# Quantum-enhanced causal discovery for a small number of samples

arXiv: https://arxiv.org/abs/2501.05007 · HTML: https://mlsanity.com/paper/2501.05007/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 63 references that are in the map.
- First posted on arXiv 9 Jan 2025.

## Builds on (most cited first, 20 of 20)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [A Survey on Causal Discovery Methods for I.I.D. and Time Series Data](https://mlsanity.com/paper/2303.15027/) (2023)
- [Capacity and quantum geometry of parametrized quantum circuits](https://mlsanity.com/paper/2102.01659/) (2021)
- [Enhancing Causal Discovery from Robot Sensor Data in Dynamic Scenarios](https://mlsanity.com/paper/2302.10135/) (2023)
- [Practical Kernel Tests of Conditional Independence](https://mlsanity.com/paper/2402.13196/) (2024)
- [Quantum Multiple Kernel Learning](https://mlsanity.com/paper/2011.09694/) (2020)
- [Optimal Kernel Choice for Score Function-based Causal Discovery](https://mlsanity.com/paper/2407.10132/) (2024)
- [Application of quantum computing to a linear non-Gaussian acyclic model for novel medical knowledge discovery](https://mlsanity.com/paper/2110.04485/) (2021)

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

- [Classical and quantum kernel fusion for two-sample testing](https://mlsanity.com/paper/2511.20941/) (2025)

## Abstract (arXiv)

The discovery of causal relations from observed data has attracted significant interest from disciplines such as economics, social sciences, and biology. In practical applications, considerable knowledge of the underlying systems is often unavailable, and real data are usually associated with nonlinear causal structures, which makes the direct use of most conventional causality analysis methods difficult. This study proposes a novel quantum Peter-Clark (qPC) algorithm for causal discovery that does not require any assumptions about the underlying model structures. Based on conditional independence tests in a class of reproducing kernel Hilbert spaces characterized by quantum circuits, the proposed algorithm can explore causal relations from the observed data drawn from arbitrary distributions. We conducted systematic experiments on fundamental graphs of causal structures, demonstrating that the qPC algorithm exhibits better performance, particularly with smaller sample sizes compared to its classical counterpart. Furthermore, we proposed a novel optimization approach based on Kernel Target Alignment (KTA) for determining hyperparameters of quantum kernels. This method effectively reduced the risk of false positives in causal discovery, enabling more reliable inference. Our theoretical and experimental results demonstrate that the quantum algorithm can empower classical algorithms for accurate inference in causal discovery, supporting them in regimes where classical algorithms typically fail. In addition, the effectiveness of this method was validated using the datasets on Boston housing prices, heart disease, and biological signaling systems as real-world applications. These findings highlight the potential of quantum-based causal discovery methods in addressing practical challenges, particularly in small-sample scenarios, where traditional approaches have shown significant limitations.