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Special-Unitary Parameterization for Trainable Variational Quantum Circuits

arXiv 2507.05535 ↗First posted 7 Jul 2025quant-ph cs.LGcited by 0

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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.

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References · 21

  1. 2020Variational Quantum Algorithmscited by 692
  2. 2018Barren plateaus in quantum neural network training landscapescited by 630
  3. 2020The effect of data encoding on the expressive power of variational quantum machine learning modelscited by 333
  4. 2019Parameterized quantum circuits as machine learning modelscited by 332
  5. 2019Variational Quantum Circuits for Deep Reinforcement Learningcited by 167
  6. 2024Barren Plateaus in Variational Quantum Computingcited by 133
  7. 2022Exploiting symmetry in variational quantum machine learningcited by 69
  8. 2021Variational Quantum Reinforcement Learning via Evolutionary Optimizationcited by 50
  9. 2018Quantum Variational Autoencodercited by 41
  10. 2024Quantum Kernel-Based Long Short-term Memory for Climate Time-Series Forecastingcited by 17
  11. 2024Differentiable Quantum Architecture Search in Asynchronous Quantum Reinforcement Learningcited by 14
  12. 2024Quantum-Train-Based Distributed Multi-Agent Reinforcement Learningcited by 14
9 more
  1. 2025Toward Large-Scale Distributed Quantum Long Short-Term Memory with Modular Quantum Computerscited by 14
  2. 2024CompressedMediQ: Hybrid Quantum Machine Learning Pipeline for High-Dimensional Neuroimaging Datacited by 12
  3. 2024Consensus-based Distributed Quantum Kernel Learning for Speech Recognitioncited by 10
  4. 2024Noise-Aware Distributed Quantum Approximate Optimization Algorithm on Near-term Quantum Hardwarecited by 8
  5. 2025Quantum-Enhanced Parameter-Efficient Learning for Typhoon Trajectory Forecastingcited by 7
  6. 2025Differentiable Quantum Architecture Search in Quantum-Enhanced Neural Network Parameter Generationcited by 7
  7. 2025Robust Decentralized Quantum Kernel Learning for Noisy and Adversarial Environmentcited by 6
  8. 2025Learning to Learn with Quantum Optimization via Quantum Neural Networkscited by 3
  9. 2025Distributed Quantum Neural Networks on Distributed Photonic Quantum Computingcited by 3

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