# Temporal Information Processing on Noisy Quantum Computers

arXiv: https://arxiv.org/abs/2001.09498 · HTML: https://mlsanity.com/paper/2001.09498/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2020.

## Built on by (most cited first, 23 of 23)

- [Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirs](https://mlsanity.com/paper/2307.12904/) (2023)
- [Learning Temporal Quantum Tomography](https://mlsanity.com/paper/2103.13973/) (2021)
- [Classical and Quantum Physical Reservoir Computing for Onboard Artificial Intelligence Systems: A Perspective](https://mlsanity.com/paper/2407.04717/) (2024)
- [Infinite-dimensional reservoir computing](https://mlsanity.com/paper/2304.00490/) (2023)
- [Extending echo state property for quantum reservoir computing](https://mlsanity.com/paper/2403.02686/) (2024)
- [Time-Warping Invariant Quantum Recurrent Neural Networks via Quantum-Classical Adaptive Gating](https://mlsanity.com/paper/2301.08173/) (2023)
- [Feedback-driven recurrent quantum neural network universality](https://mlsanity.com/paper/2506.16332/) (2025)
- [Nonlinear Autoregression with Convergent Dynamics on Novel Computational Platforms](https://mlsanity.com/paper/2108.08001/) (2021)
- [Role of scrambling and noise in temporal information processing with quantum systems](https://mlsanity.com/paper/2505.10080/) (2025)
- [Quantum Noise-Induced Reservoir Computing](https://mlsanity.com/paper/2207.07924/) (2022)
- [Quantum-Classical Hybrid Information Processing via a Single Quantum System](https://mlsanity.com/paper/2209.00497/) (2022)
- [Improving the Performance of Echo State Networks Through State Feedback](https://mlsanity.com/paper/2312.15141/) (2023)
- [Quantum Reservoir Computing and Risk Bounds](https://mlsanity.com/paper/2501.08640/) (2025)
- [Data-driven Modeling in Metrology -- A Short Introduction, Current Developments and Future Perspectives](https://mlsanity.com/paper/2406.16659/) (2024)
- [QuaRK: A Quantum Reservoir Kernel for Time Series Learning](https://mlsanity.com/paper/2602.13531/) (2026)
- [Theory and interpretability of Quantum Extreme Learning Machines: a Pauli-transfer matrix approach](https://mlsanity.com/paper/2602.18377/) (2026)
- [Quantum Observers: A NISQ Hardware Demonstration of Chaotic State Prediction Using Quantum Echo-state Networks](https://mlsanity.com/paper/2505.06799/) (2025)
- [Reservoir Computing as a Language Model](https://mlsanity.com/paper/2507.15779/) (2025)
- [A Solvable Molecular Switch Model for Stable Temporal Information Processing](https://mlsanity.com/paper/2508.15451/) (2025)
- [Quantum reservoir computing in Jaynes-Cummings models: Nonlinear memory and time-series prediction](https://mlsanity.com/paper/2510.00171/) (2025)
- [Recurrent Quantum Feature Maps for Reservoir Computing](https://mlsanity.com/paper/2604.03469/) (2026)
- [Quantum Reservoir Computing: Recent Advances and Future Directions](https://mlsanity.com/paper/2607.18552/) (2026)
- [Task-Resolved Fisher Spectroscopy for Quantum Reservoir Computing](https://mlsanity.com/paper/2609.29570/) (2026)

## Abstract (arXiv)

The combination of machine learning and quantum computing has emerged as a promising approach for addressing previously untenable problems. Reservoir computing is an efficient learning paradigm that utilizes nonlinear dynamical systems for temporal information processing, i.e., processing of input sequences to produce output sequences. Here we propose quantum reservoir computing that harnesses complex dissipative quantum dynamics. Our class of quantum reservoirs is universal, in that any nonlinear fading memory map can be approximated arbitrarily closely and uniformly over all inputs by a quantum reservoir from this class. We describe a subclass of the universal class that is readily implementable using quantum gates native to current noisy gate-model quantum computers. Proof-of-principle experiments on remotely accessed cloud-based superconducting quantum computers demonstrate that small and noisy quantum reservoirs can tackle high-order nonlinear temporal tasks. Our theoretical and experimental results pave the path for attractive temporal processing applications of near-term gate-model quantum computers of increasing fidelity but without quantum error correction, signifying the potential of these devices for wider applications including neural modeling, speech recognition and natural language processing, going beyond static classification and regression tasks.