# Recursive QLSTM with Dynamic Variational Quantum Circuit Adaptation

arXiv: https://arxiv.org/abs/2606.24932 · HTML: https://mlsanity.com/paper/2606.24932/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 64 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 30 of 40)

- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Dynamic Filter Networks](https://mlsanity.com/paper/1605.09673/) (2016)
- [CondConv: Conditionally Parameterized Convolutions for Efficient Inference](https://mlsanity.com/paper/1904.04971/) (2019)
- [Meta Networks](https://mlsanity.com/paper/1703.00837/) (2017)
- [Connecting ansatz expressibility to gradient magnitudes and barren plateaus](https://mlsanity.com/paper/2101.02138/) (2021)
- [Using Fast Weights to Attend to the Recent Past](https://mlsanity.com/paper/1610.06258/) (2016)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Quantum Long Short-Term Memory](https://mlsanity.com/paper/2009.01783/) (2020)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [Learning feed-forward one-shot learners](https://mlsanity.com/paper/1606.05233/) (2016)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Recurrent Quantum Neural Networks](https://mlsanity.com/paper/2006.14619/) (2020)
- [The Dawn of Quantum Natural Language Processing](https://mlsanity.com/paper/2110.06510/) (2021)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [PQLM -- Multilingual Decentralized Portable Quantum Language Model for Privacy Protection](https://mlsanity.com/paper/2210.03221/) (2022)
- [Quantum Recurrent Neural Networks for Sequential Learning](https://mlsanity.com/paper/2302.03244/) (2023)
- [Quantum deep recurrent reinforcement learning](https://mlsanity.com/paper/2210.14876/) (2022)
- [Learning to Program Variational Quantum Circuits with Fast Weights](https://mlsanity.com/paper/2402.17760/) (2024)
- [Applying QNLP to sentiment analysis in finance](https://mlsanity.com/paper/2307.11788/) (2023)
- [Quantum Kernel-Based Long Short-term Memory for Climate Time-Series Forecasting](https://mlsanity.com/paper/2412.08851/) (2024)
- [Validating Large-Scale Quantum Machine Learning: Efficient Simulation of Quantum Support Vector Machines Using Tensor Networks](https://mlsanity.com/paper/2405.02630/) (2024)
- [Quantum Long Short-Term Memory (QLSTM) vs Classical LSTM in Time Series Forecasting: A Comparative Study in Solar Power Forecasting](https://mlsanity.com/paper/2310.17032/) (2023)

## Built on by (most cited first, 2 of 2)

- [Stable Self-Modulating Quantum Fast-Weight Programmers with Bounded Memory Gates](https://mlsanity.com/paper/2607.02363/) (2026)
- [Recursive Quantum Long Short-Term Memory for Stable Short-Horizon Temperature Forecasting](https://mlsanity.com/paper/2609.20594/) (2026)

## Abstract (arXiv)

Recent advances in quantum computing and machine learning have motivated the development of quantum models for sequential data processing. In this paper, we propose a Recursive Quantum Long Short-Term Memory model, or Recursive QLSTM, which extends QLSTM through metacore-based recursive constructions. We numerically test the model under different input sequence lengths, metacore designs, and recursive rules, and identify the best-performing architecture among these variants. For this selected model, we further provide theoretical arguments explaining why its recursive structure improves temporal information propagation and enhances learning performance. Our results suggest that Recursive QLSTM offers a flexible and effective framework for quantum recurrent learning over input time series of various lengths.