# Neural Error Mitigation of Near-Term Quantum Simulations

arXiv: https://arxiv.org/abs/2105.08086 · HTML: https://mlsanity.com/paper/2105.08086/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 58 references that are in the map.
- First posted on arXiv 17 May 2021.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Stabilizing Transformers for Reinforcement Learning](https://mlsanity.com/paper/1910.06764/) (2019)
- [Noisy intermediate-scale quantum (NISQ) algorithms](https://mlsanity.com/paper/2101.08448/) (2021)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Machine learning & artificial intelligence in the quantum domain](https://mlsanity.com/paper/1709.02779/) (2017)
- [Neural network wave functions and the sign problem](https://mlsanity.com/paper/2002.04613/) (2020)
- [Geometry of learning neural quantum states](https://mlsanity.com/paper/1910.11163/) (2019)

## Built on by (most cited first, 15 of 15)

- [Machine Learning for Practical Quantum Error Mitigation](https://mlsanity.com/paper/2309.17368/) (2023)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [ShadowNet for Data-Centric Quantum System Learning](https://mlsanity.com/paper/2308.11290/) (2023)
- [Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice](https://mlsanity.com/paper/2405.20384/) (2024)
- [Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations](https://mlsanity.com/paper/2408.08639/) (2024)
- [Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits](https://mlsanity.com/paper/2408.12199/) (2024)
- [Investigating Topological Order using Recurrent Neural Networks](https://mlsanity.com/paper/2303.11207/) (2023)
- [Retentive Neural Quantum States: Efficient Ans"atze for Ab Initio Quantum Chemistry](https://mlsanity.com/paper/2411.03900/) (2024)
- [Noise-Agnostic Quantum Error Mitigation with Data Augmented Neural Models](https://mlsanity.com/paper/2311.01727/) (2023)
- [Streaming IoT Data and the Quantum Edge: A Classic/Quantum Machine Learning Use Case](https://mlsanity.com/paper/2402.15542/) (2024)
- [Large Language Model Scaling Laws for Neural Quantum States in Quantum Chemistry](https://mlsanity.com/paper/2509.12679/) (2025)
- [Scalable Quantum Error Mitigation with Physically Informed Graph Neural Networks](https://mlsanity.com/paper/2604.16815/) (2026)
- [Sample-efficient quantum error mitigation via classical learning surrogates](https://mlsanity.com/paper/2511.07092/) (2025)
- [Weakly Supervised Quantum Error Mitigation](https://mlsanity.com/paper/2609.25555/) (2026)
- [Neural Fourier Surrogates for Data Reuploading Quantum Neural Networks](https://mlsanity.com/paper/2610.00841/) (2026)

## Abstract (arXiv)

Near-term quantum computers provide a promising platform for finding ground states of quantum systems, which is an essential task in physics, chemistry, and materials science. Near-term approaches, however, are constrained by the effects of noise as well as the limited resources of near-term quantum hardware. We introduce "neural error mitigation," which uses neural networks to improve estimates of ground states and ground-state observables obtained using near-term quantum simulations. To demonstrate our method's broad applicability, we employ neural error mitigation to find the ground states of the H2 and LiH molecular Hamiltonians, as well as the lattice Schwinger model, prepared via the variational quantum eigensolver (VQE). Our results show that neural error mitigation improves numerical and experimental VQE computations to yield low energy errors, high fidelities, and accurate estimations of more-complex observables like order parameters and entanglement entropy, without requiring additional quantum resources. Furthermore, neural error mitigation is agnostic with respect to the quantum state preparation algorithm used, the quantum hardware it is implemented on, and the particular noise channel affecting the experiment, contributing to its versatility as a tool for quantum simulation.