# Enhancing variational quantum algorithms by balancing training on classical and quantum hardware

arXiv: https://arxiv.org/abs/2503.16361 · HTML: https://mlsanity.com/paper/2503.16361/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 118 references that are in the map.
- First posted on arXiv 20 Mar 2025.

## Builds on (most cited first, 24 of 24)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Entanglement Induced Barren Plateaus](https://mlsanity.com/paper/2010.15968/) (2020)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [Learning to learn with quantum neural networks via classical neural networks](https://mlsanity.com/paper/1907.05415/) (2019)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Gradient-Free Methods for Deterministic and Stochastic Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2209.05045/) (2022)
- [Challenges and Opportunities in Quantum Optimization](https://mlsanity.com/paper/2312.02279/) (2023)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [On quantum backpropagation, information reuse, and cheating measurement collapse](https://mlsanity.com/paper/2305.13362/) (2023)
- [Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits](https://mlsanity.com/paper/2001.00550/) (2020)
- [Optimal training of variational quantum algorithms without barren plateaus](https://mlsanity.com/paper/2104.14543/) (2021)
- [Avoiding Barren Plateaus with Classical Deep Neural Networks](https://mlsanity.com/paper/2205.13418/) (2022)
- [A Unified Theory of Quantum Neural Network Loss Landscapes](https://mlsanity.com/paper/2408.11901/) (2024)
- [Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Data](https://mlsanity.com/paper/2306.07331/) (2023)
- [Investigating and Mitigating Barren Plateaus in Variational Quantum Circuits: A Survey](https://mlsanity.com/paper/2407.17706/) (2024)
- [Randomized gradient-free methods in convex optimization](https://mlsanity.com/paper/2211.13566/) (2022)
- [A unifying account of warm start guarantees for patches of quantum landscapes](https://mlsanity.com/paper/2502.07889/) (2025)
- [Efficient quantum-enhanced classical simulation for patches of quantum landscapes](https://mlsanity.com/paper/2411.19896/) (2024)
- [The Quantum Alternating Operator Ansatz for Satisfiability Problems](https://mlsanity.com/paper/2301.11292/) (2023)
- [Quantum Shadow Gradient Descent for Variational Quantum Algorithms](https://mlsanity.com/paper/2310.06935/) (2023)

## Built on by (most cited first, 3 of 3)

- [Meta-learning of Gibbs states for many-body Hamiltonians with applications to Quantum Boltzmann Machines](https://mlsanity.com/paper/2507.16373/) (2025)
- [Quantum Generative Adversarial Autoencoders: Learning latent representations for quantum data generation](https://mlsanity.com/paper/2509.16186/) (2025)
- [Model selection in hybrid quantum neural networks with applications to quantum transformer architectures](https://mlsanity.com/paper/2603.21749/) (2026)

## Abstract (arXiv)

Quantum computers offer a promising route to tackling problems that are classically intractable such as in prime-factorization, solving large-scale linear algebra and simulating complex quantum systems, but potentially require fault-tolerant quantum hardware. On the other hand, variational quantum algorithms (VQAs) are a promising approach for leveraging near-term quantum computers to solve complex problems. However, there remain major challenges in their trainability and resource costs on quantum hardware. Here we address these challenges by adopting Hardware Efficient and dynamical LIe algebra supported Ansatz (HELIA), and propose two training methods that combine an existing classical-enhanced g-sim method and the quantum-based Parameter-Shift Rule (PSR). Our improvement comes from distributing the resources required for gradient estimation and training to both classical and quantum hardware. We numerically evaluate our approach for ground-state estimation of 6 to 18-qubit Hamiltonians using the Variational Quantum Eigensolver (VQE) and quantum phase classification for up to 12-qubit Hamiltonians using quantum neural networks. For VQE, our method achieves higher accuracy and success rates, with an average reduction in quantum hardware calls of up to 60% compared to purely quantum-based PSR. For classification, we observe test accuracy improvements of up to 2.8%. We also numerically demonstrate the capability of HELIA in mitigating barren plateaus, paving the way for training large-scale quantum models.