qutrit-entropy-neural-estimation

name	qutrit-entropy-neural-estimation
description	Von Neumann entropy estimation in multi-qutrit systems using VQA and classical CNN approaches. CNN achieves accurate estimation using only 12.5% of full tomography measurements. Use when estimating quantum state entropy, benchmarking VQA ansatzes, or applying neural networks to quantum state characterization.
metadata	{"arxiv_id":"2606.20504","published":"2026-06-18","authors":"Daniel Molpeceres et al.","tags":["quantum-entropy","qutrit","vqa","cnn","quantum-state-estimation","tomography"]}

Qutrit Entropy Neural Estimation

Core Idea

Estimate von Neumann entropy in multi-qutrit systems using two complementary approaches:

• VQAs (effective for small systems up to 3 qutrits)
• Classical CNNs (scale to 5+ qutrits, use only 12.5% of full tomography measurements)

VQA Approach (Small Systems)

SU(3)-Inspired Ansatzes

• 11 hardware-efficient ansatz architectures evaluated
• Accuracy primarily determined by number of trainable parameters (~120 optimal)
• Sufficient entanglement is prerequisite for accuracy
• Increasing entangling gates beyond threshold yields marginal improvements

Parameter Sweep Results

• Fix parameter count to ~120 for balanced accuracy/complexity
• Beyond threshold, more entangling gates don't significantly improve results

CNN Approach (Larger Systems)

Architecture

• Classical CNN trained on measurement outcomes
• Uses tensor-product mutually unbiased bases (MUBs)
• Input: measurement outcome statistics
• Output: von Neumann entropy estimate

Performance

• 2-5 qutrit systems: Systematic improvement with system size
• Measurement efficiency: 12.5% of full tomography sufficient for 90th-percentile errors ~0.13-0.16 nats
• Shot noise robustness: Maintains accuracy under realistic measurement noise
• OOD generalization: Generalizes well to out-of-distribution states

Decision Guide

System Size	Recommended Method	Reason
1-2 qutrits	VQA	Simple, effective
3 qutrits	VQA or CNN	Both viable
4-5+ qutrits	CNN	Better scalability
Noisy hardware	CNN	Shot noise robustness

Workflow

1. Determine system size: Count qutrits in target system
2. Choose method: VQA for small, CNN for large
3. VQA path: Select ansatz, fix ~120 parameters, optimize
4. CNN path: Collect MUB measurements (12.5% of full set), train CNN
5. Validate: Compare against known entropy values if available

Pitfalls

• VQA entanglement requirement: VQAs need sufficient entanglement in ansatz
• CNN training data: Requires diverse training set covering state space
• MUB availability: Mutually unbiased bases may not exist for all dimensions
• Simulation-only: Results validated on noiseless simulator — hardware performance TBD
• Entropy range: May not work well for extreme entropy values

Activation Keywords

• quantum entropy estimation
• qutrit entropy
• von Neumann entropy neural
• VQA entropy
• quantum state tomography reduction
• MUB measurements
• multi-qutrit systems