# QuEst: Graph Transformer for Quantum Circuit Reliability Estimation

arXiv: https://arxiv.org/abs/2210.16724 · HTML: https://mlsanity.com/paper/2210.16724/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 12 references that are in the map.
- First posted on arXiv 30 Oct 2022.

## Builds on (most cited first, 4 of 4)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [QuantumNAT: Quantum Noise-Aware Training with Noise Injection, Quantization and Normalization](https://mlsanity.com/paper/2110.11331/) (2021)
- [QOC: Quantum On-Chip Training with Parameter Shift and Gradient Pruning](https://mlsanity.com/paper/2202.13239/) (2022)
- [Variational Quantum Algorithms for Trace Distance and Fidelity Estimation](https://mlsanity.com/paper/2012.05768/) (2020)

## Built on by (most cited first, 13 of 13)

- [Diffusion-Inspired Quantum Noise Mitigation in Parameterized Quantum Circuits](https://mlsanity.com/paper/2406.00843/) (2024)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [QMoE: A Quantum Mixture of Experts Framework for Scalable Quantum Neural Networks](https://mlsanity.com/paper/2507.05190/) (2025)
- [QuMoS: A Framework for Preserving Security of Quantum Machine Learning Model](https://mlsanity.com/paper/2304.11511/) (2023)
- [iLoRE: Dynamic Graph Representation with Instant Long-term Modeling and Re-occurrence Preservation](https://mlsanity.com/paper/2309.02012/) (2023)
- [Predictive Models from Quantum Computer Benchmarks](https://mlsanity.com/paper/2305.08796/) (2023)
- [Graph Neural Networks for Parameterized Quantum Circuits Expressibility Estimation](https://mlsanity.com/paper/2405.08100/) (2024)
- [RobustState: Boosting Fidelity of Quantum State Preparation via Noise-Aware Variational Training](https://mlsanity.com/paper/2311.16035/) (2023)
- [What is my quantum computer good for? Quantum capability learning with physics-aware neural networks](https://mlsanity.com/paper/2406.05636/) (2024)
- [Quantum vs. Classical Machine Learning: A Benchmark Study for Financial Prediction](https://mlsanity.com/paper/2601.03802/) (2026)
- [Nonstabilizerness Estimation using Graph Neural Networks](https://mlsanity.com/paper/2511.23224/) (2025)
- [QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits](https://mlsanity.com/paper/2401.05571/) (2024)
- [Quantum Rationale-Aware Graph Contrastive Learning for Jet Discrimination](https://mlsanity.com/paper/2411.01642/) (2024)

## Abstract (arXiv)

Among different quantum algorithms, PQC for QML show promises on near-term devices. To facilitate the QML and PQC research, a recent python library called TorchQuantum has been released. It can construct, simulate, and train PQC for machine learning tasks with high speed and convenient debugging supports. Besides quantum for ML, we want to raise the community's attention on the reversed direction: ML for quantum. Specifically, the TorchQuantum library also supports using data-driven ML models to solve problems in quantum system research, such as predicting the impact of quantum noise on circuit fidelity and improving the quantum circuit compilation efficiency. This paper presents a case study of the ML for quantum part. Since estimating the noise impact on circuit reliability is an essential step toward understanding and mitigating noise, we propose to leverage classical ML to predict noise impact on circuit fidelity. Inspired by the natural graph representation of quantum circuits, we propose to leverage a graph transformer model to predict the noisy circuit fidelity. We firstly collect a large dataset with a variety of quantum circuits and obtain their fidelity on noisy simulators and real machines. Then we embed each circuit into a graph with gate and noise properties as node features, and adopt a graph transformer to predict the fidelity. Evaluated on 5 thousand random and algorithm circuits, the graph transformer predictor can provide accurate fidelity estimation with RMSE error 0.04 and outperform a simple neural network-based model by 0.02 on average. It can achieve 0.99 and 0.95 R2 scores for random and algorithm circuits, respectively. Compared with circuit simulators, the predictor has over 200X speedup for estimating the fidelity.