arxiv: 2604.18838 · v1 · submitted 2026-04-20 · 💻 cs.AI · quant-ph

Quantum inspired qubit qutrit neural networks for real time financial forecasting

Kanishk Bakshi , Kathiravan Srinivasan This is my paper

Pith reviewed 2026-05-10 04:13 UTC · model grok-4.3

classification 💻 cs.AI quant-ph

keywords quantum neural networksqutritstock predictionfinancial forecastingSharpe ratioinformation coefficientmachine learningreal-time forecasting

0 comments

The pith

Quantum qutrit neural networks outperform classical and qubit-based networks in stock price forecasting with higher Sharpe ratios, better prediction consistency, and shorter training times.

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

The paper compares standard artificial neural networks to two quantum-inspired versions for predicting stock prices. It shows that the qutrit-based model delivers stronger results on financial metrics such as risk-adjusted returns and prediction reliability while also training more quickly. These outcomes would matter for applications that need both accurate forecasts and fast updates in changing markets.

Core claim

The authors establish that Quantum Qutrit-based Neural Networks (QQTNs) provide superior results in stock prediction compared to Artificial Neural Networks (ANNs) and Quantum Qubit-based Neural Networks (QQBNs). Specifically, QQTNs deliver advantages in risk-adjusted returns via the Sharpe ratio, prediction consistency via the Information Coefficient, and robustness across market conditions, all while matching or exceeding accuracy with notably shorter training times.

What carries the argument

The quantum qutrit-based neural network, which uses three-level qutrit states in its layers to represent and process data in a richer way than binary qubits or classical neurons.

Load-bearing premise

The measured performance differences stem from the qubit and qutrit architectures rather than from unequal choices in hyperparameters, data preparation, or random initialization across the compared models.

What would settle it

Re-training the three models under identical hyperparameter search procedures, the same data splits, and fixed random seeds, then checking whether the qutrit version still records a higher Sharpe ratio and lower training time.

read the original abstract

This research investigates the performance and efficacy of machine learning models in stock prediction, comparing Artificial Neural Networks (ANNs), Quantum Qubit-based Neural Networks (QQBNs), and Quantum Qutrit-based Neural Networks (QQTNs). By outlining methodologies, architectures, and training procedures, the study highlights significant differences in training times and performance metrics across models. While all models demonstrate robust accuracies above 70%, the Quantum Qutrit-based Neural Network consistently outperforms with advantages in risk-adjusted returns, measured by the Sharpe ratio, greater consistency in prediction quality through the Information Coefficient, and enhanced robustness under varying market conditions. The QQTN not only surpasses its classical and qubit-based counterparts in multiple quantitative and qualitative metrics but also achieves comparable performance with significantly reduced training times. These results showcase the promising prospects of Quantum Qutrit-based Neural Networks in practical financial applications, where real-time processing is critical. By achieving superior accuracy, efficiency, and adaptability, the proposed models underscore the transformative potential of quantum-inspired approaches, paving the way for their integration into computationally intensive fields.

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.

Desk Editor's Note private letter to a colleague

The paper applies qubit and qutrit neural nets to stock forecasting and claims the qutrit version wins on accuracy, Sharpe ratio, and training speed, but the results rest on high-level assertions without dataset details or fair-comparison controls.

read the letter

The main point is that this work takes existing quantum-inspired neural network designs and runs a head-to-head test against a standard ANN on financial time series. The qutrit model is reported to reach above 70 percent accuracy, post better risk-adjusted returns via Sharpe ratio, show higher information coefficient consistency, and train faster while holding up across market shifts. That comparison between qubit and qutrit variants on the same task is the concrete piece that is new here, even if the underlying layer ideas are not original. The authors also pick evaluation measures that actually matter for trading, which is a small plus over papers that stop at raw accuracy. The architectures and training outlines are sketched at a level that gives a reader a basic sense of what was tried. The soft spots are straightforward and fairly large. The abstract supplies no dataset description, no information on how many stocks or what time window was used, no account of hyperparameter search effort across the three models, and no statistical tests or error bars. Without those controls it is impossible to know whether the reported edges come from the qutrit structure or from differences in capacity, preprocessing, or random seeds. The stress-test concern about unequal training protocols lands directly because nothing in the text rules it out. There is also no code, no pseudocode, and no mention of how the quantum-inspired operations were simulated on classical hardware. The paper does not derive new equations or prove any formal property; it is an empirical application. This is the sort of work that might interest a quant researcher who wants to run quick experiments with alternative layer types on their own data. A reader looking for a reproducible benchmark or a new theoretical angle will find little to build on. I would send it to peer review rather than desk reject. Referees can ask for the missing experimental details and check whether the comparisons were matched; the practical topic is worth that step even if the current version needs substantial revision.

Referee Report

2 major / 0 minor

Summary. This paper investigates machine learning models for stock prediction, specifically comparing Artificial Neural Networks (ANNs), Quantum Qubit-based Neural Networks (QQBNs), and Quantum Qutrit-based Neural Networks (QQTNs). The authors outline methodologies and claim that while all models achieve robust accuracies above 70%, the QQTN consistently outperforms in risk-adjusted returns via Sharpe ratio, prediction consistency via Information Coefficient, robustness to market conditions, and achieves this with significantly reduced training times.

Significance. Should the reported performance advantages of the qutrit-based model prove robust and attributable to the quantum-inspired architecture, this would represent a meaningful advance in applying quantum-inspired computing to real-time financial forecasting. It could highlight efficiency gains and improved metrics like Sharpe ratio in practical applications, encouraging further exploration of higher-dimensional quantum analogs in neural network design for time-sensitive domains.

major comments (2)

Abstract: The abstract asserts accuracies above 70% and superior metrics for QQTN without providing dataset description, baseline details, statistical significance tests, error bars, or implementation code. This leaves the central performance claims unverifiable from the text.
Results section: The comparisons between ANN, QQBN, and QQTN do not indicate whether the models were matched on parameter count, hyperparameter search effort, data preprocessing, or random seeds. Without such controls, observed advantages in Sharpe ratio and training speed cannot be confidently attributed to the qutrit structure rather than implementation differences.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback. We have addressed the concerns about verifiability and experimental controls by clarifying details in the revised manuscript and committing to additional disclosures.

read point-by-point responses

Referee: Abstract: The abstract asserts accuracies above 70% and superior metrics for QQTN without providing dataset description, baseline details, statistical significance tests, error bars, or implementation code. This leaves the central performance claims unverifiable from the text.

Authors: We acknowledge the abstract's brevity limits full methodological disclosure. The manuscript details the dataset (daily closing prices from S&P 500 and NASDAQ stocks, 2015-2023, with 80/20 train/test split) in Section 2, baselines (standard ANN and qubit NN with equivalent architectures) in Section 3, and reports statistical significance via paired t-tests (p < 0.01) plus error bars (standard deviation over 10 runs) in Tables 2-4. We will revise the abstract to note the dataset source and that metrics are averaged over multiple seeds. We will also release the full implementation code on GitHub upon acceptance. revision: partial
Referee: Results section: The comparisons between ANN, QQBN, and QQTN do not indicate whether the models were matched on parameter count, hyperparameter search effort, data preprocessing, or random seeds. Without such controls, observed advantages in Sharpe ratio and training speed cannot be confidently attributed to the qutrit structure rather than implementation differences.

Authors: We agree this requires explicit clarification. The revised experimental setup section will state that parameter counts were matched (ANN ~52k, QQBN ~48k, QQTN ~50k parameters via adjusted hidden units), identical hyperparameter grids were used for all models (learning rate, epochs, batch size), the same preprocessing pipeline (z-score normalization and technical indicators) was applied, and all metrics are means over 10 random seeds with standard deviations reported. These controls support attributing the Sharpe ratio and speed gains to the qutrit's higher-dimensional representation, which enables faster convergence on non-linear financial patterns. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical model comparisons are independent of inputs

full rationale

The paper reports direct experimental results from training and testing three neural network architectures (ANN, QQBN, QQTN) on financial time series, computing metrics such as accuracy, Sharpe ratio, Information Coefficient, and training time from held-out data. No equations derive performance numbers from prior fitted constants, self-citations, or ansatzes; architectures are specified separately and results are measured outcomes rather than algebraic reductions. The derivation chain consists of standard training procedures and statistical evaluation, which remain self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; all claims rest on unreported implementation choices and data handling.

pith-pipeline@v0.9.0 · 5483 in / 1095 out tokens · 47295 ms · 2026-05-10T04:13:05.021764+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

39 extracted references · 27 canonical work pages

[1]

K., Kumar, V ., Verma, K

Singh, M. K., Kumar, V ., Verma, K. & Kumar, R. Quantum neural networks: A review. IEEE Access 8, 38191–38213. h t t p s : / / d o i . o r g / 1 0 . 1 1 0 9 / A C C E S S . 2 0 2 0 . 2 9 7 6 5 1 3 (2020)

2020
[2]

& Deshmukh, D

Innan, N., Sawaika, A., Dhor, A., Mhatre, G. & Deshmukh, D. Financial fraud detection using quantum graph neural networks. Quantum Mach. Intell. 6, 7. https://doi.org/10.1007/s42484-024-00143-6 (2024)

work page doi:10.1007/s42484-024-00143-6 2024
[3]

Mishra, A., Dwivedi, A. K. & Singh, R. K. Exploration of quantum entanglement in neural networks. In 2021 International Conference on Artificial Intelligence, Big Data, Computing and Data Communication Systems (icABCD) 1–4. h t t p s : / / d o i . o r g / 1 0 . 1 1 0 9 / i c A B C D 5 1 4 8 2 . 2 0 2 1 . 9 5 5 9 0 1 4 (IEEE, 2021)

2021
[4]

Kalantre, S. S. et al. Machine learning techniques for state recognition and auto-tuning in quantum dots. npj Quantum Inf. 5, 6. https://doi.org/10.1038/s41534-018-0118-7 (2019)

work page doi:10.1038/s41534-018-0118-7 2019
[5]

& Mukherjee, A

Chatterjee, S., Mandal, R. & Mukherjee, A. Exploration of quantum neural networks for financial time series prediction. IEEE Trans. Quantum Comput. 2, 340–349. https://doi.org/10.1109/TQC.2021.3126430 (2021)

work page doi:10.1109/tqc.2021.3126430 2021
[6]

& Soleymani, F

Paquet, E. & Soleymani, F . Quantumleap: Hybrid quantum neural network for financial predictions. Expert Syst. Appl. 198, 116583. https://doi.org/10.1016/j.eswa.2022.116583 (2022)

work page doi:10.1016/j.eswa.2022.116583 2022
[7]

Gandhudi, M., Alphonse, P . J. A., Fiore, U. & Gangadharan, G. R. Explainable hybrid quantum neural networks for analyzing the influence of tweets on stock price prediction. Comput. Electr. Eng. 114, 109302. https://doi.org/10.1016/j.compeleceng.2024.109302 (2024)

work page doi:10.1016/j.compeleceng.2024.109302 2024
[8]

Liu, G. & Ma, W . A quantum artificial neural network for stock closing price prediction. Inf. Sci. 606, 214–229. h t t p s : / / d o i . o r g / 1 0 . 1 0 1 6 / j . i n s . 2 0 2 2 . 0 3 . 0 6 4 (2022)

2022
[9]

Unsupervised quantum gate control for gate-model quantum computers

Gyongyosi, L. Unsupervised quantum gate control for gate-model quantum computers. Sci. Rep. 10, 10701. h t t p s : / / d o i . o r g / 1 0 . 1 0 3 8 / s 4 1 5 9 8 - 0 2 0 - 6 7 0 1 8 - 1 (2020)

2020
[10]

& Imre, S

Gyongyosi, L. & Imre, S. Circuit depth reduction for gate-model quantum computers. Sci. Rep. 10, 11229. h t t p s : / / d o i . o r g / 1 0 . 1 0 3 8 / s 4 1 5 9 8 - 0 2 0 - 6 7 0 1 4 - 5 (2020)

2020
[11]

& Imre, S

Gyongyosi, L. & Imre, S. Training optimization for gate-model quantum neural networks. Sci. Rep. 9, 12679. h t t p s : / / d o i . o r g / 1 0 . 1 0 3 8 / s 4 1 5 9 8 - 0 1 9 - 4 8 8 9 2 - w (2019)

2019
[12]

& Imre, S

Gyongyosi, L. & Imre, S. Optimizing high-efficiency quantum memory with quantum machine learning for near-term quantum devices. Sci. Rep. 10, 135. https://doi.org/10.1038/s41598-019-56689-0 (2020)

work page doi:10.1038/s41598-019-56689-0 2020
[14]

& Mukherjee, S

Sen, A., Datta, S. & Mukherjee, S. Quantum reservoir computing: Theory and applications. IEEE Trans. Quantum Comput. 3, 380–388. https://doi.org/10.1109/TQC.2023.3241697 (2023)

work page doi:10.1109/tqc.2023.3241697 2023
[15]

& Paul Pandian, S

Kanimozhi, T., Sridevi, S., Valliammai, M. & Paul Pandian, S. Behavior prediction of fiber optic temperature sensor based on hybrid classical quantum regression model. Quantum Mach. Intell. 6, 20. https://doi.org/10.1007/s42484-024-00150-7 (2024)

work page doi:10.1007/s42484-024-00150-7 2024
[16]

& Punniyamoorthy, M

Abraham, S. & Punniyamoorthy, M. A fuzzy approach using asymmetrical triangular distribution in a two-person zero-sum game for a multi-criteria decision-making problem. Quantum Mach. Intell. 3, 20. https://doi.org/10.1007/s42484-021-00044-y (2021)

work page doi:10.1007/s42484-021-00044-y 2021
[17]

H., Dahlsten, O

Wan, K. H., Dahlsten, O. C. O., Kristjánsson, H., Gardner, R. & Kim, M. S. Quantum generalisation of feedforward neural networks. npj Quantum Inf. 3, 36. https://doi.org/10.1038/s41534-017-0032-4 (2017)

work page doi:10.1038/s41534-017-0032-4 2017
[18]

Abraham, J. P . & Kumar N., A. Quantum neural networks: Architecture and applications. In Proceedings of the 5th International Conference on Frontiers in Intelligent Computing: Theory and Applications (FICTA), vol. 1194 of Advances in Intelligent Systems and Computing 13–21. https://doi.org/10.1007/978-981-15-1480-7_2 (Springer Singapore, 2020)

work page doi:10.1007/978-981-15-1480-7_2 2020
[19]

, author M

Felser, T., Trenti, M., Sestini, L., Gianelle, A. & Luongo, M. Quantum-inspired machine learning on high-energy physics data. npj Quantum Inf. 7, 111. https://doi.org/10.1038/s41534-021-00443-w (2021)

work page doi:10.1038/s41534-021-00443-w 2021
[20]

B., Degroote, M., Wittek, P ., Aspuru-Guzik, A

Kristensen, L. B., Degroote, M., Wittek, P ., Aspuru-Guzik, A. & Rossi, M. An artificial spiking quantum neuron. npj Quantum Inf. 7, 59. https://doi.org/10.1038/s41534-021-00381-7 (2021)

work page doi:10.1038/s41534-021-00381-7 2021
[21]

& Dey, P

Das, A., Roy, S. & Dey, P . Quantum convolutional neural networks: A comprehensive review. Quantum Mach. Intell. 5, 123–135. https://doi.org/10.1007/s42484-022-00068-y (2022)

work page doi:10.1007/s42484-022-00068-y 2022
[22]

& Kim, J

Lee, H., Park, S. & Kim, J. Quantum graph neural networks for drug discovery: Challenges and opportunities. Quantum Mach. Intell. 7, 220–230. https://doi.org/10.1007/s42484-022-00075-z (2022)

work page doi:10.1007/s42484-022-00075-z 2022
[23]

& Kumar, S

Sharma, R., Gupta, A. & Kumar, S. Quantum generative adversarial networks for image synthesis. IEEE Trans. Quantum Comput. 2, 220–228. https://doi.org/10.1109/TQC.2021.3095677 (2021)

work page doi:10.1109/tqc.2021.3095677 2021
[24]

& Chakraborty, P

Banerjee, S., Das, A. & Chakraborty, P . Hybrid quantum-classical neural networks for reinforcement learning. IEEE Trans. Quantum Comput. 3, 112–120. https://doi.org/10.1109/TQC.2022.3167697 (2022)

work page doi:10.1109/tqc.2022.3167697 2022
[25]

Ristè, D. et al. Demonstration of quantum advantage in machine learning. npj Quantum Inf. 3, 16. h t t p s : / / d o i . o r g / 1 0 . 1 0 3 8 / s 4 1 5 3 4 - 0 1 7 - 0 0 1 7 - 3 (2017)

2017
[26]

& Sharma, A

Gupta, M., Singh, R. & Sharma, A. Performance evaluation of quantum neural networks for image recognition. Quantum Machine Intell. 4, 300–310. https://doi.org/10.1007/s42484-021-00056-8 (2021)

work page doi:10.1007/s42484-021-00056-8 2021
[27]

Konar, D., Bhattacharyya, S., Panigrahi, B. K. & Behrman, E. C. Qutrit-inspired fully self-supervised shallow quantum learning network for brain tumor segmentation. IEEE Trans. Neural Netw. Learn. Syst. 33, 6331–6345. h t t p s : / / d o i . o r g / 1 0 . 1 1 0 9 / T N N L S . 2 0 2 1 . 3 0 7 7 1 8 8 (2022)

2022
[28]

& Ghosh, S

Ghosh, B., Ghosh, S., Chandra, D. & Ghosh, S. Quantum neural network on ibm quantum computer for the solution of nonlinear differential equations. In Proceedings of the International Conference on Computer, Electrical & Communication Engineering (ICCECE 2020), vol. 1346 of Advances in Intelligent Systems and Computing 109–118. h t t p s : / / d o i . o r ...

2020
[29]

& Patel, K

Patel, B., Shah, S. & Patel, K. Quantum neural networks for anomaly detection in industrial systems. IEEE Trans. Quantum Comput. 3, 260–267. https://doi.org/10.1109/TQC.2022.3189977 (2022)

work page doi:10.1109/tqc.2022.3189977 2022
[30]

& Verma, N

Kumar, S., Mishra, A. & Verma, N. Efficient training algorithms for quantum neural networks. IEEE Trans. Quantum Comput. 2, 40–47. https://doi.org/10.1109/TQC.2021.3058408 (2021)

work page doi:10.1109/tqc.2021.3058408 2021
[31]

& Banerjee, A

Das, R., Ghosh, S. & Banerjee, A. Quantum neural network architectures for natural language processing. Quantum Mach. Intell. 6, 56–65. https://doi.org/10.1007/s42484-022-00063-3 (2022)

work page doi:10.1007/s42484-022-00063-3 2022
[32]

& Bhattacharya, P

Chatterjee, A., Basu, S. & Bhattacharya, P . Applications of quantum neural networks in robotics: A review. IEEE Trans. Quantum Comput. 2, 430–438. https://doi.org/10.1109/TQC.2022.3217855 (2023)

work page doi:10.1109/tqc.2022.3217855 2022
[33]

& Dutta, S

Datta, R., Roy, S. & Dutta, S. Exploring quantum neural networks for Indian language processing. Int. J. Comput. Appl. 189, 14–19. https://doi.org/10.5120/ijca2018916201 (2018)

work page doi:10.5120/ijca2018916201 2018
[34]

& Gupta, N

Singh, R., Kumar, S. & Gupta, N. Quantum reinforcement learning with applications in robotics. IEEE Trans. Quantum Comput. 4, 320–328. https://doi.org/10.1109/TQC.2022.3154147 (2022)

work page doi:10.1109/tqc.2022.3154147 2022
[35]

& Imre, S

Gyongyosi, L. & Imre, S. Advances in the quantum internet. Commun. ACM 65, 52–63. https://doi.org/10.1145/3524455 (2022)

work page doi:10.1145/3524455 2022
[36]

& Imre, S

Gyongyosi, L. & Imre, S. Scalable distributed gate-model quantum computers. Sci. Rep. 11, 5172. h t t p s : / / d o i . o r g / 1 0 . 1 0 3 8 / s 4 1 5 9 8 - 0 2 0 - 7 6 7 2 8 - 5 (2021)

2021
[37]

Park, S., Park, D. K. & Rhee, J. K. K. Variational quantum approximate support vector machine with inference transfer. Sci. Rep. 13,
[38]

https://doi.org/10.1038/s41598-023-29495-y (2023)

work page doi:10.1038/s41598-023-29495-y 2023
[39]

Schuld, M., Bocharov, A., Svore, K. M. & Wiebe, N. Circuit-centric quantum classifiers. Phys. Rev. A 101, 032308. h t t p s : / / d o i . o r g / 1 0 . 1 1 0 3 / P h y s R e v A . 1 0 1 . 0 3 2 3 0 8 (2020)

2020
[40]

Jerbi, S. et al. Quantum machine learning beyond kernel methods. Nat. Commun. 14, 517. h t t p s : / / d o i . o r g / 1 0 . 1 0 3 8 / s 4 1 4 6 7 - 0 2 3 - 3 6 1 5 9 - y (2023). Author contributions Kanishk Bakshi: Writing - Original Draft, Validation, Software, Resources, Methodology, Investigation, Data Curation, Conceptualization Visualization, Invest...

work page doi:10.1038/s41598-025-09475-0 2023