propose a regularization-based framework combining a Huberized data fidelity with generalized folded-concave penalties.<n>We derive estimation error bounds of order $sqrtslog(n)/m$ that hold at emphevery localized stationary point.
  arXiv  Detail & Related papers  (2026-07-12T07:29:39Z)
• How Neural Reward Models Learn Features for Policy Optimization: A Single-Index Analysis [53.063298916923976]
  We study the feedback in a Gaussian single-index model with $r*(x) = *(langle *, xrangle)$ and $x sim N(0, I_d)$.<n>We analyze a two-stage neural reward model that first learns the hidden direction $*$ from reward-weighted samples and then fits the readout layer by weighted ridge regression.
  arXiv  Detail & Related papers  (2026-05-23T22:00:38Z)
• Wavelet Variance Equipartition as a Threshold for World-Model Quality and Quantum Kernel TN-Simulability [0.0]
  We identify the wavelet scaling exponent $$ as a critical diagnostic.<n>We establish $= 1/2$ as a sharp transition boundary for the classical simulability of amplitude-encoded quantum kernels.<n>We prove this variance scales strictly as $Var[X] = (d-2)$.
  arXiv  Detail & Related papers  (2026-05-12T05:41:12Z)
• Accelerated Relax-and-Round for Concave Coverage Problems [7.984421247931201]
  We present an accelerated relax-and-round algorithm for concave coverage problems.<n>Our algorithm outperforms approaches that use state-of-the-art LP solvers.
  arXiv  Detail & Related papers  (2026-05-07T20:00:40Z)
• Blind Catalytic Quantum Error Correction: Target-State Estimation and Fidelity Recovery Without \textit{A Priori} Knowledge [0.0]
  We introduce emphblind CQEC, which estimates the target from the noisy output alone before catalytic recovery.<n>Five estimation strategies are benchmarked across three noise models.
  arXiv  Detail & Related papers  (2026-04-13T08:27:08Z)
• Provably Adaptive Linear Approximation for the Shapley Value and Beyond [73.0940890296463]
  A fundamental and long-standing challenge is their efficient approximation.<n>We develop a linear-space algorithm that requires $P(|hatboldsymbol-boldsymbol|_2geq)leq $ for all commonly used semi-values.<n>Our algorithm allows explicit minimization of the mean square error for each specific utility function.
  arXiv  Detail & Related papers  (2026-04-09T16:38:14Z)
• Sublinear Time Quantum Sensitivity Sampling [57.356528942341534]
  We present a unified framework for quantum sensitivity sampling, extending the advantages of quantum computing to a broad class of classical approximation problems.<n>Our framework provides a streamlined approach for constructing coresets and offers significant runtime improvements in applications such as clustering, regression, and low-rank approximation.
  arXiv  Detail & Related papers  (2025-09-20T20:18:49Z)
• Convergence Rate Analysis of LION [54.28350823319057]
  LION converges iterations of $cal(sqrtdK-)$ measured by gradient Karush-Kuhn-T (sqrtdK-)$. We show that LION can achieve lower loss and higher performance compared to standard SGD.
  arXiv  Detail & Related papers  (2024-11-12T11:30:53Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Bounding the Width of Neural Networks via Coupled Initialization -- A Worst Case Analysis [121.9821494461427]
  We show how to significantly reduce the number of neurons required for two-layer ReLU networks. We also prove new lower bounds that improve upon prior work, and that under certain assumptions, are best possible.
  arXiv  Detail & Related papers  (2022-06-26T06:51:31Z)
• Scale-free Unconstrained Online Learning for Curved Losses [1.5147172044848798]
  We investigate the possibility of adapting simultaneously to the norm $U$ of the comparator and the maximum norm $G$ of the gradients. Surprisingly, recent results show that no such price for adaptivity is needed in the specific case of $1$-Lipschitz losses.
  arXiv  Detail & Related papers  (2022-02-11T14:10:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.