# Accuracy vs Memory Advantage in the Quantum Simulation of Stochastic Processes

arXiv: https://arxiv.org/abs/2312.13473 · HTML: https://mlsanity.com/paper/2312.13473/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 38 references that are in the map.
- First posted on arXiv 20 Dec 2023.

## Builds on (most cited first, 5 of 5)

- [Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning](https://mlsanity.com/paper/1907.03741/) (2019)
- [Spectral State Compression of Markov Processes](https://mlsanity.com/paper/1802.02920/) (2018)
- [Statistical Complexity of Quantum Learning](https://mlsanity.com/paper/2309.11617/) (2023)
- [Memory compression and thermal efficiency of quantum implementations of non-deterministic hidden Markov models](https://mlsanity.com/paper/2105.06285/) (2021)
- [Learning Quantum Graphical Models using Constrained Gradient Descent on the Stiefel Manifold](https://mlsanity.com/paper/1903.03730/) (2019)

## Built on by (most cited first, 1 of 1)

- [Analysis of Quantum Image Representations for Supervised Classification](https://mlsanity.com/paper/2507.22039/) (2025)

## Abstract (arXiv)

Many inference scenarios rely on extracting relevant information from known data in order to make future predictions. When the underlying stochastic process satisfies certain assumptions, there is a direct mapping between its exact classical and quantum simulators, with the latter asymptotically using less memory. Here we focus on studying whether such quantum advantage persists when those assumptions are not satisfied, and the model is doomed to have imperfect accuracy. By studying the trade-off between accuracy and memory requirements, we show that quantum models can reach the same accuracy with less memory, or alternatively, better accuracy with the same memory. Finally, we discuss the implications of this result for learning tasks.