# Variational Denoising for Variational Quantum Eigensolver

arXiv: https://arxiv.org/abs/2304.00549 · HTML: https://mlsanity.com/paper/2304.00549/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 2 Apr 2023.

## Builds on (most cited first, 12 of 12)

- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [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)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Trainability of Dissipative Perceptron-Based Quantum Neural Networks](https://mlsanity.com/paper/2005.12458/) (2020)
- [Enhancing Generative Models via Quantum Correlations](https://mlsanity.com/paper/2101.08354/) (2021)
- [Entangled Datasets for Quantum Machine Learning](https://mlsanity.com/paper/2109.03400/) (2021)
- [Denoising quantum states with Quantum Autoencoders -- Theory and Applications](https://mlsanity.com/paper/2012.14714/) (2020)
- [Error mitigation of entangled states using brainbox quantum autoencoders](https://mlsanity.com/paper/2303.01134/) (2023)

## Built on by (most cited first, 4 of 4)

- [Quantum Generative Adversarial Autoencoders: Learning latent representations for quantum data generation](https://mlsanity.com/paper/2509.16186/) (2025)
- [PALQO: Physics-informed Model for Accelerating Large-scale Quantum Optimization](https://mlsanity.com/paper/2509.20733/) (2025)
- [Quantum Machine Learning via Contrastive Training](https://mlsanity.com/paper/2511.13497/) (2025)
- [Universality of Many-body Projected Ensemble for Learning Quantum Data Distribution](https://mlsanity.com/paper/2601.18637/) (2026)

## Abstract (arXiv)

The variational quantum eigensolver (VQE) is a hybrid algorithm that has the potential to provide a quantum advantage in practical chemistry problems that are currently intractable on classical computers. VQE trains parameterized quantum circuits using a classical optimizer to approximate the eigenvalues and eigenstates of a given Hamiltonian. However, VQE faces challenges in task-specific design and machine-specific architecture, particularly when running on noisy quantum devices. This can have a negative impact on its trainability, accuracy, and efficiency, resulting in noisy quantum data. We propose variational denoising, an unsupervised learning method that employs a parameterized quantum neural network to improve the solution of VQE by learning from noisy VQE outputs. Our approach can significantly decrease energy estimation errors and increase fidelities with ground states compared to noisy input data for the H2, LiH, and BeH2 molecular Hamiltonians, and the transverse field Ising model. Surprisingly, it only requires noisy data for training. Variational denoising can be integrated into quantum hardware, increasing its versatility as an end-to-end quantum processing for quantum data.