# Computing the gradients with respect to all parameters of a quantum neural network using a single circuit

arXiv: https://arxiv.org/abs/2307.08167 · HTML: https://mlsanity.com/paper/2307.08167/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 44 references that are in the map.
- First posted on arXiv 16 Jul 2023.

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

- [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)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [On quantum backpropagation, information reuse, and cheating measurement collapse](https://mlsanity.com/paper/2305.13362/) (2023)
- [Quantum Deep Hedging](https://mlsanity.com/paper/2303.16585/) (2023)
- [A Hybrid Quantum-Classical Neural Network Architecture for Binary Classification](https://mlsanity.com/paper/2201.01820/) (2022)
- [Hybrid Quantum-Classical Neural Network for Cloud-supported In-Vehicle Cyberattack Detection](https://mlsanity.com/paper/2110.07467/) (2021)

## Abstract (arXiv)

Finding gradients is a crucial step in training machine learning models. For quantum neural networks, computing gradients using the parameter-shift rule requires calculating the cost function twice for each adjustable parameter in the network. When the total number of parameters is large, the quantum circuit must be repeatedly adjusted and executed, leading to significant computational overhead. Here we propose an approach to compute all gradients using a single circuit only, significantly reducing both the circuit depth and the number of classical registers required. We experimentally validate our approach on both quantum simulators and IBM's real quantum hardware, demonstrating that our method significantly reduces circuit compilation time compared to the conventional approach, resulting in a substantial speedup in total runtime.