Optimizing Variational Quantum Circuits

Quantum computing has the potential to unlock computational advantages unreachable by classical systems—particularly in machine learning tasks. One approach that has gained considerable attention is the Variational Quantum Circuit (VQC). VQCs rely on parameterized quantum gates whose parameters are trained via classical optimization methods. However, effectively training and scaling these circuits can be challenging, especially given today’s noisy, intermediate-scale quantum (NISQ) hardware.

In this post, I want to walk you through some of my own work (along with coauthors) on optimizing VQCs—from refining parameter initialization to investigating ideas like the Lottery Ticket Hypothesis in quantum settings.

Why Focus on VQC Optimization?

When you train a variational quantum circuit, you typically feed in data (classical or quantum) and then adjust gate parameters (often angles of rotational gates) to minimize a loss function. Unfortunately, VQCs can suffer from:

Barren plateaus, where gradients vanish and training stalls.
Parameter redundancy, making the search space too large for stable convergence.
Noise effects, since today’s quantum hardware is imperfect.

Improving the training process—be it with clever parameter mapping or pruning unneeded components—can yield faster learning and more robust models.

Weight Re-Mapping to Improve Convergence

In our 2023 work [1], we introduced the idea of weight re-mapping, which takes trainable parameters originally intended for rotation-gate angles and reshapes them into an interval of length (2\pi). Essentially, instead of letting parameters grow arbitrarily large (often modded by (2\pi) inside the circuit anyway), we “rescale” them in a structured way. This helps avoid unwieldy angle values and can make training more stable and consistent.

We continued this line of research in 2024 [2], evaluating multiple weight re-mapping functions across a variety of classification tasks. The results showed that re-mapping not only speeds up convergence but can also bump up final accuracy.

Quantum Transfer Learning

Large inputs often exceed the capacity of near-term quantum hardware. One way around this is hybrid transfer learning, where a classical network performs heavy feature extraction, and its low-dimensional output then feeds into a smaller quantum model. In Quantum Transfer Learning: The Impact of Classical Preprocessing (2024) [3], we explored how the classical feature-compression step (via an autoencoder, for instance) interacts with a variational quantum layer. Our experiments revealed that while quantum circuits can indeed play a strong role in classification, careful design of the classical preprocessing is crucial—sometimes the classical encoder is doing much more “heavy lifting” than anticipated.

The Lottery Ticket Hypothesis in Quantum ML

One of the most exciting findings in deep learning was the Lottery Ticket Hypothesis (LTH), which states that large networks often contain a small subnetwork (a “winning ticket”) that can train as effectively as the original. In 2025 [4], we investigated if this hypothesis might translate into the quantum realm. The quick answer? We did find small, pruned versions of VQCs that match (or nearly match) the performance of the full circuit—suggesting that quantum circuits, too, can contain these hidden gems.

This is particularly relevant for quantum machine learning, where every qubit is precious. If we can cut away extraneous parameters without hurting accuracy, we not only speed up training but also reduce sensitivity to noise.

Comparing Parametric Efficiency

Finally, in a 2025 study [5], we benchmarked parameter-based training performance of both neural networks and VQCs on simple supervised and reinforcement learning tasks. Our goal was to see how many parameters each approach really needed to learn effectively. We found that, under certain conditions, VQCs matched the accuracy of classical networks with significantly fewer parameters. While quantum hardware constraints remain a bottleneck, these results highlight a promising direction for quantum efficiency once hardware matures.

The Road Ahead

Optimizing VQCs remains an active research area as we move toward more powerful quantum devices and larger training datasets. Here are some open challenges and areas of ongoing work:

Noise Mitigation: As circuits scale, so does the impact of hardware noise.
Hybrid Optimization: Balancing gradient-free and gradient-based strategies might unlock more robust training.
Real-World Deployment: Applying these optimized circuits to real industrial or scientific problems remains a major milestone.

For those venturing into quantum machine learning, exploring VQC optimization is both essential and exciting. Each incremental improvement—be it a more clever parameter mapping, better pruning strategy, or robust integration with classical networks—brings us one step closer to harnessing quantum mechanics for tangible machine learning advantages.

References

Michael Kölle, Alessandro Giovagnoli, Jonas Stein, Maximilian Mansky, Julian Hager, Claudia Linnhoff-Popien. “Improving Convergence for Quantum Variational Classifiers Using Weight Re-Mapping”. Proceedings of the 15th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, pp. 251-258, 2023. DOI: 10.5220/0011696300003393 [PDF] [Code]
Michael Kölle, Alessandro Giovagnoli, Jonas Stein, Maximilian Balthasar Mansky, Julian Hager, Tobias Rohe, Robert Müller, Claudia Linnhoff-Popien. “Weight Re-mapping for Variational Quantum Algorithms”. Agents and Artificial Intelligence: 15th International Conference, ICAART 2023, Lisbon, Portugal, February 22–24, 2023, Revised Selected Papers, pp. 286-309, 2024. DOI: 10.1007/978-3-031-55326-4_14 [PDF] [Code]
Michael Kölle, Leonhard Klingert, Julian Schönberger, Philipp Altmann, Maximilian Mansky, Claudia Linnhoff-Popien. “Investigating the Lottery Ticket Hypothesis for Variational Quantum Circuits”. 2025.
Michael Kölle, Alexander Feist, Jonas Stein, Claudia Linnhoff-Popien. “Evaluating Parameter-Based Training Performance of Neural Networks and Variational Quantum Circuits”. Computational Science – ICCS 2025. To appear. [Preprint] [Code]