# A quantum generative model for multi-dimensional time series using Hamiltonian learning

arXiv: https://arxiv.org/abs/2204.06150 · HTML: https://mlsanity.com/paper/2204.06150/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 41 references that are in the map.
- First posted on arXiv 13 Apr 2022.

## Builds on (most cited first, 4 of 4)

- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Quantum constraint learning for quantum approximate optimization algorithm](https://mlsanity.com/paper/2105.06770/) (2021)
- [Generalized quantum similarity learning](https://mlsanity.com/paper/2201.02310/) (2022)

## Built on by (most cited first, 3 of 3)

- [Dynamical simulation via quantum machine learning with provable generalization](https://mlsanity.com/paper/2204.10269/) (2022)
- [UWM-JEPA: Predictive World Models That Imagine in Belief Space](https://mlsanity.com/paper/2605.25313/) (2026)
- [Application of time-series quantum generative model to financial data](https://mlsanity.com/paper/2405.11795/) (2024)

## Abstract (arXiv)

Synthetic data generation has proven to be a promising solution for addressing data availability issues in various domains. Even more challenging is the generation of synthetic time series data, where one has to preserve temporal dynamics, i.e., the generated time series must respect the original relationships between variables across time. Recently proposed techniques such as generative adversarial networks (GANs) and quantum-GANs lack the ability to attend to the time series specific temporal correlations adequately. We propose using the inherent nature of quantum computers to simulate quantum dynamics as a technique to encode such features. We start by assuming that a given time series can be generated by a quantum process, after which we proceed to learn that quantum process using quantum machine learning. We then use the learned model to generate out-of-sample time series and show that it captures unique and complex features of the learned time series. We also study the class of time series that can be modeled using this technique. Finally, we experimentally demonstrate the proposed algorithm on an 11-qubit trapped-ion quantum machine.