pith. sign in

arxiv: 2601.03654 · v2 · submitted 2026-01-07 · 💻 cs.LG · math.OC· math.QA

Hybrid Quantum-Classical Ridgelet Neural Networks for Portfolio Optimization

Bahadur Yadav , Sanjay Kumar Mohanty This is my paper

Pith reviewed 2026-05-16 16:50 UTC · model grok-4.3

classification 💻 cs.LG math.OCmath.QA
keywords hybrid quantum-classicalridgelet transformportfolio optimizationQAOAtime-series forecastingQUBOneural networksfinancial forecasting
0
0 comments X

The pith

Ridgelet transforms let quantum circuits forecast financial time series with far fewer qubits before QAOA solves portfolio selection.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a hybrid Quantum Ridgelet Neural Network that applies ridgelet transforms to break financial time-series data into multi-resolution components capturing both local and global patterns. These reduced features feed into parametrized quantum circuits whose outputs become a QUBO formulation of mean-variance optimization solved by QAOA. The authors first derive the model for a single qubit and then extend it to the multi-qubit case, showing that the pipeline retains a significant fraction of the original predictive signal. If the reduction in qubit count holds while accuracy remains useful, quantum optimization could scale to asset universes that exceed the capacity of direct quantum approaches on present hardware.

Core claim

Integrating the ridgelet transform into quantum processing pipelines decomposes time-series data into multi-resolution components that identify local and global trends, allowing parametrized quantum circuits and subsequent QAOA-based portfolio optimization to operate with substantially fewer qubits while capturing a significant fraction of the predictive signal in both single-qubit and multi-qubit formulations.

What carries the argument

The ridgelet transform, which decomposes financial time-series into multi-resolution components to capture local and global trends, integrated with parametrized quantum circuits and QAOA for QUBO mean-variance optimization.

If this is right

  • Larger asset sets become tractable on near-term quantum hardware because the feature reduction lowers qubit demand.
  • Portfolio choices incorporate both short-term fluctuations and longer trends extracted by the ridgelet decomposition.
  • The single-to-multi-qubit extension demonstrates that signal fidelity survives scaling of the quantum component.
  • Mean-variance optimization formulated as QUBO becomes solvable directly from quantum forecasts of asset behavior.
  • Forecasts generated this way support asset selection that balances expected return against variance more effectively than classical baselines alone.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same multi-resolution feature step could be paired with other variational quantum algorithms for sequential prediction tasks outside finance.
  • If qubit savings persist across datasets, analogous wavelet-style transforms might lower resource needs in quantum machine learning more broadly.
  • Empirical tests on varied market regimes would show whether the claimed signal retention produces measurable improvements in out-of-sample portfolio performance.
  • Hybrid pipelines of this form may reduce the classical pre-processing burden when preparing optimization problems for quantum solvers.

Load-bearing premise

Ridgelet-based features can cut the number of qubits required while preserving enough predictive information that the QAOA step outperforms classical portfolio methods on real financial data.

What would settle it

A side-by-side run on historical stock returns where the hybrid model either consumes the same qubit count as a non-ridgelet quantum baseline or yields portfolios with lower risk-adjusted returns than standard classical solvers.

Figures

Figures reproduced from arXiv: 2601.03654 by Bahadur Yadav, Sanjay Kumar Mohanty.

Figure 1
Figure 1. Figure 1: Comparison of the test data set of APPL stock to compare predicted QRNN and real prices. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
read the original abstract

In this study, we introduce a quantum computing method that incorporates Ridglet transforms into quantum processing pipelines for financial time-series forecasting with Quantum Approximate Optimization Algorithm (QAOA)-based portfolio optimization. We propose a Quantum Ridgelet Neural Network (QRNN) model for forecasting time-series data that integrates Parametrized Quantum Circuits (PQCs) with ridgelet-based feature transformations and QAOA-based portfolio optimization for asset selection. By breaking down financial time-series data into multi-resolution components, the ridgelet transform enables the identification of both local and global trends. Ridgelet-based features improve the scalability and accuracy of quantum computing by significantly reducing the number of qubits needed. However, the predicted results are turned into a QUBO-based mean-variance optimization problem and solved with QAOA to select the best stocks. Our study begins with a theoretical formulation of the single-qubit system for our proposed model. This formulation is further extended to a multi-qubit system, and we show that it captures a significant fraction of the predictive signal.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces a Hybrid Quantum-Classical Ridgelet Neural Network (QRNN) for financial time-series forecasting. It integrates ridgelet transforms with parametrized quantum circuits (PQCs) to reduce qubit requirements, provides a theoretical single-qubit formulation extended to multi-qubit systems, and uses QAOA to solve the resulting QUBO for portfolio optimization. The central claim is that the ridgelet-based features allow the model to capture a significant fraction of the predictive signal.

Significance. If the unshown derivations and validations hold, the work could contribute to hybrid quantum methods in finance by addressing qubit scalability through ridgelet feature extraction. The paper supplies neither machine-checked proofs, reproducible code, nor parameter-free derivations, so the significance remains conditional on future empirical support.

major comments (3)
  1. [Abstract] Abstract: the claim that the multi-qubit extension 'captures a significant fraction of the predictive signal' is presented without any quantitative metric (correlation, explained variance, forecast MSE) or baseline comparison to classical ridgelet or neural-network forecasters.
  2. [Theoretical formulation] Theoretical formulation (single-to-multi-qubit extension): no explicit circuit construction, gate decomposition, or error analysis for the ridgelet-PQC mapping is supplied, which is load-bearing for the asserted qubit-count reduction.
  3. [Portfolio optimization] Portfolio-optimization step: the encoding of QRNN forecasts into the QUBO mean-variance objective is not detailed, preventing evaluation of whether the QAOA step can outperform classical solvers on real financial data.
minor comments (2)
  1. [Model description] The ridgelet scale parameters are listed as free parameters but their initialization and optimization procedure are not specified.
  2. [Ridgelet transform] Notation for the ridgelet transform coefficients is introduced without a clear reference to the standard continuous ridgelet definition.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and will incorporate the suggested clarifications and additions in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the multi-qubit extension 'captures a significant fraction of the predictive signal' is presented without any quantitative metric (correlation, explained variance, forecast MSE) or baseline comparison to classical ridgelet or neural-network forecasters.

    Authors: We agree that the abstract claim requires quantitative backing. The current manuscript states the claim at a high level based on the ridgelet feature extraction properties, but does not include explicit metrics or baselines in the abstract. In revision we will add concrete values (e.g., forecast MSE, correlation, explained variance) from the experiments and include a brief comparison to classical ridgelet and neural-network forecasters, then update the abstract accordingly. revision: yes

  2. Referee: [Theoretical formulation] Theoretical formulation (single-to-multi-qubit extension): no explicit circuit construction, gate decomposition, or error analysis for the ridgelet-PQC mapping is supplied, which is load-bearing for the asserted qubit-count reduction.

    Authors: The manuscript presents the single-qubit formulation and its formal extension to the multi-qubit case, but we acknowledge that explicit circuit diagrams, gate decompositions, and error analysis are not provided. We will add these elements in the revised theoretical section, including a concrete circuit construction for the ridgelet-PQC mapping and a basic error bound to substantiate the qubit-count reduction. revision: yes

  3. Referee: [Portfolio optimization] Portfolio-optimization step: the encoding of QRNN forecasts into the QUBO mean-variance objective is not detailed, preventing evaluation of whether the QAOA step can outperform classical solvers on real financial data.

    Authors: We will expand the portfolio-optimization section to provide the explicit mapping from QRNN forecasts to the QUBO formulation, including the precise mean-variance objective function and how forecast values enter the quadratic and linear terms. This will enable readers to assess the QAOA step against classical solvers. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in the derivation chain

full rationale

The paper presents a theoretical formulation of a single-qubit QRNN, extends the construction to a multi-qubit system using ridgelet transforms, and states that the extension captures a significant fraction of the predictive signal. No equations, parameter-fitting steps, or self-referential definitions are exhibited that would reduce this claim to an input by construction (e.g., no fitted scale parameter renamed as a prediction, no ansatz smuggled via self-citation, and no uniqueness theorem invoked from prior author work). The available text contains only a high-level assertion rather than a load-bearing derivation that collapses into its own premises. Absence of numerical benchmarks or external verification is a question of evidence strength, not circularity under the enumerated patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on the unproven premise that ridgelet multi-resolution features compress the qubit requirement without destroying the signal needed for downstream mean-variance optimization. No free parameters are explicitly named, but the ridgelet scale and quantum circuit depth choices function as such. No new physical entities are postulated.

free parameters (1)
  • ridgelet scale parameters
    Chosen to decompose the time series; their specific values determine both qubit count and retained signal.
axioms (1)
  • domain assumption Ridgelet transform preserves sufficient predictive signal while reducing qubit count
    Invoked when the abstract states that ridgelet features improve scalability and accuracy of quantum computing.
invented entities (1)
  • Quantum Ridgelet Neural Network (QRNN) no independent evidence
    purpose: Forecasting financial time series inside a quantum circuit
    New named architecture introduced in the abstract; no independent evidence supplied beyond the claim itself.

pith-pipeline@v0.9.0 · 5476 in / 1366 out tokens · 28842 ms · 2026-05-16T16:50:58.860198+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages

  1. [1]

    Short-term wind power forecasting using ridgelet neural network

    Amjady, N., Keynia, F., Zareipour, H., 2011. Short-term wind power forecasting using ridgelet neural network. Electric power systems Research 81, 2099–2107

    work page 2011

  2. [2]

    A functional wavelet–kernel approach for time series prediction

    Antoniadis, A., Paparoditis, E., Sapatinas, T., 2006. A functional wavelet–kernel approach for time series prediction. Journal of the Royal Statistical Society Series B: Statistical Methodology 68, 837–857

    work page 2006

  3. [3]

    A hybrid quantum–classical lstm approach for predicting the stock market, in: Quantum Machine Learning in Industrial Automation

    Arora, S., Kumar, D., Gupta, S., 2025. A hybrid quantum–classical lstm approach for predicting the stock market, in: Quantum Machine Learning in Industrial Automation. Springer, pp. 75–98

    work page 2025

  4. [4]

    Quantum supremacy using a programmable supercon- ducting processor

    Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Boixo, S., Brandao, F.G., Buell, D.A., et al., 2019. Quantum supremacy using a programmable supercon- ducting processor. Nature 574, 505–510

    work page 2019

  5. [5]

    Quantum machine learning and optimisation in finance

    Jacquier, A., Kondratyev, O., Lipton, A., López de Prado, M., 2022. Quantum machine learning and optimisation in finance. Birmingham: Packt Publishing Ltd

    work page 2022

  6. [6]

    Short-term photovoltaic power forecasting based on hybrid quantum gated recurrent unit

    Jeong, S.G., Do, Q.V., Hwang, W.J., 2024. Short-term photovoltaic power forecasting based on hybrid quantum gated recurrent unit. ICT Express 10, 608–613

    work page 2024

  7. [7]

    Quantum circuit learning

    Mitarai, K., Negoro, M., Kitagawa, M., Fujii, K., 2018. Quantum circuit learning. Physical Review A 98, 032309

    work page 2018

  8. [8]

    A hybrid quantum classical framework and a method for fore- casting stock prices

    Mohanty, S.K., Yadav, B., 2025. A hybrid quantum classical framework and a method for fore- casting stock prices. Indian Patent IN202541114225

    work page 2025

  9. [9]

    Quantum computation and quantum information

    Nielsen, M.A., Chuang, I.L., 2010. Quantum computation and quantum information. Cambridge university press

    work page 2010

  10. [10]

    Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer

    Shor, P.W., 1999. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM review 41, 303–332

    work page 1999

  11. [11]

    Financial time series forecast- ing using optimized multistage wavelet regression approach

    Syamala Rao, P., Parthasaradhi Varma, G., Durga Prasad, C., 2022. Financial time series forecast- ing using optimized multistage wavelet regression approach. International Journal of Information Technology 14, 2231–2240

    work page 2022

  12. [12]

    Quantum information processing with superconducting circuits: a review

    Wendin, G., 2017. Quantum information processing with superconducting circuits: a review. Reports on Progress in Physics 80, 106001

    work page 2017

  13. [13]

    Hybrid ridgelet deep neural networks for data-driven arbitrage strategies

    Yadav, B., Mohanty, S.K., 2025. Hybrid ridgelet deep neural networks for data-driven arbitrage strategies. arXiv preprint arXiv:2510.10599

    work page arXiv 2025

  14. [14]

    A quantum-transformer hybrid architecture for polymer propertyprediction: Addressingdatasparsityissues

    Zhang, A., Bao, C., Zhu, Z., Ji, W., 2025. A quantum-transformer hybrid architecture for polymer propertyprediction: Addressingdatasparsityissues. ComputationalMaterialsScience256, 113950. 6

    work page 2025