# Multivariate Time Series Forecasting with Gate-Based Quantum Reservoir Computing on NISQ Hardware

arXiv: https://arxiv.org/abs/2510.13634 · HTML: https://mlsanity.com/paper/2510.13634/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 45 references that are in the map.
- First posted on arXiv 15 Oct 2025.

## Builds on (most cited first, 6 of 6)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Higher-Order Quantum Reservoir Computing](https://mlsanity.com/paper/2006.08999/) (2020)
- [Optimal training of finitely-sampled quantum reservoir computers for forecasting of chaotic dynamics](https://mlsanity.com/paper/2409.01394/) (2024)
- [User Trajectory Prediction in Mobile Wireless Networks Using Quantum Reservoir Computing](https://mlsanity.com/paper/2301.08796/) (2023)
- [Exploring the Common Principal Subspace of Deep Features in Neural Networks](https://mlsanity.com/paper/2110.02863/) (2021)
- [Application of Quantum Extreme Learning Machines for QoS Prediction of Elevators' Software in an Industrial Context](https://mlsanity.com/paper/2402.12777/) (2024)

## Built on by (most cited first, 4 of 4)

- [Quantum Reservoir Computing for Short-Term Power Load Forecasting in Resource-Constrained Energy Systems](https://mlsanity.com/paper/2606.12806/) (2026)
- [RF Spectrogram Anomaly Detection with Quantum Kitchen Sinks: Architecture, Representation, and Hardware Validation](https://mlsanity.com/paper/2607.13897/) (2026)
- [A Quantum-Classical Hybrid Framework for Multivariate Time-Series Forecasting Complexity-Fidelity Trade-offs and Limitations](https://mlsanity.com/paper/2607.16358/) (2026)
- [Hybrid Variational Quantum Circuits for Multivariate Regression and High-Dimensional Data Reconstruction](https://mlsanity.com/paper/2609.17358/) (2026)

## Abstract (arXiv)

Quantum reservoir computing (QRC) offers a hardware-friendly approach to temporal learning, yet most studies target univariate signals and overlook near-term hardware constraints. This work introduces a gate-based QRC for multivariate time series (MTS-QRC) that pairs injection and memory qubits and uses a Trotterized nearest-neighbor transverse-field Ising evolution optimized for current device connectivity and depth. On Lorenz-63 and ENSO, the method achieves a mean square error (MSE) of 0.0087 and 0.0036, respectively, performing on par with classical reservoir computing on Lorenz and above learned RNNs on both, while NVAR and clustered ESN remain stronger on some settings. On IBM Heron R2, MTS-QRC sustains accuracy with realistic depths and, interestingly, outperforms a noiseless simulator on ENSO; singular value analysis indicates that device noise can concentrate variance in feature directions, acting as an implicit regularizer for linear readout in this regime. These findings support the practicality of gate-based QRC for MTS forecasting on NISQ hardware and motivate systematic studies on when and how hardware noise benefits QRC readouts.