Entropy Estimation in Multi-Qutrit Systems via Variational and Classical Neural Networks

2026-06-18 · Source: Machine Learning · Field: Science & Research — Physical Sciences & Chemistry, Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

We present a systematic study of von Neumann entropy estimation in multi-qutrit quantum systems using two complementary approaches: variational quantum algorithms (VQAs) and classical convolutional neural networks (CNNs), evaluated on an ideal quantum simulator. For systems up to three qutrits, 11 hardware-efficient SU(3)-inspired ansatzes were constructed and evaluated. A parameter sweep showed estimation accuracy is primarily determined by the number of trainable parameters, provided sufficient entanglement. The parameter count was fixed to approximately 120, observing marginal improvements beyond a threshold of entangling-gate counts. For larger systems (two to five qutrits), a CNN trained on measurement outcomes from tensor-product mutually unbiased bases was used. This CNN achieved accurate and stable predictions, improving with system size, showing highest errors for two-qutrit and lowest for five-qutrit systems. It required only 12.5% of full state tomography measurements to reach 90th-percentile absolute errors of approximately 0.13-0.16 nats for four- and five-qutrit systems. The CNN was robust to shot noise and generalized to out-of-distribution states. The study indicates VQAs are effective for small systems, while CNNs offer improved scalability and robustness for larger qutrit systems.

Key takeaway

For research scientists developing quantum algorithms for entropy estimation, consider the system size when choosing your approach. If working with small multi-qutrit systems, VQAs are effective. However, for larger systems (two to five qutrits), CNN-based estimators offer superior scalability and robustness, requiring significantly fewer measurements than full state tomography. You can achieve high accuracy with only 12.5% of measurements, making CNNs a more efficient choice for complex systems.

Key insights

VQAs are effective for small multi-qutrit systems, while CNNs offer scalable and robust entropy estimation for larger ones.

Principles

• Estimation accuracy depends on trainable parameters and entanglement.
• Increasing entangling-gate counts beyond a threshold yields marginal improvements.
• CNN performance systematically improves with system size for entropy estimation.

Method

For small systems, VQAs with SU(3)-inspired ansatzes are used. For larger systems, a CNN is trained on 12.5% of measurement outcomes from tensor-product mutually unbiased bases.

In practice

• Use VQAs for entropy estimation in small qutrit systems.
• Employ CNNs for scalable entropy estimation in larger qutrit systems.
• 12.5% of measurements suffice for accurate CNN-based entropy estimation.

Topics

• Quantum Systems
• Qutrit Systems
• Von Neumann Entropy
• Variational Quantum Algorithms
• Convolutional Neural Networks
• Quantum Simulation

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.