# QOC: Quantum On-Chip Training with Parameter Shift and Gradient Pruning

arXiv: https://arxiv.org/abs/2202.13239 · HTML: https://mlsanity.com/paper/2202.13239/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 23 references that are in the map.
- First posted on arXiv 26 Feb 2022.

## Builds on (most cited first, 11 of 11)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [SpAtten: Efficient Sparse Attention Architecture with Cascade Token and Head Pruning](https://mlsanity.com/paper/2012.09852/) (2020)
- [APQ: Joint Search for Network Architecture, Pruning and Quantization Policy](https://mlsanity.com/paper/2006.08509/) (2020)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [SpArch: Efficient Architecture for Sparse Matrix Multiplication](https://mlsanity.com/paper/2002.08947/) (2020)
- [QuantumNAT: Quantum Noise-Aware Training with Noise Injection, Quantization and Normalization](https://mlsanity.com/paper/2110.11331/) (2021)
- [Can Noise on Qubits Be Learned in Quantum Neural Network? A Case Study on QuantumFlow](https://mlsanity.com/paper/2109.03430/) (2021)
- [Exploration of Quantum Neural Architecture by Mixing Quantum Neuron Designs](https://mlsanity.com/paper/2109.03806/) (2021)
- [Progressive Gradient Pruning for Classification, Detection and DomainAdaptation](https://mlsanity.com/paper/1906.08746/) (2019)

## Built on by (most cited first, 23 of 23)

- [QuEst: Graph Transformer for Quantum Circuit Reliability Estimation](https://mlsanity.com/paper/2210.16724/) (2022)
- ['Eliv'agar: Efficient Quantum Circuit Search for Classification](https://mlsanity.com/paper/2401.09393/) (2024)
- [Transformer-QEC: Quantum Error Correction Code Decoding with Transferable Transformers](https://mlsanity.com/paper/2311.16082/) (2023)
- [Quantum Federated Learning: A Comprehensive Survey](https://mlsanity.com/paper/2508.15998/) (2025)
- [Hyperparameter Importance of Quantum Neural Networks Across Small Datasets](https://mlsanity.com/paper/2206.09992/) (2022)
- [Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey](https://mlsanity.com/paper/2409.07626/) (2024)
- [QuMoS: A Framework for Preserving Security of Quantum Machine Learning Model](https://mlsanity.com/paper/2304.11511/) (2023)
- [Fast Quantum Convolutional Neural Networks for Low-Complexity Object Detection in Autonomous Driving Applications](https://mlsanity.com/paper/2401.01370/) (2023)
- [RobustAnalog: Fast Variation-Aware Analog Circuit Design Via Multi-task RL](https://mlsanity.com/paper/2207.06412/) (2022)
- [PristiQ: A Co-Design Framework for Preserving Data Security of Quantum Learning in the Cloud](https://mlsanity.com/paper/2404.13475/) (2024)
- [Quantum Split Neural Network Learning using Cross-Channel Pooling](https://mlsanity.com/paper/2211.06524/) (2022)
- [QAdaPrune: Adaptive Parameter Pruning For Training Variational Quantum Circuits](https://mlsanity.com/paper/2408.13352/) (2024)
- [Review of Ansatz Designing Techniques for Variational Quantum Algorithms](https://mlsanity.com/paper/2212.04913/) (2022)
- [DGR: Tackling Drifted and Correlated Noise in Quantum Error Correction via Decoding Graph Re-weighting](https://mlsanity.com/paper/2311.16214/) (2023)
- [STIQ: Safeguarding Training and Inferencing of Quantum Neural Networks from Untrusted Cloud](https://mlsanity.com/paper/2405.18746/) (2024)
- [RobustState: Boosting Fidelity of Quantum State Preparation via Noise-Aware Variational Training](https://mlsanity.com/paper/2311.16035/) (2023)
- [Quantum Deep Equilibrium Models](https://mlsanity.com/paper/2410.23940/) (2024)
- [Adversarial Data Poisoning Attacks on Quantum Machine Learning in the NISQ Era](https://mlsanity.com/paper/2411.14412/) (2024)
- [Differentially Private Federated Quantum Learning via Quantum Noise](https://mlsanity.com/paper/2508.20310/) (2025)
- [TITAN: A Trajectory-Informed Technique for Adaptive Parameter Freezing in Large-Scale VQE](https://mlsanity.com/paper/2509.15193/) (2025)
- [Scalable On-Hardware Training of Quantum Neural Networks and Application to Clinical Data Imputation](https://mlsanity.com/paper/2606.03517/) (2026)
- [DyPP: Dynamic Parameter Prediction to Accelerate Convergence of Variational Quantum Algorithms](https://mlsanity.com/paper/2307.12449/) (2023)
- [QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits](https://mlsanity.com/paper/2401.05571/) (2024)

## Abstract (arXiv)

Parameterized Quantum Circuits (PQC) are drawing increasing research interest thanks to its potential to achieve quantum advantages on near-term Noisy Intermediate Scale Quantum (NISQ) hardware. In order to achieve scalable PQC learning, the training process needs to be offloaded to real quantum machines instead of using exponential-cost classical simulators. One common approach to obtain PQC gradients is parameter shift whose cost scales linearly with the number of qubits. We present QOC, the first experimental demonstration of practical on-chip PQC training with parameter shift. Nevertheless, we find that due to the significant quantum errors (noises) on real machines, gradients obtained from naive parameter shift have low fidelity and thus degrading the training accuracy. To this end, we further propose probabilistic gradient pruning to firstly identify gradients with potentially large errors and then remove them. Specifically, small gradients have larger relative errors than large ones, thus having a higher probability to be pruned. We perform extensive experiments with the Quantum Neural Network (QNN) benchmarks on 5 classification tasks using 5 real quantum machines. The results demonstrate that our on-chip training achieves over 90% and 60% accuracy for 2-class and 4-class image classification tasks. The probabilistic gradient pruning brings up to 7% PQC accuracy improvements over no pruning. Overall, we successfully obtain similar on-chip training accuracy compared with noise-free simulation but have much better training scalability. The QOC code is available in the TorchQuantum library.