quantum-neural-entropy-estimation

name	quantum-neural-entropy-estimation
description	Entropy estimation in multi-qutrit quantum systems using variational quantum algorithms and classical CNNs. Combines SU(3)-inspired ansatzes for VQAs on small systems with CNN-based estimators for larger qutrit systems. Use when: (1) estimating von Neumann entropy of quantum states, (2) designing quantum state tomography alternatives, (3) building hybrid quantum-classical ML pipelines for quantum characterization, (4) comparing VQA vs classical neural network approaches for quantum system analysis. Triggers: quantum entropy, qutrit, SU(3) ansatz, state tomography, variational quantum algorithm, CNN quantum, mutual unbiased bases, quantum state estimation, quantum machine learning characterization.
metadata	{"arxiv_id":"2606.20504","published":"2026-06-18","authors":"Sai Sakunthala Guddanti, Anil Prabhakar, Ria Rushin Joseph","tags":["quantum","neural-networks","entropy-estimation","variational-algorithms","cnn","qutrit","quantum-ml"]}

Quantum Neural Entropy Estimation

Methodology for von Neumann entropy estimation in multi-qutrit systems using VQAs (small systems) and CNNs (larger systems). arXiv:2606.20504

Core Methodology

Two-Regime Approach

• Small systems (2-3 qutrits): Use variational quantum algorithms with SU(3)-inspired hardware-efficient ansatzes
• Large systems (4-5+ qutrits): Use classical CNNs trained on measurement outcomes from tensor-product mutually unbiased bases (MUBs)

Key Findings

1. VQA accuracy depends primarily on trainable parameter count (~120 is optimal), not entangling gate count beyond a threshold
2. CNN estimators achieve 90th-percentile absolute errors of ~0.13-0.16 nats using only 12.5% of full tomography measurements
3. CNN models are robust to shot noise and generalize to out-of-distribution states
4. Systematic improvement in CNN performance with system size (best on 5-qutrit systems)

VQA Ansatz Design

For systems up to 3 qutrits:

• Construct 11 hardware-efficient SU(3)-inspired ansatzes
• Optimize parameter count (~120) over gate depth
• Entangling gates beyond threshold yield marginal improvements
• Evaluate using noise-free quantum simulator

CNN Estimator Architecture

For 2-5 qutrit systems:

1. Generate measurement outcomes from tensor-product MUBs
2. Train CNN to predict von Neumann entropy from measurement statistics
3. Use 12.5% of full tomography measurements (significant reduction)
4. Model improves with system size (counter-intuitive but validated)

Implementation Steps

1. System size determination: Count qutrits; select VQA (< 4) or CNN (>= 2)
2. VQA path: Implement SU(3) ansatz, optimize 120 parameters, minimize energy expectation
3. CNN path: Collect MUB measurements, train CNN on measurement histograms, predict entropy
4. Validation: Compare against full state tomography baseline when feasible

Activation Keywords

quantum entropy estimation, qutrit systems, SU(3) ansatz, variational quantum algorithm, CNN quantum state, mutual unbiased bases, von Neumann entropy, quantum state tomography, quantum machine learning, hybrid quantum-classical, quantum characterization, qutrit neural network, entropy nats, quantum simulator, shot noise robustness