# Training Variational Quantum Circuits Using Particle Swarm Optimization

arXiv: https://arxiv.org/abs/2509.15726 · HTML: https://mlsanity.com/paper/2509.15726/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 8 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 6 of 6)

- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [Quantum Architecture Search: A Survey](https://mlsanity.com/paper/2406.06210/) (2024)
- [Optimizing Variational Quantum Circuits Using Metaheuristic Strategies in Reinforcement Learning](https://mlsanity.com/paper/2408.01187/) (2024)

## Abstract (arXiv)

In this work, the Particle Swarm Optimization (PSO) algorithm has been used to train various Variational Quantum Circuits (VQCs). This approach is motivated by the fact that commonly used gradient-based optimization methods can suffer from the barren plateaus problem. PSO is a stochastic optimization technique inspired by the collective behavior of a swarm of birds. The dimension of the swarm, the number of iterations of the algorithm, and the number of trainable parameters can be set. In this study, PSO has been used to train the entire structure of VQCs, allowing it to select which quantum gates to apply, the target qubits, and the rotation angle, in case a rotation is chosen. The algorithm is restricted to choosing from four types of gates: Rx, Ry, Rz, and CNOT. The proposed optimization approach has been tested on various datasets of the MedMNIST, which is a collection of biomedical image datasets designed for image classification tasks. Performance has been compared with the results achieved by classical stochastic gradient descent applied to a predefined VQC. The results show that the PSO can achieve comparable or even better classification accuracy across multiple datasets, despite the PSO using a lower number of quantum gates than the VQC used with gradient descent optimization.