# Do Quantum Circuit Born Machines Generalize?

arXiv: https://arxiv.org/abs/2207.13645 · HTML: https://mlsanity.com/paper/2207.13645/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 36 references that are in the map.
- First posted on arXiv 27 Jul 2022.

## Builds on (most cited first, 7 of 7)

- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Enhancing Generative Models via Quantum Correlations](https://mlsanity.com/paper/2101.08354/) (2021)
- [An Introduction to Image Synthesis with Generative Adversarial Nets](https://mlsanity.com/paper/1803.04469/) (2018)
- [Effective dimension of machine learning models](https://mlsanity.com/paper/2112.04807/) (2021)
- [Revisiting Precision and Recall Definition for Generative Model Evaluation](https://mlsanity.com/paper/1905.05441/) (2019)

## Built on by (most cited first, 19 of 19)

- [Trainability barriers and opportunities in quantum generative modeling](https://mlsanity.com/paper/2305.02881/) (2023)
- [Generative quantum machine learning via denoising diffusion probabilistic models](https://mlsanity.com/paper/2310.05866/) (2023)
- [A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models](https://mlsanity.com/paper/2303.15626/) (2023)
- [Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metric](https://mlsanity.com/paper/2303.13462/) (2023)
- [Building Continuous Quantum-Classical Bayesian Neural Networks for a Classical Clinical Dataset](https://mlsanity.com/paper/2406.06307/) (2024)
- [Generalization Bounds in Hybrid Quantum-Classical Machine Learning Models](https://mlsanity.com/paper/2504.08456/) (2025)
- [Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning](https://mlsanity.com/paper/2505.05151/) (2025)
- [Shuffle-QUDIO: accelerate distributed VQE with trainability enhancement and measurement reduction](https://mlsanity.com/paper/2209.12454/) (2022)
- [A supplemental investigation of non-linearity in quantum generative models with respect to simulatability and optimization](https://mlsanity.com/paper/2302.00788/) (2023)
- [Application-Oriented Benchmarking of Quantum Generative Learning Using QUARK](https://mlsanity.com/paper/2308.04082/) (2023)
- [Quantum Computing-Enhanced Algorithm Unveils Novel Inhibitors for KRAS](https://mlsanity.com/paper/2402.08210/) (2024)
- [Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning](https://mlsanity.com/paper/2602.00048/) (2026)
- [Trainability of IQP Quantum Circuit Born Machines Under Gaussian Initialization](https://mlsanity.com/paper/2606.10179/) (2026)
- [Quantum Generative Modeling using Parameterized Quantum Circuits](https://mlsanity.com/paper/2303.16955/) (2023)
- [Randomized Benchmarking of Local Zeroth-Order Optimizers for Variational Quantum Systems](https://mlsanity.com/paper/2310.09468/) (2023)
- [A method for quantifying the generalization capabilities of generative models for solving Ising models](https://mlsanity.com/paper/2405.03435/) (2024)
- [Hybrid Classical-Quantum architecture for vectorised image classification of hand-written sketches](https://mlsanity.com/paper/2407.06416/) (2024)
- [Quantum Scrambling Born Machine](https://mlsanity.com/paper/2602.17281/) (2026)
- [Quantum-Enhanced Synthetic Data Generation Using Quantum Circuit Born Machines for Imbalanced Tabular Learning](https://mlsanity.com/paper/2607.09113/) (2026)

## Abstract (arXiv)

In recent proposals of quantum circuit models for generative tasks, the discussion about their performance has been limited to their ability to reproduce a known target distribution. For example, expressive model families such as Quantum Circuit Born Machines (QCBMs) have been almost entirely evaluated on their capability to learn a given target distribution with high accuracy. While this aspect may be ideal for some tasks, it limits the scope of a generative model's assessment to its ability to memorize data rather than generalize. As a result, there has been little understanding of a model's generalization performance and the relation between such capability and the resource requirements, e.g., the circuit depth and the amount of training data. In this work, we leverage upon a recently proposed generalization evaluation framework to begin addressing this knowledge gap. We first investigate the QCBM's learning process of a cardinality-constrained distribution and see an increase in generalization performance while increasing the circuit depth. In the 12-qubit example presented here, we observe that with as few as 30% of the valid data in the training set, the QCBM exhibits the best generalization performance toward generating unseen and valid data. Lastly, we assess the QCBM's ability to generalize not only to valid samples, but to high-quality bitstrings distributed according to an adequately re-weighted distribution. We see that the QCBM is able to effectively learn the reweighted dataset and generate unseen samples with higher quality than those in the training set. To the best of our knowledge, this is the first work in the literature that presents the QCBM's generalization performance as an integral evaluation metric for quantum generative models, and demonstrates the QCBM's ability to generalize to high-quality, desired novel samples.