# Special-Unitary Parameterization for Trainable Variational Quantum Circuits

arXiv: https://arxiv.org/abs/2507.05535 · HTML: https://mlsanity.com/paper/2507.05535/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 53 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Builds on (most cited first, 21 of 21)

- [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 effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Quantum Variational Autoencoder](https://mlsanity.com/paper/1802.05779/) (2018)
- [Quantum Kernel-Based Long Short-term Memory for Climate Time-Series Forecasting](https://mlsanity.com/paper/2412.08851/) (2024)
- [Differentiable Quantum Architecture Search in Asynchronous Quantum Reinforcement Learning](https://mlsanity.com/paper/2407.18202/) (2024)
- [Quantum-Train-Based Distributed Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2412.08845/) (2024)
- [Toward Large-Scale Distributed Quantum Long Short-Term Memory with Modular Quantum Computers](https://mlsanity.com/paper/2503.14088/) (2025)
- [CompressedMediQ: Hybrid Quantum Machine Learning Pipeline for High-Dimensional Neuroimaging Data](https://mlsanity.com/paper/2409.08584/) (2024)
- [Consensus-based Distributed Quantum Kernel Learning for Speech Recognition](https://mlsanity.com/paper/2409.05770/) (2024)
- [Noise-Aware Distributed Quantum Approximate Optimization Algorithm on Near-term Quantum Hardware](https://mlsanity.com/paper/2407.17325/) (2024)
- [Quantum-Enhanced Parameter-Efficient Learning for Typhoon Trajectory Forecasting](https://mlsanity.com/paper/2505.09395/) (2025)
- [Differentiable Quantum Architecture Search in Quantum-Enhanced Neural Network Parameter Generation](https://mlsanity.com/paper/2505.09653/) (2025)
- [Robust Decentralized Quantum Kernel Learning for Noisy and Adversarial Environment](https://mlsanity.com/paper/2504.13782/) (2025)
- [Learning to Learn with Quantum Optimization via Quantum Neural Networks](https://mlsanity.com/paper/2505.00561/) (2025)
- [Distributed Quantum Neural Networks on Distributed Photonic Quantum Computing](https://mlsanity.com/paper/2505.08474/) (2025)

## Abstract (arXiv)

We propose SUN-VQC, a variational-circuit architecture whose elementary layers are single exponentials of a symmetry-restricted Lie subgroup, SU(2k) subset SU(2n) with k ll n. Confining the evolution to this compact subspace reduces the dynamical Lie-algebra dimension from O(4n) to O(4k), ensuring only polynomial suppression of gradient variance and circumventing barren plateaus that plague hardware-efficient ans"atze. Exact, hardware-compatible gradients are obtained using a generalized parameter-shift rule, avoiding ancillary qubits and finite-difference bias. Numerical experiments on quantum auto-encoding and classification show that SUN-VQCs sustain order-of-magnitude larger gradient signals, converge 2--3× faster, and reach higher final fidelities than depth-matched Pauli-rotation or hardware-efficient circuits. These results demonstrate that Lie-subalgebra engineering provides a principled, scalable route to barren-plateau-resilient VQAs compatible with near-term quantum processors.