Variational Quantum Circuits Integrated with Deep Learning for Supply Chain Forecasting
Keywords:
Demand prediction, Hybrid quantum–classical models, Quantum machine learning, Supply chain forecasting, Time-series forecasting, Variational quantum circuitsAbstract
The demand changes, shorter product cycles, and external shocks are becoming more vulnerable to supply chains, and the classical models of forecasting are displaying the limit of their ability to represent nonlinear, multi-echelon, and complex relationships. This paper explores a quantum-classical hybrid model using Variational Quantum Circuits (VQCs) and deep learning to address the demand forecasting and other time-related issues in the supply chains. VQCs are parameterised quantum circuits that are optimised using classical gradient-based methods and have been demonstrated to be useful in machine learning, optimisation, and time series prediction in the noisy intermediate-scale quantum (NISQ) era. The initial contribution is the introduction of VQCs, their expressiveness, noise tolerance, and how they can be applicable to hybrid architectures. Then, the study consider the developments in quantum and hybrid time-series forecasting with parameterised quantum circuits and encoder-quantum-decoder models on the electricity load, stock markets, and other multivariate time series. Based on these frameworks, the study suggests a conceptual hybrid design of supply chain forecasting: the traditional deep neural encoders are used to extract structured features of previous demand, promotions, and external drivers, which are processed with a VQC layer and decoded to demand forecasts. The expected advantages are the global enhancement of feature entanglement, the ability to model long-range correlations effectively, and the low dimension of effective models for some datasets. It talks of critical design choices, such as encoding of data, choice of ansatz, training policy, trade-offs, and evaluation metrics, as well as practical constraints arising due to the existing NISQ hardware. Lastly, the study projects open research and experimental avenues that can be used to prove quantum-enhanced forecasting with real-life supply chain data. It posits that the next generation of computational technology will see an intelligent, adaptive, and efficient supply chain with hybrid VQC-deep learning models showing a possible and potentially revolutionary route.
References
P. Lara-Benítez, M. Carranza-García, and J. C. Riquelme, “An experimental review on deep learning architectures for time series forecasting,” International Journal of Neural Systems, vol. 31, no. 3, 2021.
M. Cerezo et al., “Variational quantum algorithms,” Nature Reviews Physics, vol. 3, pp. 625–644, Aug. 2021.
Y. Du, M.-H. Hsieh, T. Liu, and D. Tao, “Expressive power of parametrized quantum circuits,” Physical Review Research, vol. 2, no. 3, Jul. 2020.
M. Dimitrijevs, M. Kālis, and I. Repko, “Exploring hybrid quantum-classical methods for practical time-series forecasting,” arXiv preprint, 2024.
H. Bhoite, “Optimizing hybrid quantum-classical models using parameterized quantum circuits for time-series forecasting,” TechRxiv, Jul. 2025.
P. Gachnang, J. Ehrenthal, T. Hanne, and R. Dornberger, “Quantum computing in supply chain management state of the art and research directions,” Asian Journal of Logistics Management, vol. 1, no. 1, pp. 57–73, May 2022.
S. Y. -C. Chen, S. Yoo and Y. -L. L. Fang, “Quantum long short-term memory,” ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Singapore, Singapore, 2022, pp. 8622-8626.
K. Mandal, T. Chatterjee, A. Sarkar, J. Ghosh, and S. Gupta, “Theoretical overview of quantum machine learning applications in enhancing demand forecasting for supply chain management,” in Quantum Computing and Supply Chain Management: A New Era of Optimization, A. Hassan, P. Bhattacharya, P. K. Dutta, J. P. Verma, and N. K. Kundu, Eds. IGI Global Scientific Publishing, 2024, pp. 64–71.
A. W. Harrow and J. C. Napp, “Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms,” Physical Review Letters, vol. 126, no. 14, Apr. 2021.
Z. Abohashima, M. Elhosen, E. H. Houssein, and W. M. Mohamed, “Classification with quantum machine learning: A survey,” arXiv, 2020.
Y. Wang, Y. Wang, C. Chen, R. Jiang, and W. Huang, “Development of variational quantum deep neural networks for image recognition,” Neurocomputing, vol. 501, pp. 566–582, Aug. 2022.
F. Phillipson, “Quantum computing in logistics and supply chain management an overview,” arXiv, Feb. 2024.
S. J. Weinberg, F. Sanches, T. Ide, K. Kamiya, and R. Correll, “Supply chain logistics with quantum and classical annealing algorithms,” Scientific Reports, vol. 13, Mar. 2023.
M. Shamsuddoha, M. A. Kashem, T. Nasir, A. I. Hossain, and M. F. Ahmed, “Quantum computing applications in supply chain information and optimization: Future scenarios and opportunities,” Information, vol. 16, no. 8, pp. 693–693, Aug. 2025.
L. A. Moncayo-Martínez and N. He, “Quantum optimisation for supply chain: QUBO formulations and QAOA solutions for facility location and load balancing,” Results in Engineering, vol. 29, Mar. 2026.
Y. Du, T. Huang, S. You, M.-H. Hsieh, and D. Tao, “Quantum circuit architecture search for variational quantum algorithms,” npj Quantum Information, vol. 8, May 2022.
H. Jiang, Z.-J. M. Shen and J. Liu, “Quantum computing methods for supply chain management," 2022 IEEE/ACM 7th Symposium on Edge Computing (SEC), Seattle, WA, USA, 2022, pp. 400–405.
Quantum News, “Quantum computing in logistics: Optimizing supply chains,” Quantum Zeitgeist, Oct. 07, 2024.
F. Fedouaki, M. Fri, K. Douaioui, and A. Asmae, “Quantum computing for supply chain optimization: algorithms, hybrid frameworks, and industry applications,” Logistics, vol. 10, no. 3, Mar. 2026.
M. R. Laskar and R. Goel, “Shallow entangled circuits for quantum time series prediction on IBM devices,” Scientific Reports, vol. 15, Dec. 2025.
R. Sharma, “How quantum computing in logistics can transform supply chain systems,” Shiprocket Cargo, Aug. 2025.
J. Yao, Reinforcement learning and variational quantum algorithms, Ph.D. dissertation, University of California, Berkeley, CA, USA, 2023.
MindQuantum. Variational Quantum Circuit. MindSpore. 2026.
M. Ivezic, “Quantum technology use cases in supply chain & logistics,” PostQuantum, Jun. 10, 2023.
M. Irhuma, A. Alzubi, T. Öz, and K. Iyiola, “Migrative armadillo optimization enabled a one-dimensional quantum convolutional neural network for supply chain demand forecasting,” PLOS ONE, vol. 20, no. 3, Mar. 2025.
G. F. de Jesus, M. H. F. da Silva, O. M. Pires, L.C. da Silva, C. dos Santos Cruz, V. L. da Silva, “Exploring quantum neural networks for demand forecasting,” Entropy, vol. 27, no. 5, May 2025.
K. R. Ahmed, M. E. Ansari, M. N. Ahsan, A. Rohan, M. B. Uddin, and M. A. H. Rivin, “Deep learning framework for interpretable supply chain forecasting using SOM ANN and SHAP,” Scientific Reports, vol. 15, Jul. 2025.
A. Jawad, E. Stefan-Henningsen, and A. Kiani, “Applications of classical and quantum machine learning in manufacturing: predictive maintenance, scheduling and tribology,” Next Research, vol. 7, May 2026.
